A structural design and preparation method of a bionic negative poisson's ratio metamaterial based on a double gradient structure

Abstract

The application relates to a design and preparation method of a bionic negative Poisson's ratio metamaterial based on a double-gradient structure, and belongs to the technical field of mechanical metamaterial structure design. The method solves the problem that key parameters affecting the negative Poisson's ratio phenomenon of a sunflower core structure cannot be accurately obtained, so that a bionic negative Poisson's ratio material based on the sunflower core structure cannot be prepared. The method comprises the following steps: determining key parameters for preparing a bionic negative Poisson's ratio metamaterial based on buckling phenomena generated in a compression test of a sunflower core structure with a double-gradient structure of a hole diameter and a wall thickness; and obtaining parameter values of the key parameters for preparing the bionic negative Poisson's ratio metamaterial by using classical analytical mechanics theory. The bionic negative Poisson's ratio material based on the sunflower core structure is prepared.

Description

Technical Field

[0001] This invention relates to the field of mechanical metamaterial structure design technology, and in particular to a design and fabrication method for a biomimetic negative Poisson's ratio metamaterial based on a dual-gradient structure. Background Technology

[0002] Metamaterials are a class of man-made materials with special properties, capable of achieving attributes not found in conventional materials through unique structural designs. The mechanical properties of metamaterials are generally closely related to Young's modulus (E), shear modulus (G), bulk modulus (K), and Poisson's ratio (v). The first three constants are related to the material's hardness, stiffness, and compressive properties, reflecting its resistance to deformation. In contrast, Poisson's ratio is another crucial physical variable.

[0003] Poisson's ratio is a mechanical property of a material or structure, used to measure the coefficient of the Poisson effect and characterize the lateral deformation characteristics of a material or structure perpendicular to the direction of the applied force. The negative Poisson's ratio of a material is not affected by scale and can be attributed to either the overall behavior of the material or its internal structure.

[0004] Currently, the negative Poisson's ratio effect is mainly obtained through special geometric configurations. Its design relies on researchers' innovative geometric inspiration, such as drawing geometric inspiration from materials in nature that have a negative Poisson's ratio.

[0005] For example, CN103214728A discloses a biomimetic negative Poisson's ratio material and its preparation method. By imitating the structure of sunflower pith tissue in cross-section, a negative Poisson's ratio porous foam material is constructed. The structural parameters of the negative Poisson's ratio porous foam material are determined based on the model size difference in orthogonal directions. That is, the material is prepared by stretching and setting different pore wall thicknesses. However, its understanding of the mechanism by which the sunflower pith structure produces the negative Poisson's ratio phenomenon is wrong. The parameters given based on this wrong understanding of the mechanism cannot be used to prepare the biomimetic negative Poisson's ratio material.

[0006] In summary, it is currently impossible to accurately obtain the key parameters that affect the negative Poisson's ratio phenomenon in the sunflower pith structure, thus making it impossible to prepare biomimetic negative Poisson's ratio materials based on the sunflower pith structure. Summary of the Invention

[0007] In view of the above analysis, the present invention aims to provide a design and preparation method for biomimetic negative Poisson's ratio metamaterials based on a dual-gradient structure, in order to solve the problem that the key parameters affecting the negative Poisson's ratio phenomenon of sunflower core structure cannot be accurately obtained, thus making it impossible to prepare biomimetic negative Poisson's ratio materials based on sunflower core structure.

[0008] On one hand, embodiments of the present invention provide a design method for biomimetic negative Poisson's ratio metamaterials based on a dual-gradient structure, comprising:

[0009] Based on the buckling phenomenon generated by compression tests of a sunflower pith structure with a dual gradient structure of pore size and wall thickness, the key parameters for preparing biomimetic negative Poisson's ratio metamaterials were determined.

[0010] The key parameters for preparing biomimetic negative Poisson's ratio metamaterials were designed and obtained using classical analytical mechanics theory.

[0011] Based on further improvements to the above design method, the method for determining the sunflower pith core structure with a dual gradient structure of pore size and wall thickness includes:

[0012] Step 1: Characterize the sunflower pith structure to obtain the sunflower pith structure;

[0013] Step 2: Based on the sunflower pith structure, determine the sunflower pith structure with a dual gradient structure of pore size and wall thickness.

[0014] Based on further improvements to the above design method, the process of determining the buckling phenomenon generated by the compression test includes:

[0015] Step a: Perform a compression test on the sunflower core structure with a dual gradient structure of pore size and wall thickness to obtain the value of Poisson's ratio, and obtain complete information on the highly non-uniform distribution of strain field in the cross-sectional surface of the sunflower core, as well as the deformation process of the cell wall of each unit structure in the strain concentration zone.

[0016] Step b: Based on the complete information on the highly non-uniform distribution of strain field within the cross-sectional surface of the sunflower pith, and the deformation process of the cell walls of each unit structure within the strain concentration zone, determine the relationship between the negative Poisson's ratio phenomenon and the buckling phenomenon in the sunflower pith structure.

[0017] Based on further improvements to the above design method, for biomimetic negative Poisson's ratio metamaterials with two-dimensional structures, the key parameters are the radial pore size variation gradient and the wall thickness variation gradient.

[0018] For biomimetic negative Poisson's ratio metamaterials with three-dimensional structures, the key parameters are pore size gradient and edge diameter gradient.

[0019] Based on further improvements to the above design method, the relationship between the negative Poisson's ratio phenomenon and the buckling phenomenon in the sunflower core structure is determined according to the elastic buckling instability and negative Poisson's ratio phenomenon during the compression process.

[0020] Based on further improvements to the above design method, for biomimetic negative Poisson's ratio metamaterials with two-dimensional structures, the parameter values ​​of the key parameters for preparing biomimetic negative Poisson's ratio metamaterials using classical analytical mechanics theory include:

[0021] S51: The wall thickness of microstructural units in multiple sunflower core samples was measured using SEM to obtain the average wall thickness at different locations and the gradient value of wall thickness variation.

[0022] S52: Use SEM to measure the pore size of microstructural units in multiple sunflower core samples, and obtain the average pore size value at different locations and the gradient value of pore size change.

[0023] S53: Set the wall thickness and aperture values ​​to ensure that the elongated deformation unit structures in the honeycomb structure exhibit an elastic asymmetric distribution relative to the two orthogonal directions, and to ensure that as the strain increases, the unit structures with different degrees of stretching and wall thicknesses in the entire honeycomb structure will gradually exhibit elastic buckling instability.

[0024] For biomimetic negative Poisson's ratio metamaterials with three-dimensional structures, the key parameter values ​​for fabricating these metamaterials, designed using classical analytical mechanics theory, include:

[0025] S61: The wall thickness of microstructural units in multiple sunflower core samples was measured using SEM to obtain the average wall thickness at different locations and the gradient value of wall thickness variation.

[0026] S62: Use SEM to measure the pore size of microstructural units in multiple sunflower core samples, and obtain the average pore size value at different locations and the gradient value of pore size change.

[0027] S63: Set the relative density value and the aspect ratio of the unit cell to ensure that the elongated unit structure in the 3D honeycomb structure exhibits an elastic asymmetric distribution relative to the two orthogonal directions, and to ensure that the unit structures with different edge diameters and pore sizes in the entire 3D honeycomb structure will gradually exhibit elastic buckling instability under gradually increasing strain.

[0028] Based on a further improvement to the above design method, step S53 includes:

[0029] S531: Based on the structure of the sunflower pith in the cross section, the key structure is extracted and abstracted as an elongated hexagonal honeycomb structure with varying wall thickness.

[0030] Wherein, the modulus Ey of the stretched hexagon in the elongation direction and the modulus Ex perpendicular to the elongation direction are functions of the geometric parameters h, l, and θ of the structure, and the functions satisfy:

[0031]

[0032]

[0033] Where l and h are the lengths of the cell wall in the radial and tangential directions, respectively;

[0034] t is the thickness of the cell wall;

[0035] θ is the angle between the side length l and the vertical direction y, θ = 30°;

[0036] Es is the Young's modulus of the constituent material of the cell wall;

[0037] S532: Perform stress analysis on a single elongated hexagonal unit structure and establish the correlation between the applied load F and the internal stress σ of the radial cell wall CD inside the unit structure;

[0038] The relationship between the applied load F and the internal stress σ of the radial cell wall CD within the unit structure satisfies:

[0039] F=F′cosθ=σ(h+l sinθ)b Formula (3)

[0040] in,

[0041] l and h are the lengths of the radial and transverse cell walls, respectively;

[0042] t is the thickness of the cell wall;

[0043] F is the applied compressive load; F' is the load component borne by the radial wall CD under the action of the applied load F...

[0044] The value of θ is independent of the increment of l, and θ = 30°;

[0045] b is the out-of-plane thickness of the radial wall CD;

[0046] S533: Based on the classical Euler beam theory, analyze the elastic instability of an elongated hexagonal honeycomb structure with variable wall thickness under compressive load.

[0047] Among them, when F' reaches the buckling critical load F euller_CD At this time, the radial wall CD will experience buckling instability, and the critical buckling load F euller_CD satisfy:

[0048] F euler_CD =n 2 π 2 E s I / l 2 Equation (4)

[0049] Where n is a coefficient used to characterize the fixation conditions at both ends of the cell wall;

[0050] I is the moment of inertia of the cross-sectional area of ​​the cell wall CD, I = bt 3 / 12;

[0051] Es is the Young's modulus of the constituent material of the cell wall;

[0052] l is the length of the radial cell wall;

[0053] b is the out-of-plane thickness of the radial wall CD;

[0054] t is the thickness of the cell wall;

[0055] S534: Based on the correlation between the applied load F and the stress σ in the radial cell wall CD of the unit structure, and the elastic instability of the elongated variable wall thickness hexagonal honeycomb structure under compressive load, the critical buckling stress in the radial wall CD is determined.

[0056] Among them, based on equations (3) and (4), the critical buckling stress in the radial wall CD is determined, and the critical buckling stress F is... euler_CD satisfy:

[0057]

[0058] Wherein, n is given by the formula n = 2k / π;

[0059] k is calculated using the formula tank = 2l / hk;

[0060] l and h are the lengths of the radial and transverse cell walls, respectively;

[0061] Es is the Young's modulus of the constituent material of the cell wall;

[0062] I is the moment of inertia of the cross-sectional area of ​​the cell wall CD;

[0063] σ e It is the elastic buckling stress;

[0064] t is the thickness of the cell wall;

[0065] θ is the angle between the side length l and the vertical direction y, θ = 30°;

[0066] S535: Based on the critical buckling stress within the radial wall CD, determine the effect of variations in aperture and wall thickness on the elastic buckling stress σ of the radial wall CD. e The impact;

[0067] Substituting the variations in aperture and wall thickness into equation (5), the effects of the increase in thickness t and radial wall length l on the elastic buckling stress σ of the radial wall CD are analyzed and calculated using MATLAB software. e The impact;

[0068] S536: Effect of variations in aperture and wall thickness on the elastic buckling stress σ of the radial wall CD e The influence of this was used to determine the aperture gradient and wall thickness gradient parameters.

[0069] Based on a further improvement to the above design method, step S63 includes:

[0070] S631: Based on the structure of the sunflower pith in the cross section, the key structure is extracted and abstracted as an open tetrahedron with an elongated and variable edge diameter;

[0071] The geometry of a single elongated tetrahedron is determined by three independent parameters: the tilt angle θ and the two side lengths a and b;

[0072] Where θ represents the angle between the hexagonal face and the elongation direction, θ≥π / 4;

[0073] The height H and width D of the unit cell are defined by these three parameters: H = 4asin and D, respectively. Applying the principle of minimum potential energy to the deformation of the unit cell, the modulus of the elongated tetrahedron in its two principal directions is a function of the unit cell dimensions a, b and θ, the cross-sectional area A of the edge edges and the moment of inertia I, and the Young's modulus Es of the constituent material.

[0074] Among them, the two principal directions are the elongation directions E y and perpendicular to the elongation direction E x ;

[0075] The moduli in the two principal directions satisfy:

[0076]

[0077]

[0078] Where x, y, and z represent three mutually perpendicular directions;

[0079] Es is the Young's modulus of the constituent material of the cell wall;

[0080] The modulus ratio of the two orthogonal directions is defined as λ = Ex / Ey, and an additional condition is imposed on the geometry of the unit cell, namely... To reduce the number of variables related to microstructure size and simplify the analysis process;

[0081] At this point, the modulus ratio of the elongated tetrahedron in the two principal directions satisfies:

[0082]

[0083]

[0084] Where Ar = H / D is the aspect ratio of the unit cell, and its value directly reflects the degree of elongation and deformation of the unit structure.

[0085] ρ *Ar is the relative density, defined as the ratio of the apparent density of the polygon to the density of the constituent material. When Ar is a fixed value, its value is entirely determined by the change in the diameter of the edge of the unit structure.

[0086] S632: Perform stress analysis on a single elongated tetrahedral unit structure, constructing an external compressive load P along the

[001] lattice direction and the internal stress σ of the radial edge CD inside the unit structure. y The relationship between them;

[0087] Among them, the external compressive load P along the

[001] lattice direction and the internal stress σ of the radial edge CD inside the unit structure are... y The relationship between them satisfies:

[0088]

[0089] Where θ represents the angle between the hexagonal face and the elongation direction, θ≥π / 4;

[0090] a and b are the two side lengths of the tetrahedron;

[0091] S633: Based on the classic Timoshenko beam theory, analyze the elastic instability of an elongated variable wall thickness hexagonal honeycomb structure under compressive load.

[0092] When the applied compressive load reaches the critical buckling load, the prism CD will buckle in an energy-minimizing mode, and its critical buckling load satisfies:

[0093]

[0094] Where Es is the Young's modulus of the constituent material of the unit cell;

[0095] I is the moment of inertia of the cross-sectional area of ​​edge CD;

[0096] Combined with P CD_Cr sinθ=P, then:

[0097]

[0098] Among them, P CD_Cr The critical buckling load of the prism CD;

[0099] Es is the Young's modulus of the constituent material of a unit cell;

[0100] I is the moment of inertia of the cross-sectional area of ​​the cell wall CD;

[0101] S634: Based on equations (10) and (12), determine the critical buckling stress within the radial ridge CD;

[0102] The critical buckling stress within the radial ridge CD satisfies:

[0103]

[0104] S635: Based on Equation (13), determine the effect of changes in the aspect ratio and relative density of the unit cell on the elastic buckling stress σy of the radial edge CD;

[0105] Substituting the aspect ratio and relative density changes of the unit cell into equation (13), MATLAB software was used to analyze and calculate the effect of the increase in edge diameter and the degree of elongation deformation of the unit cell on the elastic buckling stress σ of the radial edge CD. y The impact;

[0106] S636: Elastic buckling stress σ of radial edge CD based on variations in aperture and edge diameter y The influence of this determines the aperture gradient and edge diameter gradient parameters.

[0107] Based on the further improvement of the above design method, for biomimetic negative Poisson's ratio metamaterials with two-dimensional structures: after setting the pore size and wall thickness values ​​at the center, the pore size and wall thickness parameters of the biomimetic negative Poisson's ratio metamaterial can be determined based on the pore size gradient and wall thickness gradient.

[0108] For biomimetic negative Poisson's ratio metamaterials with three-dimensional structures: after setting the aperture and edge diameter values ​​at the center, the aperture and edge diameter parameters of the biomimetic negative Poisson's ratio metamaterial can be determined based on the aperture gradient and edge diameter gradient.

[0109] Furthermore, this invention also provides a method for preparing a biomimetic negative Poisson's ratio metamaterial based on a dual-gradient structure, comprising using the preparation parameters of the biomimetic negative Poisson's ratio metamaterial obtained by the design method of the aforementioned biomimetic negative Poisson's ratio metamaterial based on a dual-gradient structure, and employing additive printing technology to construct the biomimetic negative Poisson's ratio metamaterial.

[0110] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0111] 1. This invention determines the key parameters for preparing biomimetic negative Poisson's ratio metamaterials based on the buckling phenomenon generated by compression tests of sunflower pith structures with dual gradient structures of pore size and wall thickness. The invention also uses classical analytical mechanics theory to design the parameter values ​​of the key parameters for preparing biomimetic negative Poisson's ratio metamaterials. Based on these parameter values, biomimetic materials with two-dimensional or three-dimensional structures can be prepared with guaranteed reliability.

[0112] 2. Based on the complete information obtained about the highly non-uniform distribution of strain field within the cross-sectional surface of the sunflower pith, and the deformation process of the cell walls of each unit structure within the strain concentration zone, this invention determines the relationship between the negative Poisson's ratio phenomenon and the buckling phenomenon in the sunflower pith structure. Under this relationship, the key parameters for preparing biomimetic negative Poisson's ratio metamaterials are determined and designed, enabling the preparation of biomimetic materials with two-dimensional or three-dimensional structures with guaranteed reliability. Furthermore, by adjusting the dual gradient values ​​during the preparation process, biomimetic negative Poisson's ratio metamaterials of different sizes can be prepared, demonstrating universality.

[0113] 3. This invention determines that the mechanism by which the sunflower pith core structure generates a negative Poisson's ratio is attributed to buckling. The unique dual-gradient structure introduces local alternating buckling behavior under radial load within the cross-section. Based on this, the pore size and wall thickness parameters along the radial pore size variation gradient and wall thickness variation gradient are determined to be key parameters for preparing biomimetic negative Poisson's ratio metamaterials. Through mechanical analysis, these pore size and wall thickness values ​​are obtained. Based on this correctly understood mechanism, it is possible to prepare biomimetic negative Poisson's ratio metamaterials.

[0114] 4. This invention employs classical analytical mechanics theory to determine the effect of variations in aperture and wall thickness on the elastic buckling stress σ of the radial wall CD. e Based on this, the synergistic relationship between aperture and wall thickness was determined, which caused the unit structure at each position in the honeycomb structure with double gradient changes to gradually buckle as the strain increases. That is, when the wall thickness and aperture increase at the same time, it is necessary to ensure that the aperture change gradient is greater than the wall thickness change gradient in order to reduce the critical buckling stress, realize the macroscopic negative Poisson's ratio effect under large strain, and ensure sufficient structural strength.

[0115] 5. Based on equation (5), changing the wall thickness and aperture will directly affect the value of the critical buckling stress. Buckling behavior is the core reason for the negative Poisson's ratio effect of the biomimetic negative Poisson's ratio metamaterial based on the dual gradient structure mentioned in this invention. Adjusting the rate of change and relative magnitude of the two parameters can change the number and speed of buckling instability of the unit structure under large strain, thereby ultimately affecting the macroscopic negative Poisson's ratio value.

[0116] In this invention, the above-described technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of this invention will be set forth in the following description, and some advantages may become apparent from the description or be learned by practicing the invention. The objects and other advantages of this invention can be realized and obtained from what is particularly pointed out in the description and drawings. Attached Figure Description

[0117] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0118] Figure 1 This is a schematic diagram of the unit structure of the elongated hexagonal honeycomb porous structure under uniaxial compression in this invention;

[0119] Figure 2 This invention illustrates the effect of variations in aperture and wall thickness on the critical buckling stress of the elongated hexagonal unit structure.

[0120] Figure 3 This invention relates to a double-gradient structure for sunflower pith core; wherein, (a) and (b) the particle size varies radially in the cross-section, gradually elongating towards the periphery; and (c) the wall thickness varies gradually, increasing from approximately 200 nm at the center to 500 nm towards the periphery.

[0121] Figure 4 Micro-CT images of continuous deformation inside the sunflower core under radial / lateral uniaxial compression and the mechanism of the anisotropic negative Poisson bit property of the sunflower core;

[0122] Figure 5 To experimentally verify the mechanism of the negative Poisson effect in sunflower pith, multiple sets of control models were prepared by 3D printing in this invention.

[0123] Figure 6 This is a schematic diagram of the repeating unit cell in the three-dimensional elongated tetrahedral porous structure of the present invention;

[0124] Figure 7 This is a schematic diagram of the tetrahedral structure under uniaxial compression along the

[001] direction in this invention;

[0125] Figure 8 The buckling stress σ of the elongated tetrahedron in the

[010] direction in this invention is... y The trends of aspect ratio Ar and relative density ρ* of unit cell body;

[0126] Figure 9 The results are experimental findings from the compression test of the 3D-printed double-gradient tetrahedral porous structure in this invention.

[0127] Figure label:

[0128] l - Length of the radial cell wall in a two-dimensional hexagon; h - Length of the radial and transverse cell walls in a two-dimensional hexagon; t - Thickness of the cell wall in a two-dimensional hexagon; F - External compressive load; θ - Angle between l and the vertical direction y in a two-dimensional hexagon; t* / t - Ratio of the increased cell wall thickness to the original thickness in a two-dimensional hexagon; l* / l - Ratio of the length of the elongated radial cell wall to the original length l in a two-dimensional hexagon. Detailed Implementation

[0129] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0130] Poisson's ratio is a mechanical property of a material or structure, used to measure the Poisson effect and characterize the lateral deformation characteristics of a material or structure perpendicular to the direction of the applied force. It is defined as the lateral strain (ε) of the material or structure in the direction of elastic loading. x ) and longitudinal strain (ε y The negative of the ratio of ), i.e., ν = -ε x / ε y The Poisson's ratio of a material can be positive or negative, and it is determined by two factors: the geometry of the material's internal structure and its deformation mechanism. A structure or material with a negative Poisson's ratio exhibits a unique mechanical response to strain applied from the outside: when longitudinal tensile or compressive strain is applied, it expands or contracts laterally.

[0131] The negative Poisson's ratio property of a material is not affected by scale and can be attributed to both the overall behavior of the material and its internal structure. Currently, the negative Poisson's ratio effect is mainly obtained through special geometric configurations, and the design relies on researchers' innovative geometric inspiration, such as drawing geometric inspiration from materials with negative Poisson's ratios in nature.

[0132] For example, CN103214728A identifies elongated pores as the cause of the difference in Young's modulus in the core structure in two orthogonal directions, thus resulting in the negative Poisson phenomenon. Based on this understanding, the parameters given include: the long axis of the elongated honeycomb micropores, the ratio of the long side to the short side, and the pore wall thickness. It also provides the variation law of the material's outer dimensions and wall thickness during preparation.

[0133] However, the relationship between the hole wall thickness and the hole size variation is unclear, and the spatial structure of the hexagon cannot be determined solely by the ratio of the long side to the short side of the outermost hole, i.e., the angle between the sides cannot be determined. In addition, the designed and prepared sample does not have the orthogonal modulus difference mentioned above on a macroscopic scale. Therefore, the parameters given based on the above understanding and mechanism cannot be used to prepare biomimetic negative Poisson's ratio materials, and the obtained parameters are not reliable.

[0134] To address the above problems, this invention provides a method for designing and fabricating biomimetic negative Poisson's ratio metamaterials based on a dual-gradient structure, comprising:

[0135] Based on the buckling phenomenon generated by compression tests of a sunflower pith structure with a dual gradient structure of pore size and wall thickness, the key parameters for preparing biomimetic negative Poisson's ratio metamaterials were determined.

[0136] The key parameters for preparing biomimetic negative Poisson's ratio metamaterials were designed and obtained using classical analytical mechanics theory.

[0137] Based on the obtained preparation parameters of the biomimetic negative Poisson's ratio metamaterial, the biomimetic negative Poisson's ratio metamaterial can be constructed.

[0138] In this process, compression tests were conducted on the structure with a dual gradient structure of pore size and wall thickness to obtain the value of Poisson's ratio, complete information on the highly non-uniform distribution of strain field within the cross-sectional surface of the sunflower pith, and the deformation process of the cell walls of each unit structure within the strain concentration zone. Based on this, the relationship between the negative Poisson's ratio phenomenon and the buckling phenomenon of the sunflower pith structure was determined, and then based on this relationship, the key parameters for preparing biomimetic negative Poisson's ratio metamaterials were determined.

[0139] Compared with existing technologies, this invention, based on the complete information of the highly non-uniform distribution of strain field within the cross-sectional surface of sunflower pith and the deformation process of the cell walls of each unit structure within the strain concentration zone, determines the relationship between the negative Poisson's ratio phenomenon and the buckling phenomenon in the sunflower pith structure. Under this relationship, the key parameters for preparing biomimetic negative Poisson's ratio metamaterials are determined and designed, enabling the preparation of biomimetic materials with two-dimensional or three-dimensional structures with guaranteed reliability.

[0140] Specifically, the method for determining the sunflower pith core structure with a dual gradient structure of pore size and wall thickness includes:

[0141] Step 1: Characterize the sunflower pith structure to obtain the sunflower pith structure;

[0142] Step 2: Based on the sunflower pith structure, determine the sunflower pith structure with a dual gradient structure of pore size and wall thickness.

[0143] In step 1, the sunflower pith structure is obtained by micro-CT and SEM electron microscopy at different cross-sections and longitudinal sections along different parts of the sunflower stem diameter.

[0144] In step 2, on the cross-section of the sunflower, the central cell pores are smaller and the peripheral cell pores are relatively larger, thus determining the existence of a pore size gradient.

[0145] In the cross-section of the sunflower pith, the wall thickness gradually increases from 200 nm at the center to 500 nm at the outermost layer, thus confirming the existence of a wall thickness gradient.

[0146] Specifically, the process of determining the buckling phenomenon produced by the compression test includes:

[0147] Step a: Perform a compression test on the structure with the dual gradient structure of aperture and wall thickness to obtain the value of Poisson's ratio, and obtain complete information on the highly uneven distribution of strain field in the cross-sectional surface of the sunflower pith, as well as the deformation process of the cell wall of each unit structure in the strain concentration zone.

[0148] Step b: Based on the complete information on the highly non-uniform distribution of strain field within the cross-sectional surface of the sunflower pith, and the deformation process of the cell walls of each unit structure within the strain concentration zone, determine the relationship between the negative Poisson's ratio phenomenon and the buckling phenomenon in the sunflower pith structure.

[0149] Step a includes:

[0150] S301: Black spots are evenly sprayed onto the front side of the sunflower pith sample;

[0151] The black spots serve as markers to track the relative displacement of the front surface of the specimen, used to detect the elongation / narrowing of the test sample and the evolution of the local strain field.

[0152] S302: Compress the sunflower pith sample on the loading platform;

[0153] S303: During the compression process, the value of Poisson's ratio is obtained based on the non-contact optical measurement technology DIC, and complete information on the highly non-uniform distribution of the strain field within the cross-sectional surface of the sunflower pith is obtained, as well as the deformation process of the cell walls of each unit structure within the strain concentration zone.

[0154] Among them, the complete information map of Poisson's ratio and the corresponding high non-uniform distribution of strain field in the cross-section of sunflower pith was calculated by MATLAB program from the data of 700x700 pixels in the central region of 1624x1236 pixels on the entire sample surface.

[0155] Among them, a complete information map based on Poisson's ratio and the corresponding highly non-uniform distribution of strain field within the cross-sectional surface of sunflower pith can determine whether a negative Poisson's ratio phenomenon occurs.

[0156] In step b, during the compression process, the stress concentration zone exhibits elastic buckling instability, changing from a convex polygon to a concave polygon, collapsing inward, and exhibiting a negative Poisson's ratio.

[0157] Based on this, according to the elastic buckling instability and negative Poisson's ratio phenomenon during compression, the relationship between the negative Poisson's ratio phenomenon and the buckling phenomenon in the sunflower core structure is determined, and the unique double gradient structure introduces local alternating buckling behavior under radial load in the cross section.

[0158] The buckling phenomenon is directly manifested by changes in pore size and wall thickness. Furthermore, the sunflower pith structure has a dual gradient structure in terms of pore size and wall thickness. Based on this, for biomimetic negative Poisson's ratio metamaterials with two-dimensional structures, the key parameters are the radial gradient of pore size and the gradient of wall thickness.

[0159] For biomimetic negative Poisson's ratio metamaterials with three-dimensional structures, the key parameters are pore size gradient and edge diameter gradient.

[0160] Specifically, the steps for designing and obtaining the key parameter values ​​for preparing biomimetic negative Poisson's ratio metamaterials using classical analytical mechanics theory include the following:

[0161] Biomimetic negative Poisson's ratio metamaterials with two-dimensional structures include:

[0162] S51: The wall thickness of microstructural units in multiple sunflower core samples was measured using SEM to obtain the average wall thickness at different locations and the gradient value of wall thickness variation.

[0163] S52: Use SEM to measure the pore size of microstructural units in multiple sunflower core samples, and obtain the average pore size value at different locations and the gradient value of pore size change.

[0164] S53: Set the wall thickness and aperture values ​​to ensure that the elongated deformation unit structure in the honeycomb structure exhibits an elastic asymmetric distribution relative to the two orthogonal directions, and to ensure that the entire honeycomb structure will gradually exhibit elastic buckling under gradually increasing strain.

[0165] Under the combined effect of changes in wall thickness gradient and pore size gradient, microstructural units with different wall thickness and pore size values ​​at different locations gradually buckle and become unstable, thus causing the entire structure to gradually exhibit a negative Poisson's ratio effect as strain increases.

[0166] Biomimetic negative Poisson's ratio metamaterials with three-dimensional structures include:

[0167] S61: The wall thickness of microstructural units in multiple sunflower core samples was measured using SEM to obtain the average wall thickness at different locations and the gradient value of wall thickness variation.

[0168] S62: Use SEM to measure the pore size of microstructural units in multiple sunflower core samples, and obtain the average pore size value at different locations and the gradient value of pore size change.

[0169] S63: Set the relative density value and the aspect ratio of the unit cell to ensure that the elongated unit structure in the 3D honeycomb structure exhibits an elastic asymmetric distribution relative to the two orthogonal directions, and to ensure that the entire 3D honeycomb structure will gradually exhibit elastic buckling under gradually increasing strain.

[0170] Specifically, S53 includes:

[0171] S531: Based on the structure of the sunflower pith in the cross section, the key structure is extracted and abstracted as an elongated hexagonal honeycomb structure with varying wall thickness.

[0172] Specifically, the modulus (Ey) of the stretched hexagon in the elongation direction and the modulus (Ex) perpendicular to the elongation direction are functions of the geometric parameters (h, l, and θ) of the structure, and these functions satisfy:

[0173]

[0174]

[0175] Where l and h are the lengths of the cell wall in the radial and tangential directions, respectively;

[0176] t is the thickness of the cell wall;

[0177] θ is the angle between the side length l and the vertical direction y. The value of θ is independent of the increment of l, and θ = 30°.

[0178] Es is the Young's modulus of the constituent material of the cell wall.

[0179] S532: Perform stress analysis on a single elongated hexagonal element structure, and establish the correlation between the applied load F and the internal stress σ of the radial cell wall CD within the element structure (see...). Figure 1 ),satisfy:

[0180] F=F′cosθ=σ(h+l sinθ)b Formula (3)

[0181] Where l and h are the lengths of the radial and transverse cell walls, respectively;

[0182] t is the thickness of the cell wall;

[0183] F is the applied compressive load; F' is the load component borne by the radial wall CD under the action of the applied load F;

[0184] b is the out-of-plane thickness of the radial wall CD;

[0185] The value of θ is independent of the increment of l, and θ = 30°.

[0186] S533: Based on the classical Euler beam theory, analyze the elastic instability of an elongated hexagonal honeycomb structure with variable wall thickness under compressive load.

[0187] Specifically, when F' reaches the buckling critical load F euller_CD At this time, the radial wall CD will experience buckling instability, and the critical buckling load F euller_CD satisfy:

[0188]

[0189] Where n is a coefficient used to characterize the fixation conditions at both ends of the cell wall;

[0190] I is the moment of inertia of the cross-sectional area of ​​the cell wall CD, I = bt3 / 12;

[0191] Es is the Young's modulus of the constituent material of the cell wall;

[0192] l is the length of the radial cell wall;

[0193] b is the out-of-plane thickness of the radial wall CD;

[0194] t represents the thickness of the cell wall.

[0195] S534: Based on equations (3) and (4), determine the critical buckling stress within the radial wall CD;

[0196] Specifically, the critical buckling stress F within the radial wall CD euler_CD satisfy:

[0197]

[0198] Wherein, n is given by the formula n = 2k / π;

[0199] k is calculated using the formula tank = 2l / hk;

[0200] l and h are the lengths of the radial and transverse cell walls, respectively;

[0201] Es is the Young's modulus of the constituent material of the cell wall;

[0202] I is the moment of inertia of the cross-sectional area of ​​the cell wall CD.

[0203] σ e It is the elastic buckling stress;

[0204] t is the thickness of the cell wall;

[0205] θ is the angle between the side length l and the vertical direction y, θ = 30°;

[0206] S535: Based on equation (5), determine the effect of variations in aperture and wall thickness on the elastic buckling stress σ of the radial wall CD. e The impact;

[0207] Specifically, by substituting the changes in aperture and wall thickness into equation (5) and using MATLAB software for analysis and calculation, the effects of increasing thickness t and radial wall length l on the elastic buckling stress σ of the radial wall CD are visually demonstrated. e The impact (see) Figure 2 ).

[0208] S536: Effect of variations in aperture and wall thickness on the elastic buckling stress σ of the radial wall CD e The influence of this was used to determine the aperture gradient and wall thickness gradient parameters.

[0209] Specifically, step S63 includes:

[0210] S631: Based on the structure of the sunflower pith in the cross section, the key structure is extracted and abstracted as an open tetrahedron with an elongated and variable edge diameter;

[0211] The geometry of a single elongated tetrahedron is determined by three independent parameters: the tilt angle and the two side lengths a and b;

[0212] Where θ represents the angle between the hexagonal face and the elongation direction, θ≥π / 4;

[0213] The height H and width D of the unit cell are defined by these three parameters: H = 4asin and D, respectively. Applying the principle of minimum potential energy to the deformation of the unit cell, the modulus of the elongated tetrahedron in its two principal directions is a function of the unit cell dimensions a, b and θ, the cross-sectional area A of the edge edges and the moment of inertia I, and the Young's modulus Es of the constituent material.

[0214] Among them, the two principal directions are the elongation directions E y and perpendicular to the elongation direction E x ;

[0215] The moduli in the two principal directions satisfy:

[0216]

[0217]

[0218] Where x, y, and z represent three mutually perpendicular directions;

[0219] Es is the Young's modulus of the constituent material of a unit cell;

[0220] The modulus ratio of the two orthogonal directions is defined as λ = Ex / Ey, and an additional condition is imposed on the geometry of the unit cell, namely... To reduce the number of variables related to microstructure size and simplify the analysis process;

[0221] At this point, the modulus ratio of the elongated tetrahedron in the two principal directions satisfies:

[0222]

[0223]

[0224] Where Ar = H / D is the aspect ratio of the unit cell, and its value directly reflects the degree of elongation and deformation of the unit structure.

[0225] ρ *Ar is the relative density, defined as the ratio of the apparent density of a polygon to the density of the constituent material. When Ar is a fixed value, its value changes directly reflect the change in the diameter of the edge of the unit structure.

[0226] S632: Perform stress analysis on a single elongated tetrahedral unit structure, constructing an external compressive load P along the

[001] lattice direction and the internal stress σ of the radial edge CD inside the unit structure. y The relationship between them;

[0227] Among them, the external compressive load P along the

[001] lattice direction and the internal stress σ of the radial edge CD inside the unit structure are... y The relationship between them satisfies:

[0228]

[0229] Where θ represents the angle between the hexagonal face and the elongation direction, θ≥π / 4;

[0230] a and b are the two side lengths of the tetrahedron;

[0231] S633: Based on the classic Timoshenko beam theory, analyze the elastic instability of an elongated variable wall thickness hexagonal honeycomb structure under compressive load.

[0232] When the applied compressive load reaches the critical buckling load, the prism CD will buckle in an energy-minimizing mode, and its critical buckling load satisfies:

[0233]

[0234] Where Es is the Young's modulus of the constituent material of the unit cell;

[0235] I is the moment of inertia of the cross-sectional area of ​​edge CD.

[0236] Combined with P CD_Cr sinθ=P, then:

[0237]

[0238] Among them, P CD_Cr The critical buckling load of the prism CD;

[0239] Es is the Young's modulus of the constituent material of a unit cell;

[0240] I is the moment of inertia of the cross-sectional area of ​​the cell wall CD;

[0241] S634: Based on equations (10) and (12), determine the critical buckling stress within the radial ridge CD;

[0242] The critical buckling stress within the radial ridge CD satisfies:

[0243]

[0244] S635: Based on equation (13), the changes in the aspect ratio and relative density of the unit cell affect the elastic buckling stress σ of the radial ridge CD. y The impact;

[0245] Substituting the aspect ratio and relative density changes of the unit cell into equation (13), and using MATLAB software for analysis and calculation, the effects of the increase in edge diameter and the degree of elongation deformation of the unit cell on the elastic buckling stress σ of the radial edge CD are visually demonstrated. y The impact;

[0246] S636: Determine the aperture gradient and edge diameter gradient parameters based on the influence of variations in aperture and edge diameter on the elastic buckling stress σy of the radial edge CD;

[0247] The aperture gradient and edge diameter gradient parameters are 2.8 and 2.5, respectively.

[0248] Specifically, for biomimetic negative Poisson's ratio metamaterials with two-dimensional structures: after setting the pore size and wall thickness values ​​at the center, the pore size and wall thickness parameters of the biomimetic negative Poisson's ratio metamaterial can be determined based on the pore size gradient and wall thickness gradient;

[0249] For biomimetic negative Poisson's ratio metamaterials with three-dimensional structures: after setting the aperture and edge diameter values ​​at the center, the aperture and edge diameter parameters of the biomimetic negative Poisson's ratio metamaterial can be determined based on the aperture gradient and edge diameter gradient.

[0250] Furthermore, this invention also provides a method for preparing biomimetic negative Poisson's ratio metamaterials based on a dual-gradient structure. The method utilizes the preparation parameters of the biomimetic negative Poisson's ratio metamaterials obtained by the design method of biomimetic negative Poisson's ratio metamaterials based on a dual-gradient structure, and employs additive printing technology to construct two-dimensional or three-dimensional biomimetic negative Poisson's ratio metamaterials.

[0251] Compared with existing technologies, this invention determines the key parameters for preparing biomimetic negative Poisson's ratio metamaterials based on the buckling phenomenon generated by compression tests of a sunflower pith structure with a dual gradient structure of pore size and wall thickness. The invention also uses classical analytical mechanics theory to design the parameter values ​​of these key parameters for preparing biomimetic negative Poisson's ratio metamaterials. Based on these parameter values, biomimetic materials with two-dimensional or three-dimensional structures can be prepared with guaranteed reliability.

[0252] This invention, based on complete information on the highly non-uniform distribution of strain field within the cross-sectional surface of sunflower pith and the deformation process of cell walls in each unit structure within the strain concentration zone, determines the relationship between the negative Poisson's ratio phenomenon and buckling phenomenon in the sunflower pith structure. Under this relationship, key parameters for preparing biomimetic negative Poisson's ratio metamaterials are determined and designed, enabling the preparation of biomimetic materials with two-dimensional or three-dimensional structures with guaranteed reliability. Furthermore, by adjusting the dual gradient values ​​during the preparation process, biomimetic negative Poisson's ratio metamaterials of different sizes can be prepared, demonstrating universality.

[0253] This invention identifies the mechanism by which the sunflower core structure exhibits a negative Poisson's ratio as a result of buckling. The unique dual-gradient structure introduces localized alternating buckling behavior under radial loads within the cross-section. Based on this, the pore size and wall thickness parameters along the radial pore size and wall thickness gradients are identified as key parameters for preparing biomimetic negative Poisson's ratio metamaterials. Through mechanical analysis, these pore size and wall thickness values ​​are obtained. Based on this correctly understood mechanism, the preparation of biomimetic negative Poisson's ratio metamaterials can be achieved.

[0254] This invention employs classical analytical mechanics theory to determine the effect of variations in aperture and wall thickness on the elastic buckling stress σ of the radial wall CD. e Based on this, the synergistic relationship between aperture and wall thickness was determined, which caused the unit structure at each position in the honeycomb structure with double gradient changes to gradually buckle as the strain increases. That is, when the wall thickness and aperture increase at the same time, it is necessary to ensure that the aperture change gradient is greater than the wall thickness change gradient in order to reduce the critical buckling stress, realize the macroscopic negative Poisson's ratio effect under large strain, and ensure sufficient structural strength.

[0255] Based on equation (5), changing the wall thickness and aperture will directly affect the value of the critical buckling stress. Buckling behavior is the core reason for the negative Poisson's ratio effect of the biomimetic negative Poisson's ratio metamaterial based on the dual gradient structure mentioned in this invention. Adjusting the rate of change of the two parameters can change the number and speed of buckling instability of the unit structure under large strain, thereby ultimately affecting the macroscopic negative Poisson's ratio value.

[0256] Example 1

[0257] A design method for biomimetic negative Poisson's ratio metamaterials based on a 2D honeycomb model, wherein the 2D honeycomb model is a honeycomb structure based on a two-dimensional stretched hexagon, specifically including:

[0258] Step 1: Characterize the sunflower pith structure to obtain the sunflower pith structure;

[0259] Specifically, such as Figure 3 As shown, the core structure of sunflower was obtained by micro-CT, SEM electron microscopy, or optical microscopy at different parts of the sunflower stem diameter, including cross-sections and longitudinal sections.

[0260] Step 2: Based on the sunflower pith structure, it was determined that the sunflower pith structure has a dual gradient structure in terms of pore size and wall thickness;

[0261] The structure of the sunflower pith is as follows: On the cross-section of the sunflower stalk pith, the main shapes of the cells are hexagonal and irregular hexagonal, which gradually elongate from the center to the periphery;

[0262] In the longitudinal section, the main shape is a twisted, flattened hexagon, stacked in layers in the longitudinal direction (i.e., the growth direction) perpendicular to the stem. The pore size of these flattened hexagonal cells is almost constant in the longitudinal direction (120 micrometers), while it gradually increases in the radial direction from 110 to 285 micrometers.

[0263] Among them, the "aperture" on the cross section (defined as the diagonal length of a polygon cell) increases radially from 105 micrometers to 295 micrometers, while remaining constant at 130 micrometers tangentially.

[0264] In the cross-section of a sunflower, the central cell pores are smaller, while the peripheral cell pores are relatively larger, thus confirming the existence of a pore size gradient.

[0265] In the cross-section of the sunflower pith, the wall thickness gradually increases from 200 nm at the center to 500 nm at the outermost layer, thus confirming the existence of a wall thickness gradient.

[0266] Step 3: Perform a compression test on the structure with the dual gradient structure of pore size and wall thickness to obtain the value of Poisson's ratio, and obtain complete information on the highly uneven distribution of strain field in the cross-sectional surface of the sunflower pith, as well as the deformation process of the cell wall of each unit structure in the strain concentration zone.

[0267] Specifically, including:

[0268] S301: Black spots are evenly sprayed onto the front side of the sunflower pith sample;

[0269] The black spots serve as markers to track the relative displacement of the front surface of the specimen, used to detect the elongation / narrowing of the test sample and the evolution of the local strain field.

[0270] Among them, the sunflower pith core sample is a cubic sunflower pith core sample (side length 7-9mm).

[0271] S302: Compress the sunflower pith sample on the loading platform;

[0272] Specifically, the compression test was conducted on a universal testing machine equipped with a 100N load sensor (UTM4103, SUNS Technology Co., Ltd., Shenzhen, China).

[0273] During the compression test, the loading platform was lubricated with grease to reduce friction between the platform and the specimen.

[0274] The compression test was conducted at a constant displacement rate of 2 mm / min.

[0275] S303: During the compression process, the value of Poisson's ratio is obtained based on the non-contact optical measurement technology DIC, and complete information on the highly uneven distribution of strain field within the cross-sectional surface of the sunflower pith is obtained, as well as the deformation process of the cell wall of each unit structure within the strain concentration zone.

[0276] Specifically, a CCD camera (TXG20, Baumer Electric AG, Switzerland, resolution 1624x1236 pixels, 256 gray levels) was used to continuously capture images from the sample surface at a speed of 1 / 3 Hz to obtain complete information about the highly uneven deformation of the sunflower pith surface.

[0277] The Poisson's ratio and the corresponding full-field strain diagram were calculated using a MATLAB program from data of 700x700 pixels in the central region of a 1624x1236 pixel area across the entire specimen surface.

[0278] Among them, the occurrence of negative Poisson's ratio can be determined based on Poisson's ratio and the corresponding full-field strain diagram.

[0279] Step 4: Based on the complete information on the highly non-uniform distribution of strain field within the cross-sectional surface of the sunflower pith, and the deformation process of the cell walls of each unit structure within the strain concentration zone, determine the relationship between the negative Poisson's ratio phenomenon and the buckling phenomenon in the sunflower pith structure.

[0280] Specifically, the deformation process and characteristics of sunflower core specimens under 20% strain were captured and carefully analyzed using full-field strain distribution micro-CT images, such as... Figure 4 As shown, local strain bands under radial compression can be observed in the middle region, with both sides contracting laterally, ultimately leading to a negative Poisson's ratio effect in the sunflower core.

[0281] Within the local deformation zone ( Figure 4 The gradual deformation process is clearly visible, thus determining the mechanism of the negative Poisson's ratio effect as follows:

[0282] As strain increases, the cell wall becomes more perpendicular to the direction of the applied force and begins to bend and buckle in an alternating pattern. During buckling, the elongated tetrahedral cells in different layers deform into more concave, curled shapes and gradually contract inward as a whole, ultimately inducing a macroscopic negative Poisson's ratio phenomenon, such as... Figure 4As shown in c. Conversely, the specimen deforms uniformly under longitudinal compression. During bending and buckling, the cell sidewalls inside the core twist into concave polygons, while the cell walls of the elongated cells on the periphery expand outward, resulting in an overall Poisson's ratio of zero for the material. Figure 4 e).

[0283] More specifically, the unique dual-gradient structure introduces localized alternating buckling behavior under radial loads within the cross-section, while generating a zero Poisson's ratio equilibrium deformation mode under longitudinal loads. This resulting anisotropic negative Poisson's ratio behavior satisfies various performance requirements across a wide range of application strains, namely, resisting collapse under radial loads and providing stable support under longitudinal loads.

[0284] In summary, during compression, the stress concentration zone exhibits elastic buckling instability, transforming from a convex polygon to a concave polygon, collapsing inward, and exhibiting a negative Poisson's ratio.

[0285] Based on this, according to the elastic buckling instability and negative Poisson's ratio phenomenon during compression, the relationship between the negative Poisson's ratio phenomenon and buckling phenomenon in the sunflower core structure is determined. The mechanism of the negative Poisson's ratio phenomenon in the sunflower core structure is attributed to the occurrence of buckling phenomenon, and the unique double gradient structure introduces local alternating buckling behavior under radial load in the cross section.

[0286] Step 5: Based on the relationship between the negative Poisson's ratio phenomenon and the buckling phenomenon in the sunflower pith structure, determine the key parameters for preparing biomimetic negative Poisson's ratio metamaterials;

[0287] Specifically, the dual-gradient structure introduces local alternating buckling behavior under radial loads within the cross-section. Therefore, the aperture and wall thickness parameters along the radial aperture variation gradient and wall thickness variation gradient are key parameters for the fabrication of biomimetic negative Poisson's ratio metamaterials.

[0288] Step 6: Using classical analytical mechanics theory, design and obtain the fabrication parameters for biomimetic negative Poisson's ratio metamaterials;

[0289] Among them, the classical mechanics analysis theory is the Euler beam theory.

[0290] Specifically, including:

[0291] S601: The wall thickness of microstructural units in multiple sunflower pith samples was measured using SEM to obtain the average wall thickness at different locations and the gradient value of wall thickness variation.

[0292] Specifically, measurements revealed that the wall thickness increased from approximately 200 nm at the center to 500 nm at the outermost edge. The radial gradient of the wall thickness was 2.5 times.

[0293] S602: Using SEM to measure the pore size of microstructural units in multiple sunflower core samples, the average pore size at different locations and the gradient value of pore size variation were obtained.

[0294] Specifically, measurements revealed that the aperture increased radially from approximately 105 μm at the center to 295 μm at the outermost edge, while remaining essentially constant in the tangential and longitudinal directions; the radial aperture variation gradient was 2.8 times.

[0295] S603: Sets the wall thickness and aperture values ​​to ensure that the elongated deformation units in the honeycomb structure exhibit an elastic asymmetric distribution relative to the two orthogonal directions, and to ensure that the entire honeycomb structure gradually exhibits elastic buckling under increasing strain.

[0296] Under the combined effect of changes in wall thickness gradient and pore size gradient, microstructural units with different wall thickness and pore size values ​​at different locations gradually buckle and become unstable, thus causing the entire structure to gradually exhibit a negative Poisson's ratio effect as strain increases.

[0297] Specifically, including:

[0298] S6031: Based on the structure of the sunflower pith in the cross-section, the key structure is extracted and abstracted as an elongated hexagonal honeycomb structure with varying wall thickness. Figure 1 );

[0299] Specifically, the modulus (Ey) of the stretched hexagon in the elongation direction and the modulus (Ex) perpendicular to the elongation direction are functions of the structure's geometric parameters (the two side lengths h and l, and the angle θ between side length l and the perpendicular direction y), and the functions satisfy:

[0300]

[0301]

[0302] Where l and h are the lengths of the cell wall in the radial and tangential directions, respectively;

[0303] t is the thickness of the cell wall;

[0304] θ is the angle between the side length l and the vertical direction y. The value of θ is independent of the increment of l. θ = 30°.

[0305] Es is the Young's modulus of the constituent material of the cell wall.

[0306] In this scenario, if the height of the hexagonal structure is stretched by 2.5 times, while the width (h0 + 2lsin) remains the same as the original regular hexagon, and t remains constant, then h = h0, l = 2.23l0 = 2.23h0, and θ = 13.35°. In this case, the ratio of the modulus of the stretched hexagon in the elongation direction (y-direction) to that of the regular hexagon will be 1.1, while the modulus of the stretched hexagon in the x-direction will decrease to 2.88% of its original value. This type of stretched hexagon has a modulus ratio of 36 in the two orthogonal directions Ey / Ex, resulting in a significant elastic asymmetry between these two principal directions.

[0307] Furthermore, without considering thickness variations, a honeycomb structure with a single pore size gradient will inevitably produce an uneven distribution of elastic modulus throughout the porous structure, with the elastic modulus of elongated unit structures always being greater.

[0308] Furthermore, according to equations (1) and (2), the thick-walled unit structure has a modulus advantage over the thin-walled unit structure in two orthogonal directions, that is, the elastic modulus is unevenly distributed inside the porous structure with a single wall thickness gradient.

[0309] Using equations (1) and (2), we can clearly see that without changing the composition of the constituent materials, increasing the wall thickness and pore size can enhance the elastic modulus of the entire structure.

[0310] S6032: Perform stress analysis on a single elongated hexagonal element structure, and establish the correlation between the applied load F and the internal stress σ of the radial cell wall CD within the element structure (see...). Figure 1 ),satisfy:

[0311] F=F′cosθ=σ(h+l sinθ)b Formula (3)

[0312] in,

[0313] l and h are the lengths of the radial and transverse cell walls, respectively;

[0314] t is the thickness of the cell wall;

[0315] F is the applied compressive load; F' is the load component borne by the radial wall CD under the action of the applied load F;

[0316] The value of θ is independent of the increment of l, and θ = 30°;

[0317] b is the out-of-plane thickness of the radial wall CD;

[0318] S6033: Based on the classical Euler beam theory, analyze the elastic instability of an elongated variable wall thickness hexagonal honeycomb structure under compressive load.

[0319] Specifically, when F' reaches the buckling critical load Feuller_CD At this time, the radial wall CD will experience buckling instability, and the critical buckling load F euller_CD satisfy:

[0320]

[0321] Where n is a coefficient used to characterize the fixation conditions at both ends of the cell wall;

[0322] I is the moment of inertia of the cross-sectional area of ​​the cell wall CD, I = bt 3 / 12;

[0323] Es is the Young's modulus of the constituent material of the cell wall;

[0324] l is the length of the radial cell wall;

[0325] b is the out-of-plane thickness of the radial wall CD;

[0326] t is the thickness of the cell wall;

[0327] S6034: Based on equations (3) and (4), determine the critical buckling stress within the radial wall CD; specifically, the critical buckling stress within the radial wall CD satisfies:

[0328]

[0329] Wherein, n is given by the formula n = 2k / π;

[0330] k is calculated using the formula tank = 2l / hk;

[0331] l and h are the lengths of the radial and transverse cell walls, respectively;

[0332] Es is the Young's modulus of the constituent material of the cell wall;

[0333] I is the moment of inertia of the cross-sectional area of ​​the cell wall CD.

[0334] σ e It is the elastic buckling stress;

[0335] t is the thickness of the cell wall;

[0336] θ is the angle between the side length l and the vertical direction y, θ = 30°;

[0337] For example, Table 1 shows the values ​​of k and n for several different l / h ratios.

[0338] Table 1 is based on stretched hexagonal elements (e.g.) Figure 1 As shown, the values ​​of the end constraint factor n of the cellular structure with l>h under uniaxial compression are...

[0339]

[0340]

[0341] S6034: Based on equation (5), determine the effect of variations in aperture and wall thickness on the elastic buckling stress σ of the radial wall CD. e The impact;

[0342] Specifically, by substituting the changes in aperture and wall thickness into equation (5) and using MATLAB software for analysis and calculation, the effects of increasing thickness t and radial wall length l on the elastic buckling stress σ of the radial wall CD are visually demonstrated. e The impact (see) Figure 2 ).

[0343] Calculations show that increasing the wall thickness and aperture separately have opposite effects on the critical buckling stress of the unit structure. That is, increasing the wall thickness will increase the critical buckling stress, while lengthening the radial side will decrease the critical buckling stress.

[0344] It can be predicted that within a honeycomb structure with a single wall thickness gradient, as strain increases, only a small portion of the core units with thinner walls may exhibit buckling. Figure 2 a) However, the outer thick-walled units are very strong and difficult to buckle, so the entire structure will not exhibit buckling-induced negative Poisson's ratio phenomenon.

[0345] Within a honeycomb structure with a single aperture gradient, the unit structures in the elongated outer region are relatively prone to buckling. Figure 2 b) The central region is relatively stable. As the strain increases, the stability and strength of the entire porous structure decrease rapidly. The structure quickly enters the "densification" stage and the negative Poisson's ratio effect cannot be reflected macroscopically.

[0346] For these two types of single-gradient structures, only certain regions are prone to buckling instability under a given strain, and the overall structure does not exhibit a negative Poisson's ratio effect of lateral contraction. Only when the wall thickness and aperture gradients work synergistically—that is, when an appropriate wall thickness gradient is combined with an appropriate aperture gradient—can the unit structures at different locations within the entire structure gradually buckle as the strain increases, ultimately leading to a negative Poisson's ratio effect on a macroscopic scale.

[0347] According to equation (5), the effect of the wall thickness variation gradient (the change in the value of t) on the critical buckling stress is cubic, while the effect of the aperture variation gradient (the change in the value of l) is relatively weak and not intuitively cubic. Therefore, when both the wall thickness and aperture increase simultaneously, in order to reduce the critical buckling stress, it is necessary to ensure that the aperture variation gradient is greater than the wall thickness variation gradient.

[0348] Calculations show that when the wall thickness variation gradient is 2.5 and the pore size variation gradient is 2.8 (i.e., ensuring that the pore size variation gradient > the wall thickness variation gradient), Figure 2 c) When the two work together, the unit structures at each position in the honeycomb structure with double gradient changes gradually buckle as the strain increases, realizing the macroscopic negative Poisson's ratio effect under large strain and ensuring sufficient structural strength.

[0349] S6035: Effect of variations in aperture and wall thickness on the elastic buckling stress σ of the radial wall CD. e The influence of these factors was investigated to determine the aperture gradient and wall thickness gradient parameters.

[0350] The aperture gradient parameter value represents the ratio of the outermost aperture to the center aperture; for example, this ratio is 2.8.

[0351] The wall thickness gradient value represents the ratio of the outermost wall thickness to the wall thickness at the center; for example, this ratio is 2.5.

[0352] After setting the aperture and wall thickness values ​​at the center, the aperture and wall thickness parameters of the biomimetic negative Poisson's ratio metamaterial can be determined based on the aperture gradient and wall thickness gradient.

[0353] A method for fabricating a biomimetic negative Poisson's ratio metamaterial for 2D cellular models includes constructing the biomimetic negative Poisson's ratio metamaterial using additive printing technology based on the obtained fabrication parameters of the biomimetic negative Poisson's ratio metamaterial.

[0354] Specifically, based on the above analysis of the structure-property relationship between the sunflower pith structure and its negative Poisson's ratio effect, the key structural parameters for constructing negative Poisson's ratio metamaterials were extracted as the gradient of pore size and wall thickness variation.

[0355] Using computer-aided graphic design, a two-dimensional hexagon was selected as the basic unit structure. Based on this, geometric double gradient changes in aperture and wall thickness were added to complete the structural design.

[0356] Using additive manufacturing technology, negative Poisson's ratio metamaterials with a dual-gradient structure are 3D printed.

[0357] The parametric model design was carried out using Autodesk's 3D Max software.

[0358] Specifically, including:

[0359] 1): Export the prepared model file as an STL file and perform slicing operations in the slicing software for photopolymerization printing;

[0360] 2) Pour the prepolymer of the elastic photocurable resin into the LCD photocurable 3D printing machine and start printing to prepare a 2D honeycomb structure model.

[0361] The gradient value for pore size variation is 2.8, and the gradient value for wall thickness variation is 2.5 (see...). Figure 5 d). The overall dimensions of the model are: width W = 45mm, length L = 45mm, and depth D = 17mm.

[0362] Example 2

[0363] A design method for a biomimetic negative Poisson's ratio metamaterial for a 3D honeycomb model, wherein the 3D honeycomb model is a three-dimensional open-cell tetrahedral honeycomb structure, which differs from Example 1 in that:

[0364] Step 6: Using classical analytical mechanics theory, design and obtain the fabrication parameters for biomimetic negative Poisson's ratio metamaterials;

[0365] Among them, the classical mechanics analysis theory is the Timoshen Coeur theory.

[0366] Specifically, including:

[0367] S601: The wall thickness of microstructural units in multiple sunflower pith samples was measured using SEM to obtain the average wall thickness at different locations and the gradient value of wall thickness variation.

[0368] Specifically, measurements revealed that the wall thickness increased from approximately 200 nm at the center to 500 nm at the outermost edge. The radial gradient of the wall thickness was 2.5 times.

[0369] S602: Using SEM to measure the pore size of microstructural units in multiple sunflower core samples, the average pore size at different locations and the gradient value of pore size variation were obtained.

[0370] Specifically, measurements revealed that the aperture increased radially from approximately 105 μm at the center to 295 μm at the outermost edge, while remaining essentially constant in the tangential and longitudinal directions; the radial aperture variation gradient was 2.8 times.

[0371] S603: Set the relative density value (analogous to the wall thickness value of 2D structure) and the aspect ratio value of the unit cell (analogous to the pore size value of 2D structure) to ensure that the elongated unit structure in the 3D honeycomb structure exhibits an elastic asymmetric distribution relative to the two orthogonal directions, and to ensure that the entire 3D honeycomb structure will gradually exhibit elastic buckling under gradually increasing strain.

[0372] Among them, under the combined effect of the gradient changes in edge diameter (equivalent to the wall thickness of a two-dimensional plane) and pore size, microstructural units with different edge diameters and cell length-to-width ratios at different positions gradually undergo buckling instability, thereby causing the entire structure to gradually exhibit a negative Poisson's ratio effect as the strain increases.

[0373] Specifically, including:

[0374] S6031: Based on the structure of the sunflower pith in the cross-section, the key structure is extracted and abstracted as an elongated, variable-diameter, open-pore tetrahedron. Figure 6 );

[0375] Specifically, the geometry of a single elongated tetrahedron (specifically, the tetrahedral unit of a body-centered cubic (BBC) in this invention) is determined by three independent parameters: the tilt angle and the two side lengths a and b.

[0376] The inclination angle represents the angle between the hexagonal surface and the elongation direction, i.e., the y-direction, where θ ≥ π / 4.

[0377] The height H and width D of the unit cell are defined by these three parameters: H = 4asin and D, respectively.

[0378] Furthermore, applying the principle of minimum potential energy to the deformation of the unit cell, the modulus of the elongated tetrahedron in its two principal directions (the elongation direction and the direction perpendicular to the elongation direction) is a function of the unit cell dimensions (a, b, and θ), the cross-sectional area A of the edge edges and the moment of inertia I, and the Young's modulus Es of the material.

[0379] If we assume that the cross-section A of the edge is circular and does not vary along the edge length, and that edges a and b have the same cross-section, then under loads in different directions, the moments of inertia of edges with lengths a and b relative to their neutral axes will be the same.

[0380] At this point, the moduli in these two principal directions satisfy:

[0381]

[0382]

[0383] Where x, y, and z represent three mutually perpendicular directions;

[0384] Es is the Young's modulus of the constituent material of the cell wall;

[0385] Furthermore, the modulus ratio of the two orthogonal directions is defined as λ = Ex / Ey, while an additional condition is imposed on the geometry of the unit cell, namely... This reduces the number of variables related to microstructure size and simplifies the analysis process.

[0386] At this point, the modulus ratio of the elongated tetrahedron in the two principal directions satisfies:

[0387]

[0388]

[0389] Where Ar = H / D is the aspect ratio of the unit cell, and its value directly reflects the degree of elongation and deformation of the unit structure.

[0390] ρ * Ar is the relative density, defined as the ratio of the apparent density of a polygon to the density of the constituent materials. When Ar is a fixed value, its value changes directly reflect the change in the diameter of the edge of the unit structure.

[0391] According to equation (9), the modulus ratio of the elongated tetrahedron can be obtained as a function of the cell aspect ratio Ar and the relative density ρ*. As shown in equation (8), the modulus ratio is a weak function of the relative density ρ*, especially when the cell aspect ratio is close to 1. When the cell aspect ratio is close to 1, all curves must converge to the same value, λ = 1. Conversely, the aspect ratio Ar has a significant effect on the modulus ratio. For example, at a relative density of 2%, when the cell aspect ratio reaches 2.0, the modulus ratio can increase by approximately 9 times. That is, when the height of the tetrahedron is twice its width, the modulus in its elongation direction is 9 times that in its orthogonal direction.

[0392] Using equations (6) to (8), we can clearly see that without changing the composition of the constituent materials, increasing the ridge diameter and the aspect ratio of the unit structure can enhance the elastic modulus of the entire 3D honeycomb structure.

[0393] S6032: Perform stress analysis on a single elongated tetrahedral unit structure, constructing an external compressive load P along the

[001] lattice direction and the internal stress σ of the radial edge CD inside the unit structure. y The relationship between them (see) Figure 7 ),satisfy:

[0394]

[0395] Where θ represents the angle between the hexagonal face and the elongation direction, θ≥π / 4;

[0396] a and b are the two side lengths of a tetrahedron, see Figure 6 .

[0397] S6033: Based on the classic Timoshenko beam theory, analyze the elastic instability of an elongated variable wall thickness hexagonal honeycomb structure under compressive load.

[0398] Specifically, when the applied compressive load reaches the critical buckling load, the prism CD will buckle in an energy-minimizing mode, and its critical buckling load satisfies:

[0399]

[0400] Where Es is the Young's modulus of the constituent material of the cell wall;

[0401] I is the moment of inertia of the cross-sectional area of ​​edge CD.

[0402] Combined with P CD_Cr sinθ=P, then:

[0403]

[0404] Among them, P CD_Cr The critical buckling load of the prism CD;

[0405] Es is the Young's modulus of the constituent material of the cell wall;

[0406] I is the moment of inertia of the cross-sectional area of ​​the cell wall CD;

[0407] S6034: Based on equations (10) and (12), determine the critical buckling stress within the radial ridge CD;

[0408] Specifically, the critical buckling stress within the radial ridge CD satisfies:

[0409]

[0410] S6034: Based on Equation (13), determine the effect of changes in the aspect ratio and relative density of the unit cell on the elastic buckling stress σy of the radial ridge CD;

[0411] Specifically, by substituting the aspect ratio and relative density changes of the unit cell into equation (13), and using MATLAB software for analysis and calculation, the effects of the increase in edge diameter and the degree of elongation deformation of the unit cell on the elastic buckling stress σ of the radial edge CD are visually demonstrated. y The impact (see) Figure 8 ).

[0412] Therefore, based on the analytical calculation results, the buckling stress σ can be established. y The relationship between the parameters of the unit cell structure (the aspect ratio Ar and the relative density ρ* of the unit structure).

[0413] Among them, the buckling stress σ of the unit structure y It exhibits a non-monotonic dependence on the aspect ratio Ar; when Ar > 1.5, σ y It gradually decreases. Simultaneously, the increase in relative density ρ* will amplify the buckling stress, i.e., σ. y It is proportional to the square of ρ*. The dimensionless ratio σ obtained from the analysis... y / Es as Figure 8 As shown.

[0414] Among them, the buckling stress of the elongated tetrahedral structure (expressed as a dimensionless ratio σ) y * The dependence of / Es (representing Ar) on increased aspect ratio and relative density ρ* is shown in the figure. Figure 8 c.

[0415] Calculations show that increasing the aspect ratio (corresponding to the aperture of the two-dimensional structure in the previous example) and the relative density (corresponding to the wall thickness of the two-dimensional structure in the previous example, since the relative density is directly related to the edge diameter when the aspect ratio is fixed, increasing the edge diameter will increase the relative density) have opposite effects on the critical buckling stress of the unit structure. That is, increasing the relative density will increase the critical buckling stress, while increasing the aspect ratio will decrease the critical buckling stress.

[0416] According to equation (13), the effect of the relative density variation gradient (equivalent to the edge diameter variation gradient) on the critical buckling stress is quadratic (fourth power relative to the edge diameter), while the aspect ratio variation gradient (equivalent to the aperture variation gradient) is relatively weaker and not intuitively quadratic. Therefore, when both the edge diameter and aperture increase simultaneously, to reduce the critical buckling stress, it is necessary to ensure that the aperture variation gradient is greater than the edge diameter variation gradient.

[0417] Calculations show that when the gradient value of the edge diameter change is 2.5 and the gradient value of the aperture change is 2.8 (i.e. ensuring that the aperture change gradient > the edge diameter change gradient), the synergistic effect of the two causes the unit structure at each position in the 3D honeycomb structure with double gradient change to gradually buckle as the strain increases, realizing the macroscopic negative Poisson's ratio effect under large strain and ensuring sufficient structural strength.

[0418] S6035: Determine the aperture gradient and edge diameter gradient parameters based on the influence of variations in aperture and edge diameter on the elastic buckling stress σy of the radial edge CD;

[0419] The aperture gradient parameter value represents the ratio of the outermost aperture to the center aperture; for example, this ratio is 2.8.

[0420] The edge diameter gradient value represents the ratio of the edge diameter of the outermost unit structure to the edge diameter at the center. For example, this ratio is 2.5.

[0421] After setting the aperture and edge diameter values ​​at the center, the aperture and edge diameter parameters of the biomimetic negative Poisson's ratio metamaterial can be determined based on the aperture gradient and edge diameter gradient.

[0422] A method for fabricating a biomimetic negative Poisson's ratio metamaterial for 3D cellular models includes constructing the biomimetic negative Poisson's ratio metamaterial using additive printing technology based on the obtained fabrication parameters of the biomimetic negative Poisson's ratio metamaterial.

[0423] Based on the above analysis of the structure-property relationship between the sunflower pith structure and its negative Poisson's ratio effect, the key structural parameters for constructing negative Poisson's ratio metamaterials were extracted as the gradients of pore size and edge diameter.

[0424] Using computer-aided graphic design, a three-dimensional tetrahedron was selected as the basic unit structure. Based on this, geometric double gradient changes in aperture and edge diameter were added to complete the structural design.

[0425] Using additive manufacturing technology, negative Poisson's ratio metamaterials with a dual-gradient structure are 3D printed.

[0426] The parametric model design was carried out using Autodesk's 3D Max software.

[0427] Specifically, including:

[0428] 1): Export the prepared model file as an STL file and perform slicing operations in the slicing software for photopolymerization printing;

[0429] 2): A radially open-cell double-gradient tetrahedral porous structure was fabricated using LCD photopolymerization 3D printing technology. The unit cells, which are gradually elongated and have continuously thickened walls, are arranged radially along three orthogonal directions to form an anisotropic porous structure.

[0430] The 3D printed sample has a width, length, and height of 52mm, 52mm, and 49mm, respectively; the outermost edge diameter and aperture of the 3D printed sample are 1.0mm and 9.0mm, respectively (see...). Figure 9 ).

[0431] Comparative Example 1

[0432] For positive Poisson's ratio metamaterials with uniform honeycomb structure (see...) Figure 5 a) The design and preparation method differs from that in Example 1 in that:

[0433] The wall thickness of a negative Poisson's ratio metamaterial is a fixed value.

[0434] The pore size of a negative Poisson's ratio metamaterial is a fixed value.

[0435] The fact that the entire structure does not exhibit a negative Poisson's ratio effect indicates that a uniform honeycomb structure without variations in wall thickness and pore size does not possess a negative Poisson's ratio effect.

[0436] Comparative Example 2

[0437] The design and fabrication method for positive Poisson's ratio metamaterials with radial thickness gradient honeycomb structures differs from that in Example 1 in the following ways:

[0438] The biomimetic negative Poisson's ratio metamaterial has a fixed pore size and a wall thickness gradient of 2.5 (see...). Figure 5 b).

[0439] The entire structure does not exhibit a negative Poisson's ratio effect; it is a positive Poisson's ratio material. This indicates that a simple change in wall thickness is insufficient to induce a negative Poisson's ratio effect.

[0440] Comparative Example 3

[0441] The design and fabrication method for zero Poisson's ratio metamaterials with radial aperture gradient honeycomb structures differs from that in Example 1 in the following ways:

[0442] The metamaterial has a fixed wall thickness and a pore size gradient of 2.8 (see...). Figure 5 c).

[0443] The entire structure exhibits an approximately zero Poisson's ratio, indicating that a simple change in aperture gradient is insufficient to induce a negative Poisson's ratio effect.

[0444] Performance Analysis:

[0445] 1. Analysis of the anisotropic negative Poisson's ratio characteristics of metamaterials

[0446] Taking a 3D-printed bigradient tetrahedral porous structure as an example, the changes in Poisson's ratio of the metamaterial sample under uniaxial compression test were observed in the cross section and longitudinal section.

[0447] The obtained data is compared, such as Figure 9 c: Poisson's ratio (blue ν) within the cross-section (xy plane). zx The curve gradually stabilizes at -0.13 as strain increases. However, within the longitudinal section (zx plane), the Poisson's ratio remains positive, reaching a maximum of 0.45.

[0448] Results Analysis: Based on the biomimetic negative Poisson's ratio metamaterial constructed using a dual-gradient structure proposed in this patent, anisotropic negative Poisson's ratio characteristics can be obtained. The Poisson's ratio values ​​are different in different compression planes, thus exhibiting different mechanical response characteristics.

[0449] 2. Stability analysis of negative Poisson's ratio and structural strength of metamaterials

[0450] 1) Taking the 3D printed double-gradient tetrahedral porous structure as an example, a uniaxial compression test was carried out to observe whether the stress-strain curve has a stable plateau region under large strain amplitude (i.e., the curve is flat, the strain increases significantly, and the stress remains stable).

[0451] Results analysis: such as Figure 9 The red curves (ν) in c and d xy and σ x As the strain value increases, within a relatively large range of strain variation (15%-60%), the stress value and Poisson's ratio of the material remain stable.

[0452] 2) Taking the 3D printed double-gradient hexagonal honeycomb structure as an example, a uniaxial compression test was carried out to observe whether the stress-strain curve has a stable plateau region under large strain amplitude (i.e., the curve is flat, the strain increases significantly, and the stress remains stable).

[0453] Results analysis: such as Figure 5 The curves marked with triangles in f and g show that, as the strain value increases, the stress value and Poisson's ratio of the material remain stable within a relatively large strain variation range (10%-45%).

[0454] Analysis of the attached diagram:

[0455] against Figure 2 :

[0456] In the figure, (a): only by increasing the wall thickness, the structural strength is enhanced, the critical buckling stress increases, and the structure is less prone to buckling.

[0457] (b): Increasing the aperture size alone rapidly reduces the structural strength and the critical buckling stress, making the structure prone to buckling.

[0458] (c): The effect of simultaneously increasing wall thickness and cell wall length on the buckling stress of the radial wall CD. The aperture gradient and wall thickness gradient act synergistically at different rates of change, resulting in a slow decrease in the critical buckling stress and making the structure relatively prone to buckling.

[0459] (d): The ratio of the buckling stress of the radial wall CD of the elongated hexagon to the buckling stress of the regular hexagon (σ) e * / σ e The dependence of the increased thickness t and length l.

[0460] against Figure 3 :

[0461] The double-gradient structure of sunflower pith. (a) and (b) The particle size changes radially in the cross-section, gradually elongating towards the periphery. (c) The wall thickness changes gradually, increasing from about 200 nm at the center to 500 nm towards the periphery.

[0462] against Figure 4 :

[0463] In the figure, (a) surface deformation images of dried sunflower pith in the xy plane (left group) and zx plane (right group) in the x and z directions were recorded using DIC technology (at 20% compressive strain), along with the corresponding vertical and horizontal strain distribution maps.

[0464] (b) Micro-CT images of cross-sections of sunflower core deformed under radial / transverse uniaxial compression (at 20% strain). Magnified views of the microstructure at different deformation stages show the mechanical deformation process involved.

[0465] (c) Schematic diagram of the deformation mechanism of the bigradient negative Poisson's ratio structure abstracted from sunflower pith in cross-section. Under radial compression, the elongated hexagonal cell walls begin to bend and buckle in an alternating pattern, resulting in a negative Poisson's ratio effect in the overall porous structure.

[0466] (d) Micro-CT image of a longitudinal section of a deformed sunflower core under longitudinal uniaxial compression (at 20% strain). Magnified views of the microstructure at different deformation stages show the mechanical deformation process.

[0467] (e) A schematic diagram of the deformation mechanism of the double-gradient negative Poisson's ratio structure derived from the sunflower pith in a longitudinal view. Under longitudinal compression, the hexagonal cell walls inside the pith bend inward and flex, while the elongated and thickened cell walls on the periphery expand outward. The combination of contraction or expansion of cell walls in different columns results in a Poisson's ratio of zero for the overall structure.

[0468] against Figure 5 :

[0469] The figure shows schematic diagrams of the four design schemes AD, (a)-(d).

[0470] Specifically, design scheme A: standard honeycomb structure; design scheme B: honeycomb structure with radial thickness gradient; design scheme C: honeycomb structure with radial aperture gradient; design scheme D: honeycomb structure with radial double gradient.

[0471] In the figure, (e): the geometric deformation of the 2D structure of the four sunflower pith cross-section structures in the four schemes at 0% strain (top) and 50% strain (bottom).

[0472] (f): Poisson's ratio curves of the four design schemes.

[0473] At the right end, from top to bottom, are schemes A, B, C, and D.

[0474] (g): Stress-strain curves obtained from compression experiments of each 3D printed structure.

[0475] Among them, the 3D printed structures of all design schemes have the same sample size and maintain almost the same relative density.

[0476] At the right end, from top to bottom, are schemes D, C, B, and A.

[0477] (h): Finite element simulation results of the Poisson ratio changes of design schemes C and D under uniaxial compression.

[0478] Among them, in the middle position, from top to bottom are schemes D and C.

[0479] against Figure 7 :

[0480] In the figure, (a): schematic diagram of the BCC lattice of the tetrahedral unit cell. When the stress y is applied in the

[001] direction, the load edges in the unit cell are represented by thick black lines.

[0481] (b): The smallest structural unit (structure cell) inside the tetrahedral structure under compressive load in the

[001] direction, the entire unit cell is symmetrical along the boundary of the structural unit. An external force P is applied in the y direction.

[0482] against Figure 8 :

[0483] In the figure, (a): with a fixed value of ρ*, the change in aspect ratio Ar affects σ. y The impact of / Es.

[0484] (b): With a fixed value for ρ*, the change in aspect ratio Ar affects σ y The impact of / Es.

[0485] (c): The effect of simultaneous changes in relative density ρ* and aspect ratio Ar on σ y / Impact

[0486] against Figure 9 :

[0487] In the figure, (a): schematic diagram of the unit structure in the three-dimensional double-gradient tetrahedral porous structure.

[0488] (b): Design schematic diagram of the three-dimensional double-gradient tetrahedral porous structure and photographs of the 3D printed sample in the xy plane (middle) and xz plane (right). The cross-section of the internal edges of this model is circular.

[0489] (c) and (d): Poisson's ratio and stress-strain curves of 3D-printed specimens under uniaxial compression. The gray area under the stress-strain curve represents the energy absorbed during compression.

[0490] In (c), from top to bottom, they represent V. ZX >0、V XY <0.

[0491] In (d), from top to bottom, they represent σ. X σ Z .

[0492] in, Figure 2-9 The figures are colored in the middle to distinguish the different conditions, so as to facilitate understanding.

[0493] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware, and the program can be stored in a computer-readable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.

[0494] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A design method for biomimetic negative Poisson's ratio metamaterials based on a dual-gradient structure, characterized in that, include: Based on the buckling phenomenon generated by compression tests of a sunflower pith structure with a dual gradient structure of pore size and wall thickness, the key parameters for preparing biomimetic negative Poisson's ratio metamaterials were determined. The process of determining the buckling phenomenon produced by the compression test includes: Step a: Perform a compression test on the sunflower core structure with a dual gradient structure of pore size and wall thickness to obtain the value of Poisson's ratio, and obtain complete information on the highly non-uniform distribution of strain field in the cross-sectional surface of the sunflower core, as well as the deformation process of the cell wall of each unit structure in the strain concentration zone. Step b: Based on the complete information on the highly non-uniform distribution of strain field in the cross-sectional surface of the sunflower pith, and the deformation process of the cell walls of each unit structure in the strain concentration zone, determine the relationship between the negative Poisson's ratio phenomenon and the buckling phenomenon in the sunflower pith structure. The key parameters for preparing biomimetic negative Poisson's ratio metamaterials were designed and obtained using classical analytical mechanics theory.

2. The design method according to claim 1, characterized in that, The method for determining the sunflower pith core structure with a dual gradient structure of pore size and wall thickness includes: Step 1: Characterize the sunflower pith structure to obtain the sunflower pith structure; Step 2: Based on the sunflower pith structure, determine the sunflower pith structure with a dual gradient structure of pore size and wall thickness.

3. The design method according to claim 1, characterized in that, For biomimetic negative Poisson's ratio metamaterials with two-dimensional structures, the key parameters are the radial pore size variation gradient and the wall thickness variation gradient. For biomimetic negative Poisson's ratio metamaterials with three-dimensional structures, the key parameters are pore size gradient and edge diameter gradient.

4. The design method according to claim 1, characterized in that, Based on the elastic buckling instability and negative Poisson's ratio phenomena during compression, the relationship between the negative Poisson's ratio phenomenon and the buckling phenomenon in the sunflower core structure was determined.

5. The design method according to claim 1, characterized in that, For biomimetic negative Poisson's ratio metamaterials with two-dimensional structures, the key parameter values ​​for fabricating these metamaterials, designed using classical analytical mechanics theory, include: S51: The wall thickness of microstructural units in multiple sunflower core samples was measured using SEM to obtain the average wall thickness at different locations and the gradient value of wall thickness variation. S52: Use SEM to measure the pore size of microstructural units in multiple sunflower core samples, and obtain the average pore size value at different locations and the gradient value of pore size change. S53: Set the wall thickness and aperture values ​​to ensure that the elongated deformation unit structures in the honeycomb structure exhibit an elastic asymmetric distribution relative to the two orthogonal directions, and to ensure that as the strain increases, the unit structures with different degrees of stretching and wall thicknesses in the entire honeycomb structure will gradually exhibit elastic buckling instability. For biomimetic negative Poisson's ratio metamaterials with three-dimensional structures, the key parameter values ​​for fabricating these metamaterials, designed using classical analytical mechanics theory, include: S61: The wall thickness of microstructural units in multiple sunflower core samples was measured using SEM to obtain the average wall thickness at different locations and the gradient value of wall thickness variation. S62: Use SEM to measure the pore size of microstructural units in multiple sunflower core samples, and obtain the average pore size value at different locations and the gradient value of pore size change. S63: Set the relative density value and the aspect ratio of the unit cell to ensure that the elongated unit structure in the 3D honeycomb structure exhibits an elastic asymmetric distribution relative to the two orthogonal directions, and to ensure that the unit structures with different edge diameters and pore sizes in the entire 3D honeycomb structure will gradually exhibit elastic buckling instability under gradually increasing strain.

6. The design method according to claim 5, characterized in that, Step S53 includes: S531: Based on the structure of the sunflower pith in the cross section, the key structure is extracted and abstracted as an elongated hexagonal honeycomb structure with varying wall thickness. Among them, the modulus Ey in the elongation direction and the modulus Ex perpendicular to the elongation direction of the stretched hexagon are the geometric parameters of the structure. h , l and θ A function of 1, wherein the function satisfies: Equation (1) Equation (2) in, l and h These are the lengths of the cell wall in the radial and tangential directions, respectively; t The thickness of the cell wall; θ 1 is the side length l The angle between the y-axis and the vertical direction. θ 1 = 30°; Es It is the Young's modulus of the constituent materials of the cell wall; S532: Perform stress analysis on a single elongated hexagonal element structure and construct external loads. F Internal stress of the radial cell wall CD within the unit structure The relationship between them; Among them, external load F Internal stress of the radial cell wall CD within the unit structure The relationship between them satisfies: Equation (3) in, l and h These are the lengths of the radial and tangential cell walls, respectively; t The thickness of the cell wall; F For external compressive load; F' To apply external load F The load component borne by the radial wall CD under the action of ; θ The value of 1 and l The increment is irrelevant. θ 1 = 30°; b is the out-of-plane thickness of the radial wall CD; S533: Based on the classical Euler beam theory, analyze the elastic instability of an elongated variable wall thickness hexagonal honeycomb structure under compressive load. Among them, when F' Reaching the critical buckling load F euler_CD At this point, the radial wall CD will experience buckling instability, and the critical buckling load... F euler_CD satisfy: Equation (4) in, n It is a coefficient used to characterize the fixation conditions at both ends of the cell wall; It is the moment of inertia of the radial cross-sectional area CD of the cell wall. = bt 3 / 12; Es It is the Young's modulus of the constituent materials of the cell wall; l The length of the radial cell wall; b is the out-of-plane thickness of the radial wall CD; t The thickness of the cell wall; S534: Based on external load F Internal stress of the radial cell wall CD within the unit structure The correlation between the elements and the elastic instability of the elongated variable wall thickness hexagonal honeycomb structure under compressive load were investigated, and the critical buckling stress in the radial wall CD was determined. Among them, based on equations (3) and (4), the critical buckling stress in the radial wall CD is determined, and the critical buckling stress is... satisfy: Equation (5) in, n From the formula n =2 k / π is given; k From the formula tan k =2 l / HK Calculated; l and h These are the lengths of the radial and tangential cell walls, respectively; Es It is the Young's modulus of the constituent materials of the cell wall; It is the moment of inertia of the cross-sectional area of ​​the cell wall CD; It is the elastic buckling stress; t The thickness of the cell wall; θ 1 is the side length l The angle between the y-axis and the vertical direction. θ 1 = 30°; S535: Determine the effect of variations in aperture and wall thickness on the elastic buckling stress of the radial wall CD based on the critical buckling stress within the radial wall CD. e The impact; Substituting the variations in aperture and wall thickness into equation (5), the thickness is calculated using MATLAB software. t and radial wall length l The increase in elastic buckling stress of the radial wall CD e The impact; S536: Elastic buckling stress of radial wall CD based on variations in aperture and wall thickness e The influence of this was used to determine the aperture gradient and wall thickness gradient parameters.

7. The design method according to claim 5, characterized in that, Step S63 includes: S631: Based on the structure of the sunflower pith in the cross section, the key structure is extracted and abstracted as an open tetrahedron with an elongated and variable edge diameter; The geometry of a single elongated tetrahedron is determined by three independent parameters: the angle of inclination. θ 2 and the lengths of the two sides a and b ; in, θ 2 represents the angle between the hexagonal face and the direction of elongation. θ 2≥π / 4; Among them, the height of the unit cell H The width D is defined by these three parameters respectively. H= 4 a and D = 2 a + b Applying the principle of minimum potential energy to the deformation of the unit cell, the modulus of the elongated tetrahedron in its two principal directions is equal to the unit cell size. a, b and Cross-sectional area of ​​edge A and moment of inertia I 2, and the Young's modulus of the constituent materials. E A function of s; Among them, the two main directions are the elongation directions. E y and perpendicular to the elongation direction E x ; The moduli in the two principal directions satisfy: Equation (6) Equation (7) Where x, y, and z represent three mutually perpendicular directions; Es It is the Young's modulus of the constituent materials of the cell wall; The modulus ratio of two orthogonal directions is defined as follows: =Ex / Ey, while imposing an additional condition on the geometry of the unit cell, namely This reduces the number of variables related to microstructure size and simplifies the analysis process; At this point, the modulus ratio of the elongated tetrahedron in the two principal directions satisfies: Equation (8) Equation (9) in, Ar=H / D It is the aspect ratio of the unit cell, and its value directly reflects the degree of elongation and deformation of the unit structure. It is relative density, defined as the ratio of the apparent density of a polygon to the density of the constituent materials. Ar When the value is fixed, its variation is entirely determined by the variation in the diameter of the unit structure edge; S632: Perform stress analysis on a single elongated tetrahedral unit structure, constructing an external compressive load P along the [001] lattice direction and the internal stress of the radial edge CD inside the unit structure. y The relationship between them; Among them, the external compressive load P along the [001] lattice direction and the stress in the radial edge CD of the unit structure are... y The relationship between them satisfies: Equation (10) in, θ 2 represents the angle between the hexagonal face and the direction of elongation. θ 2≥π / 4; a and b These are the two side lengths of a tetrahedron; S633: Based on the classic Timoshenko beam theory, analyze the elastic instability of an elongated variable wall thickness hexagonal honeycomb structure under compressive load. When the applied compressive load reaches the critical buckling load, the prism CD will buckle in an energy-minimizing mode, and its critical buckling load satisfies: Equation (11) in, Es It is the Young's modulus of the constituent material of a unit cell; It is the moment of inertia of the cross-sectional area of ​​the edge CD; Combined with P CD_Cr sin = P, then: Equation (12) Among them, P CD_Cr The critical buckling load of the prism CD; Es It is the Young's modulus of the constituent material of a unit cell; It is the moment of inertia of the cross-sectional area of ​​the edge CD; S634: Based on equations (10) and (12), determine the critical buckling stress within the radial ridge CD; The critical buckling stress within the radial ridge CD satisfies: Equation (13) S635: Based on equation (13), determine the effect of changes in the aspect ratio and relative density of the unit cell on the elastic buckling stress of the radial ridge CD. The influence of y; Substituting the aspect ratio and relative density changes of the unit cell into equation (13), MATLAB software was used to analyze and calculate the effect of the increase in edge diameter and the degree of elongation deformation of the unit cell on the elastic buckling stress of the radial edge CD. y The impact; S636: Elastic buckling stress of radial edge CD based on variations in aperture and edge diameter y The influence of this determines the aperture gradient and edge diameter gradient parameters.

8. The design method according to claim 6 or 7, characterized in that, For biomimetic negative Poisson's ratio metamaterials with two-dimensional structures: after setting the pore size and wall thickness at the center, the pore size and wall thickness parameters of the biomimetic negative Poisson's ratio metamaterial can be determined based on the pore size gradient and wall thickness gradient; For biomimetic negative Poisson's ratio metamaterials with three-dimensional structures: after setting the aperture and edge diameter values ​​at the center, the aperture and edge diameter parameters of the biomimetic negative Poisson's ratio metamaterial can be determined based on the aperture gradient and edge diameter gradient.

9. A method for preparing a biomimetic negative Poisson's ratio metamaterial based on a dual-gradient structure, characterized in that, include: Using the fabrication parameters of the biomimetic negative Poisson's ratio metamaterial obtained by the design method of the biomimetic negative Poisson's ratio metamaterial based on the dual gradient structure as described in any one of claims 1-8, the biomimetic negative Poisson's ratio metamaterial is constructed by additive printing technology.

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