Multi-attribute controllable three-dimensional mechanical metamaterial structure and design method thereof

Abstract

This application discloses a multi-attribute tunable three-dimensional mechanical metamaterial structure and its design method, relating to the field of mechanical metamaterials. This application provides a novel unit cell structure, and the properties of this three-dimensional mechanical metamaterial structure are related to the characteristic parameters of the unit cell structure. Therefore, by adjusting the characteristic parameters of the unit cell structure, the Poisson's ratio, compressibility coefficient, and coefficient of thermal expansion of the three-dimensional mechanical metamaterial structure can be adjusted. During the design process, through a combination of finite element analysis and theoretical analysis, and by simple calculation analysis and optimized selection of characteristic parameters, the three properties of the three-dimensional mechanical metamaterial structure can be individually controlled. This allows the three-dimensional mechanical metamaterial structure to possess the desired target properties, filling a gap in the industry and possessing significant industrial practical value. It can meet the actual needs of new advanced equipment with multiple functions and applications.

Description

Technical Field

[0001] This application relates to the field of mechanical metamaterials, and in particular to a three-dimensional mechanical metamaterial structure with tunable multi-property features and its design method. Background Technology

[0002] Metamaterials are renowned for their superior mechanical properties, such as exceptional specific strength, specific stiffness, and excellent impact energy absorption characteristics. In particular, metamaterials can achieve specific adjustments to their properties, including Poisson's ratio, compressibility, and thermal expansion, through the design of their microstructures. By controlling the positive, zero, and negative values ​​of these properties, different shape deformations can be achieved under the influence of temperature and force fields, which holds significant application potential in precision instruments and aerospace. For example, a negative Poisson's ratio can be achieved, causing the material to expand laterally under axial tension. Alternatively, negative compressibility can be achieved, causing the material to expand along a single direction, plane, or even its entire volume under hydrostatic pressure; these are respectively termed negative linear, negative area, and negative volume compressibility. Furthermore, negative thermal expansion can be achieved, causing the material to contract along a single direction, plane, or its entire volume when heated; these are respectively termed negative linear, negative area, and negative volume thermal expansion. In practical applications, skin sensors with adjustable Poisson's ratios can better conform to the skin during movement. Materials with adjustable thermal expansion can be used in aerospace satellite antennas and their supporting structures to reduce mechanical failures caused by excessive thermal deformation. Materials with adjustable compressibility can be used to manufacture highly sensitive hydrostatic pressure sensors.

[0003] Currently, numerous mechanical metamaterials with a single negative property have been designed and applied in various industrial fields. Another promising area of ​​research is combining different negative properties to create novel functional advanced materials that meet multi-functional and multi-purpose requirements. For example, materials with negative Poisson's ratio and negative compressibility can be used to design protective devices capable of withstanding extreme impacts and hydrostatic pressure. Materials with negative Poisson's ratio and negative thermal expansion coupling can be used to design multi-field coupled exciters sensitive to force and temperature fields. However, designing three-dimensional metamaterial structures that can simultaneously control two properties is far more challenging than designing mechanical metamaterials with single-property control. Currently, there is no complete equipment available, and three-dimensional metamaterial structures that can simultaneously control three properties are completely nonexistent, thus limiting the application of mechanical metamaterials. Summary of the Invention

[0004] To address the aforementioned problems and technical requirements, this applicant proposes a multi-attribute tunable three-dimensional mechanical metamaterial structure and its design method. The technical solution of this application is as follows:

[0005] A multi-attribute tunable three-dimensional mechanical metamaterial structure is disclosed. Each unit cell of this structure has a cubic virtual outline and includes two virtual sides parallel to the x1-x3 plane, two virtual sides parallel to the x2-x3 plane, and two virtual surfaces parallel to the x1-x2 plane. The four vertices of each virtual side are connected to the center of the virtual side by a first elastic beam. The center of each virtual surface is connected to the center of the four virtual sides by a first elastic beam. Each first elastic beam has an equal length and an angle θ relative to the x1-x2 plane. b , 0 < θ b <π / 2;

[0006] Each keypoint group has four keypoints connected to a second elastic beam, and the other ends of the four second elastic beams connected to the four keypoints in the same keypoint group are also connected. Each keypoint group includes a vertex of a virtual outline, two virtual side surfaces meeting at the vertex, and the center of each virtual surface. Each second elastic beam has the same length and an inclination angle θ relative to the x1-x2 plane. a , 0 < θ a <π / 2;

[0007] The properties of three-dimensional mechanical metamaterial structures are related to the characteristic parameters of their unit cell structure. These properties include Poisson's ratio, compressibility coefficient, and coefficient of thermal expansion.

[0008] A further technical solution involves defining the characteristic parameters of the unit cell structure as including the specifications of the two elastic beams and the inclination angle θ of the first elastic beam relative to the x1-x2 plane. b The specifications of the first elastic beam include the cross-sectional dimension R of the first elastic beam. b The coefficient of thermal expansion of the first elastic beam is α b and the length L of the first elastic beam b The specifications of the second elastic beam include the cross-sectional dimension R of the second elastic beam. a The coefficient of thermal expansion α of the second elastic beam a and the length L of the second elastic beam a .

[0009] The further technical solution is that the three-dimensional mechanical metamaterial structure includes M×N×P stacked unit cell structures, M≥1, N≥1 and P≥1, M unit cell structures are stacked sequentially along the x1 direction, N unit cell structures are stacked sequentially along the x2 direction, and P unit cell structures are stacked sequentially along the x3 direction.

[0010] A further technical solution is that the cross-sectional shape of any first elastic beam is a square, rectangle, circle, annulus or trapezoid, and the cross-sectional shape of any second elastic beam is a square, rectangle, circle, annulus or trapezoid.

[0011] A design method for three-dimensional mechanical metamaterial structures, the design method comprising:

[0012] The virtual outline of each unit cell in the designed three-dimensional mechanical metamaterial structure is a cube, comprising two virtual sides parallel to the x1-x3 plane, two virtual sides parallel to the x2-x3 plane, and two virtual surfaces parallel to the x1-x2 plane. The four vertices of each virtual side are connected to the center of the virtual side by a first elastic beam, and the center of each virtual surface is connected to the center of the four virtual sides by a first elastic beam. Each first elastic beam has an equal length and an angle θ relative to the x1-x2 plane. b , 0 < θ b <π / 2; The four key points in each key point group are connected to a second elastic beam, and are also connected to the other end of the four second elastic beams connected to the four key points in the same key point group; The four key points in each key point group include a vertex of the virtual outline and the centers of two virtual sides and a virtual surface that meet at the vertex; The length of each second elastic beam is equal and the inclination angle relative to the x1-x2 plane is θ. a , 0 < θ a <π / 2;

[0013] By adjusting the characteristic parameters of the unit cell structure and performing finite element analysis under each characteristic parameter, the properties of the three-dimensional mechanical metamaterial structure are obtained. The characteristic parameters of the unit cell structure include the specifications of the two elastic beams and the inclination angle θ of each first elastic beam relative to the x1-x2 plane. b ;

[0014] The target characteristic parameters that enable the three-dimensional mechanical metamaterial structure to achieve the target properties are determined, and the three-dimensional mechanical metamaterial structure is designed according to the target characteristic parameters.

[0015] A further technical solution is that the design method also includes:

[0016] A three-dimensional mechanical metamaterial structure is designed by stacking M unit cell structures with target characteristic parameters along the x1 direction, and / or stacking N unit cell structures with target characteristic parameters along the x2 direction, and / or stacking P unit cell structures with target characteristic parameters along the x3 direction.

[0017] The properties of the three-dimensional mechanical metamaterial structure include Poisson's ratio, compressibility coefficient, and coefficient of thermal expansion. The specifications of the first elastic beam include the cross-sectional dimension R of the first elastic beam. b The coefficient of thermal expansion of the first elastic beam is α b and the length L of the first elastic beam b The specifications of the second elastic beam include the cross-sectional dimension R of the second elastic beam. a The coefficient of thermal expansion α of the second elastic beam a and the length L of the second elastic beam a .

[0018] The further technical solution is that the designed three-dimensional mechanical metamaterial structure with the target properties simultaneously has a negative Poisson's ratio, a negative compressibility coefficient, and a negative thermal expansion coefficient.

[0019] A further technical solution involves using finite element analysis to obtain the properties of a three-dimensional mechanical metamaterial structure for each characteristic parameter. This includes:

[0020] Finite element models were established for the three-dimensional mechanical metamaterial structure with each characteristic parameter, and finite element calculations were performed to obtain the Poisson's ratio, Young's modulus, and linear thermal expansion coefficient of the three-dimensional mechanical metamaterial structure.

[0021] The compressibility coefficient of the three-dimensional mechanical metamaterial structure was calculated based on Poisson's ratio and Young's modulus.

[0022] A further technical solution is that the compressibility coefficient of the three-dimensional mechanical metamaterial structure includes the linear compressibility coefficient, the surface compressibility coefficient, and the volumetric compressibility coefficient. The methods for calculating the compressibility coefficient of the three-dimensional mechanical metamaterial structure include:

[0023] The linear compressibility coefficient of the three-dimensional mechanical metamaterial structure in the x1 direction was determined as follows: The linear compressibility coefficient in the x2 direction is The linear compressibility coefficient in the x3 direction is

[0024]

[0025] The surface compressibility coefficient of the three-dimensional mechanical metamaterial structure in the x1-x2 plane is determined to be β. A12 =2β L1 The surface compressibility coefficient on the x1-x3 plane is β. A13 =β L1 +β L3 The surface compressibility coefficient on the x2-x3 plane is β. A23 =β L1 +β L3 ;

[0026] The volume compressibility coefficient of the three-dimensional mechanical metamaterial structure is determined to be β. V =2β L1 +β L3 ;

[0027] Where E1 is the Young's modulus of the three-dimensional mechanical metamaterial structure along the x1 direction, E2 is the Young's modulus of the three-dimensional mechanical metamaterial structure along the x2 direction, and E3 is the Young's modulus of the three-dimensional mechanical metamaterial structure along the x3 direction; ν 12 It is the ratio of the strain in the x1 direction to the strain in the x2 direction of the three-dimensional mechanical metamaterial structure, ν. 31 It is the ratio of the strain in the x3 direction to the strain in the x1 direction of the three-dimensional mechanical metamaterial structure, ν. 13 It is the ratio of the strain in the x1 direction to the strain in the x3 direction of the three-dimensional mechanical metamaterial structure.

[0028] A further technical solution is that the thermal expansion coefficient of the three-dimensional mechanical metamaterial structure also includes the area thermal expansion coefficient and the volume thermal expansion coefficient. The method for obtaining the properties of the three-dimensional mechanical metamaterial structure through finite element calculation also includes:

[0029] The coefficient of area thermal expansion of the three-dimensional mechanical metamaterial structure in the x1-x2 plane is determined to be α. A12 =2α1, the coefficient of thermal expansion of the area on the x1-x3 plane is α A13 =α1+α3, and the coefficient of thermal expansion of the area on the x2-x3 plane is α. A23 =α1 + α3;

[0030] The volumetric thermal expansion coefficient of the three-dimensional mechanical metamaterial structure is determined to be α. V =2α1+α3;

[0031] Where α1 is the linear thermal expansion coefficient in the x1 direction of the three-dimensional mechanical metamaterial structure, α2 is the linear thermal expansion coefficient in the x2 direction of the three-dimensional mechanical metamaterial structure, and α3 is the linear thermal expansion coefficient in the x3 direction of the three-dimensional mechanical metamaterial structure, and α1=α2.

[0032] The beneficial technical effects of this application are:

[0033] This application discloses a multi-attribute tunable three-dimensional mechanical metamaterial structure and its design method. It provides a novel unit cell structure, and the properties of this three-dimensional mechanical metamaterial structure are related to the characteristic parameters of the unit cell structure. Therefore, by adjusting the characteristic parameters of the unit cell structure, the Poisson's ratio, compressibility coefficient, and coefficient of thermal expansion of the three-dimensional mechanical metamaterial structure can be adjusted. During the design process, through a combination of finite element analysis and theoretical analysis, and by simple calculation analysis and optimized selection of characteristic parameters, the three properties of the three-dimensional mechanical metamaterial structure can be individually controlled, thereby enabling the three-dimensional mechanical metamaterial structure to possess the desired target properties, filling a technological gap in the industry. Furthermore, the structure and method provided in this application can yield a three-dimensional mechanical metamaterial structure simultaneously possessing negative Poisson's ratio, negative compressibility, and negative thermal expansion, which has significant industrial practical value and can meet the actual needs of new advanced equipment with multiple functions and applications. Attached Figure Description

[0034] Figure 1 This is a schematic diagram of a unit cell structure in one embodiment of this application.

[0035] Figure 2 yes Figure 1 The diagram shows the characteristic parameter annotations of the unit cell structure.

[0036] Figure 3 This is a schematic diagram of a structure in which multiple single-cell structures are stacked sequentially along the x3 direction.

[0037] Figure 4 It is a schematic diagram of a structure in which multiple single-cell structures are stacked sequentially along the x1 and x2 directions.

[0038] Figure 5 This is a flowchart illustrating the design method of a three-dimensional mechanical metamaterial structure in one embodiment of this application.

[0039] Figure 6 The properties of a three-dimensional mechanical metamaterial structure vary with angle θ in this example. b The graph shows the change in Poisson's ratio ν. (a) is the curve of the change in Poisson's ratio 12 With θ b The curve of change is shown in (b), which is the linear compressibility coefficient β. L1 and β L3 With θ b The change curve, (c) is... as well as With θ b The change curve. Detailed Implementation

[0040] The specific embodiments of this application will be further described below with reference to the accompanying drawings.

[0041] This application discloses a three-dimensional mechanical metamaterial structure with tunable multi-property features. Please refer to [reference needed]. Figures 1-4 This three-dimensional mechanical metamaterial structure is based on a unit cell structure, and each unit cell structure is as follows: Figure 1 As shown, each unit cell structure consists of several first elastic beams 1 and second elastic beams 2. Figures 1-4 The white elastic beam represents the first elastic beam 1, and the black elastic beam represents the second elastic beam 2. Both the first elastic beam 1 and the second elastic beam 2 are made of elastic material.

[0042] The virtual outline of each unit cell is a cubic structure, such as... Figure 1 The virtual outline of the unit cell structure is shown by the dashed lines. The side lengths of the virtual outline along the x1 direction are L1, along the x2 direction are L2, and along the x3 direction are L3. The x1 and x2 directions are perpendicular to each other in the x1-x2 plane, the x1 and x3 directions are perpendicular to each other in the x1-x3 plane, and the x2 and x3 directions are perpendicular to each other in the x2-x3 plane. The virtual outline of the cubic structure of the unit cell structure includes two virtual lateral faces parallel to the x1-x3 plane, two virtual lateral faces parallel to the x2-x3 plane, and two virtual surfaces parallel to the x1-x2 plane.

[0043] Each of the four vertices of a virtual side is connected to the center of that virtual side by a first elastic beam 1, and the center of each virtual surface is connected to the center of the four virtual sides by a first elastic beam 1. Thus, each unit cell structure contains 24 first elastic beams 1.

[0044] Each unit cell structure's virtual outline forms eight keypoint groups. Each keypoint group includes four keypoints, and each keypoint group corresponds to a vertex of the virtual outline, including the vertex itself, two virtual side faces meeting at the vertex, and the center of each virtual surface. For example, in... Figure 1 In the diagram, the keypoint group corresponding to vertex A of the virtual outline contains four keypoints: vertex A, the center B of a virtual side parallel to the x1-x3 plane that intersects at vertex A, the center D of a virtual side parallel to the x2-x3 plane that intersects at vertex A, and the center C of the virtual surface that intersects at vertex A. Each keypoint group connects to a second elastic beam 2, and is also connected to the other end of four second elastic beams 2 connected to the four keypoints in the same keypoint group. Therefore, each unit cell structure contains 32 second elastic beams 2.

[0045] Each of the first elastic beams 1 has the same length. The specifications of the first elastic beam 1 include its cross-sectional dimension R. b The coefficient of thermal expansion α of the first elastic beam 1 b and the length L of the first elastic beam 1 bThe inclination angle of each first elastic beam 1 relative to the x1-x2 plane is θ. b , 0 < θ b <π / 2.

[0046] Each of the second elastic beams 2 is of equal length. The specifications of the second elastic beam 2 include the cross-sectional dimension R of the second elastic beam 1. a The coefficient of thermal expansion α of the second elastic beam 2 a and the length L of the second elastic beam 2 a The inclination angle of each second elastic beam 2 relative to the x1-x2 plane is θ. a , 0 < θ a <π / 2.

[0047] The cross-sectional shape of any one of the first elastic beams 1 is square, rectangular, circular, annular, or trapezoidal. The cross-sectional shape of any one of the second elastic beams 2 is square, rectangular, circular, annular, or trapezoidal. In one embodiment, all the first elastic beams 1 have the same cross-sectional shape, or at least two of the first elastic beams 1 have different cross-sectional shapes. In another embodiment, all the second elastic beams 2 have the same cross-sectional shape, or at least two of the second elastic beams 2 have different cross-sectional shapes. The cross-sectional shapes of the first elastic beams 1 and the second elastic beams 2 may be the same or different. However, in practical applications, for the convenience of analyzing, designing, and manufacturing three-dimensional mechanical metamaterial structures, it is generally configured that all the first elastic beams 1 and all the second elastic beams 2 have the same cross-sectional shape.

[0048] The illustrations in this application use a circular cross-sectional shape for both the first elastic beam 1 and the second elastic beam 2 as an example. Then, as shown... Figure 2 As shown, the cross-sectional dimension R of the first elastic beam 1 is... b This refers to the radius of the first elastic beam 1 and the cross-sectional dimension R of the second elastic beam 2. a This refers to the radius of the second elastic beam 2.

[0049] Based on the structural characteristics of this unit cell, the following geometric parameter relationships can be determined: L1 = L2 = 2L b cosθ b L3 = 2L b sinθ b , and 2L a sinθ a =L b sinθ b .

[0050] Based on the unit cell structure, this three-dimensional mechanical metamaterial structure can be extended in three dimensions, resulting in a structure comprising M×N×P stacked unit cells, where M≥1, N≥1, and P≥1. Specifically, M unit cells are stacked sequentially along the x1 direction, N unit cells are stacked sequentially along the x2 direction, and P unit cells are stacked sequentially along the x3 direction. For example... Figure 3 A schematic diagram shows multiple unit cell structures stacked sequentially along the x3 direction. (See diagram.) Figure 4 A schematic diagram showing multiple unit cell structures stacked sequentially along the x1 and x2 directions is shown.

[0051] The properties of this three-dimensional mechanical metamaterial structure are related to the characteristic parameters of each unit cell. These properties include Poisson's ratio, compressibility coefficient, and coefficient of thermal expansion. The characteristic parameters of each unit cell include the specifications of the two elastic beams and the inclination angle θ of the first elastic beam 1 relative to the x1-x2 plane. b By adjusting the characteristic parameters of the unit cell structure, it is possible to control multiple properties of three-dimensional mechanical metamaterial structures.

[0052] This application also discloses a design method for three-dimensional mechanical metamaterial structures; please refer to [reference needed]. Figure 5 The flowchart shown illustrates the design method, which includes the following steps:

[0053] Step S1: Design each unit cell structure of the three-dimensional mechanical metamaterial structure. That is, design and form the unit cell structure provided in the above embodiments, such as... Figure 1 and 2 As shown, this embodiment will not be described in detail.

[0054] Step S2: Adjust the characteristic parameters of the unit cell structure and perform finite element calculations under each characteristic parameter to obtain the properties of the three-dimensional mechanical metamaterial structure.

[0055] As mentioned above, the characteristic parameters of the unit cell structure include the specifications of the two elastic beams and the inclination angle θ of each first elastic beam relative to the x1-x2 plane. b The specifications of the first elastic beam 1 include the cross-sectional dimension R of the first elastic beam 1. b The coefficient of thermal expansion α of the first elastic beam 1 b and the length L of the first elastic beam 1 b The specifications of the second elastic beam 2 include the cross-sectional dimension R of the second elastic beam 2. a The coefficient of thermal expansion α of the second elastic beam 2 a and the length L of the second elastic beam 2 a .

[0056] The properties of three-dimensional mechanical metamaterial structures include Poisson's ratio, compressibility coefficient, and coefficient of thermal expansion. Among them, (1) the Poisson's ratio of three-dimensional mechanical metamaterial structures includes ν12 ν 21 ν 13 ν 31 ν 23 and ν 32 . ν 12 It is the ratio of the strain in the x1 direction to the strain in the x2 direction, ν 21 It is the ratio of the strain in the x2 direction to the strain in the x1 direction, ν. 13 It is the ratio of the strain in the x1 direction to the strain in the x3 direction, ν 31 It is the ratio of the strain in the x3 direction to the strain in the x1 direction, ν. 23 It is the ratio of the strain in the x2 direction to the strain in the x3 direction, ν 32 It is the ratio of strain in the x3 direction to strain in the x2 direction. (2) The compressibility coefficient of a three-dimensional mechanical metamaterial structure includes the linear compressibility coefficient, the area compressibility coefficient, and the volume compressibility coefficient. (3) The thermal expansion coefficient of a three-dimensional mechanical metamaterial structure includes the linear thermal expansion coefficient, the area thermal expansion coefficient, and the volume thermal expansion coefficient.

[0057] Step S3: Determine the target feature parameters that enable the three-dimensional mechanical metamaterial structure to achieve the target properties, and design the three-dimensional mechanical metamaterial structure according to the target feature parameters.

[0058] In one embodiment, a finite element model is established for each characteristic parameter of the three-dimensional mechanical metamaterial structure, and finite element calculations are performed to obtain the Poisson's ratio, Young's modulus, and linear thermal expansion coefficient of the three-dimensional mechanical metamaterial structure.

[0059] Then, based on Poisson's ratio and Young's modulus of the three-dimensional mechanical metamaterial structure, the compressibility coefficient of the three-dimensional mechanical metamaterial structure can be calculated. This includes calculating the linear compressibility coefficient, surface compressibility coefficient, and volumetric compressibility coefficient of the three-dimensional mechanical metamaterial structure using the following methods:

[0060] (1) Determine the linear compressibility coefficient of the three-dimensional mechanical metamaterial structure in the x1 direction as: The linear compressibility coefficient in the x2 direction is The linear compressibility coefficient in the x3 direction is E1 is the Young's modulus of the three-dimensional mechanical metamaterial structure along the x1 direction, E2 is the Young's modulus of the three-dimensional mechanical metamaterial structure along the x2 direction, and E3 is the Young's modulus of the three-dimensional mechanical metamaterial structure along the x3 direction.

[0061] (2) Determine the surface compressibility coefficient β of the three-dimensional mechanical metamaterial structure in the x1-x2 plane. A12 =2β L1 The surface compressibility coefficient on the x1-x3 plane is β. A13 =β L1+β L3 The surface compressibility coefficient on the x2-x3 plane is β. A23 =β L1 +β L3 .

[0062] (3) Determine the volume compressibility coefficient of the three-dimensional mechanical metamaterial structure as β. V =2β L1 +β L3 .

[0063] The linear thermal expansion coefficients of a three-dimensional metamaterial structure can be obtained through finite element analysis, including the linear thermal expansion coefficients α1 in the x1 direction, α2 in the x2 direction, and α3 in the x3 direction, where α1 = α2. In another embodiment, the area thermal expansion coefficient and volume thermal expansion coefficient of the three-dimensional metamaterial structure can also be calculated based on the linear thermal expansion coefficients:

[0064] (1) Determine the area thermal expansion coefficient α of the three-dimensional mechanical metamaterial structure in the x1-x2 plane. A12 =2α1, the coefficient of thermal expansion of the area on the x1-x3 plane is α A13 =α1+α3, and the coefficient of thermal expansion of the area on the x2-x3 plane is α. A23 =α1+α3.

[0065] (2) Determine the volumetric thermal expansion coefficient of the three-dimensional mechanical metamaterial structure as α. V =2α1+α3.

[0066] Based on this, the properties of a three-dimensional mechanical metamaterial structure can be adjusted by regulating the characteristic parameters of its unit cell structure, thereby ultimately achieving a specific target property. The target property of a three-dimensional mechanical metamaterial structure generally refers to one or more properties reaching a specific value range, such as making a property positive, negative, or zero, or even within other specific value intervals. In one embodiment, the designed three-dimensional mechanical metamaterial structure with the target property can simultaneously possess a negative Poisson's ratio, a negative compressibility coefficient, and a negative coefficient of thermal expansion. The negative Poisson's ratio includes a negative Poisson's ratio in at least one direction; the negative compressibility coefficient includes at least one of a negative linear compressibility coefficient, a negative area compressibility coefficient, and a negative volumetric compressibility coefficient; and the negative coefficient of thermal expansion includes at least one of a negative linear thermal expansion coefficient, a negative area thermal expansion coefficient, and a negative volumetric thermal expansion coefficient.

[0067] Building upon this, the design method can also stack M unit cell structures with target characteristic parameters sequentially along the x1 direction, and / or N unit cell structures with target characteristic parameters sequentially along the x2 direction, and / or P unit cell structures with target characteristic parameters sequentially along the x3 direction. The target characteristic parameters of each unit cell structure are determined using the same method described above, and then a three-dimensional mechanical metamaterial structure is designed, formed by stacking M×N×P unit cell structures, each with the target characteristic parameters.

[0068] After the desired three-dimensional mechanical metamaterial structure is designed, it can be prepared by casting and cutting, or it can be printed by photopolymerization or melt extrusion 3D printer.

[0069] In one example, for ease of description, the cross-sectional dimension ratio is defined. Slenderness ratio thermal expansion coefficient ratio The characteristic parameters of the unit cell structure can be obtained through parameters q, s, λ, and θ. b To determine this, in this example, to reduce the adjustment variables of the characteristic parameters of the unit cell structure, it is assumed that s = 10, q = 1, and λ = 2 are fixed, then θ b It is the only variable among the characteristic parameters of a unit cell structure.

[0070] The Poisson's ratio ν of a three-dimensional mechanical metamaterial structure can be obtained through finite element analysis. 12 With θ b The change curve is as follows Figure 6 As shown in (a), the linear compressibility coefficient β of the three-dimensional mechanical metamaterial structure L1 and β L3 With θ b The change curve is as follows Figure 6 As shown in (b), the linear thermal expansion coefficients α1 and α3 of the three-dimensional mechanical metamaterial structure are respectively related to α b ratio as well as With θ b The change curve is as follows Figure 6 As shown in (c) above. Then, by selecting an appropriate θ... b This allows three-dimensional mechanical metamaterial structures to possess a specific Poisson's ratio ν. 12 Linear compressibility coefficient β L1 and β L3 And the linear thermal expansion coefficients α1 and α3. For example, suppose the target property of a three-dimensional mechanical metamaterial structure is that the three-dimensional mechanical metamaterial structure also has a negative Poisson's ratio ν. 12 Negative linear compressibility coefficient β L1 And the negative linear thermal expansion coefficient α3, then combined Figure 6 It can be determined that when θ b >20° ν 12 Both are negative, when θ b β <38° L1 Both are negative, when θ b <38° If all are negative, then at 20° < θ b When taking any value within the range <38°, a negative Poisson's ratio ν can be obtained. 12 Negative linear compressibility coefficient β L1 A three-dimensional mechanical metamaterial structure with a negative linear thermal expansion coefficient α3. This example only uses θ b Taking the case of variables as an example, the situation is similar when changing other feature parameters to adjust the attribute. And this example only uses... Figure 6 Taking a few attributes as examples, the same applies to other attributes.

[0071] The above descriptions are merely preferred embodiments of this application, and this application is not limited to the above embodiments. It is understood that other improvements and variations that can be directly derived or conceived by those skilled in the art without departing from the spirit and concept of this application should be considered to be included within the protection scope of this application.

Claims

1. A multi-property tunable three-dimensional mechanical metamaterial structure, characterized in that, The virtual outline of each unit cell of the three-dimensional mechanical metamaterial structure is a cubic structure and includes parallel to... The two virtual sides of the plane, parallel to The two virtual sides of the plane and parallel to Two virtual surfaces are defined on a plane. The four vertices of each virtual side are connected to the center of that virtual side by a first elastic beam. The center of each virtual surface is connected to the centers of the four virtual sides by a first elastic beam. Each first elastic beam has an equal length and is relative to... The angle of inclination of the plane is , ; The four key points in each key point group are connected with a second elastic beam, and the other end of the four second elastic beams connected with the four key points in the same key point group are connected; the four key points in each key point group include one vertex of the virtual contour and the centers of two virtual side surfaces and one virtual surface intersecting at the vertex; The lengths of each of the second elastic beams are equal and are opposite The angles of inclination of the planes are all , ; The properties of the three-dimensional mechanical metamaterial structure are related to the characteristic parameters of its unit cell structure. These properties include Poisson's ratio, compressibility coefficient, and coefficient of thermal expansion. The characteristic parameters of the unit cell structure include the specifications of the two elastic beams and the first elastic beam relative to... Inclination angle of a plane The specifications of the first elastic beam include the cross-sectional dimensions of the first elastic beam. The coefficient of thermal expansion of the first elastic beam and the length of the first elastic beam The specifications of the second elastic beam include the cross-sectional dimensions of the second elastic beam. The coefficient of thermal expansion of the second elastic beam and the length of the second elastic beam .

2. The three-dimensional mechanical metamaterial structure of claim 1, wherein, The three-dimensional mechanical metamaterial structure comprises a plurality of the unit cell structures stacked with each other, , and , a plurality of the unit cell structures are stacked in sequence along a direction, a plurality of the unit cell structures are stacked in sequence along a direction, a plurality of the unit cell structures are stacked in sequence along a direction.

3. The three-dimensional mechanical metamaterial structure of claim 1, wherein, The cross section shape of any first elastic beam is square, rectangular, circular, annular or trapezoidal, and the cross section shape of any second elastic beam is square, rectangular, circular, annular or trapezoidal.

4. A method of designing a three-dimensional mechanical metamaterial structure, characterized by, The design method comprises: The virtual outline of each unit cell in the three-dimensional mechanical metamaterial structure is a cubic structure and includes parallel to... The two virtual sides of the plane, parallel to The two virtual sides of the plane and parallel to Two virtual surfaces are defined on a plane. The four vertices of each virtual side are connected to the center of that virtual side by a first elastic beam. The center of each virtual surface is connected to the centers of the four virtual sides by a first elastic beam. Each first elastic beam has an equal length and is relative to... The angle of inclination of the plane is , Each keypoint group has four keypoints connected to a second elastic beam, and the other ends of the four second elastic beams connected to the four keypoints in the same keypoint group are also connected. Each keypoint group includes a vertex of the virtual outline and the centers of two virtual sides and a virtual surface that intersect at the vertex. Each second elastic beam has an equal length and is relative to... The angle of inclination of the plane is , ; adjusting characteristic parameters of the unit cell structure, and performing finite element calculation under each characteristic parameter to obtain properties of the three-dimensional mechanical metamaterial structure, the characteristic parameters of the unit cell structure including specifications of the two elastic beams and an inclination angle of each first elastic beam relative to a plane , the specifications of the first elastic beam including a cross-sectional dimension of the first elastic beam , a thermal expansion coefficient of the first elastic beam , and a length of the first elastic beam , the specifications of the second elastic beam including a cross-sectional dimension of the second elastic beam , a thermal expansion coefficient of the second elastic beam , and a length of the second elastic beam ; the properties of the three-dimensional mechanical metamaterial structure include a Poisson's ratio, a compressibility coefficient, and a thermal expansion coefficient; determining target characteristic parameters for the three-dimensional mechanical metamaterial structure to achieve target properties, and designing the three-dimensional mechanical metamaterial structure according to the target characteristic parameters.

5. The method of designing according to claim 4, wherein, The design method further comprises: along directions, and / or, along directions, and / or, along directions, and / or, along directions, and / or, along directions, and / or, along directions, a three-dimensional mechanical metamaterial structure formed by cellular structures each having the target characteristic parameter.

6. The method of claim 4, wherein, The three-dimensional mechanical metamaterial structure designed to have the target properties simultaneously has negative Poisson's ratio, negative compressibility coefficient and negative thermal expansion coefficient.

7. The method of claim 4, wherein, The method for obtaining the properties of the three-dimensional mechanical metamaterial structure by finite element calculation for each characteristic parameter of the three-dimensional mechanical metamaterial structure comprises: establishing a finite element model for each characteristic parameter of the three-dimensional mechanical metamaterial structure to obtain the Poisson's ratio, Young's modulus and linear thermal expansion coefficient of the three-dimensional mechanical metamaterial structure by finite element calculation; calculating the compressibility coefficient of the three-dimensional mechanical metamaterial structure according to the Poisson's ratio and Young's modulus of the three-dimensional mechanical metamaterial structure.

8. The method of designing according to claim 7, wherein, The compressibility coefficient of the three-dimensional mechanical metamaterial structure includes linear compressibility coefficient, surface compressibility coefficient and volume compressibility coefficient, and the method for calculating the compressibility coefficient of the three-dimensional mechanical metamaterial structure comprises: determining that the three-dimensional metamaterial structure is in a linear compressibility coefficient in the direction of , a linear compressibility coefficient in the direction of , a linear compressibility coefficient in the direction of , a linear compressibility coefficient in the direction of , a linear compressibility coefficient in the direction of ; determining a coefficient of surface compressibility of the three-dimensional mechanical metamaterial structure in a plane , a coefficient of surface compressibility of the three-dimensional mechanical metamaterial structure in a plane , a coefficient of surface compressibility of the three-dimensional mechanical metamaterial structure in a plane ; determining a bulk compressibility coefficient of the three-dimensional metamaterial structure as ; wherein is the Young's modulus of the three-dimensional mechanical metamaterial structure along the direction, is the Young's modulus of the three-dimensional mechanical metamaterial structure along the direction, is the Young's modulus of the three-dimensional mechanical metamaterial structure along the direction; is the ratio of the strain of the three-dimensional mechanical metamaterial structure direction to the strain of the three-dimensional mechanical metamaterial structure direction, is the ratio of the strain of the three-dimensional mechanical metamaterial structure direction to the strain of the three-dimensional mechanical metamaterial structure direction, is the ratio of the strain of the three-dimensional mechanical metamaterial structure direction to the strain of the three-dimensional mechanical metamaterial structure direction.

9. The method of claim 7, wherein, The thermal expansion coefficient of the three-dimensional mechanical metamaterial structure further includes area thermal expansion coefficient and volume thermal expansion coefficient, and the method for obtaining the properties of the three-dimensional mechanical metamaterial structure by finite element calculation further comprises: determining an area thermal expansion coefficient of the three-dimensional mechanical metamaterial structure in a plane , an area thermal expansion coefficient of the three-dimensional mechanical metamaterial structure in a plane , an area thermal expansion coefficient of the three-dimensional mechanical metamaterial structure in a plane ; determining a volumetric thermal expansion coefficient of the three-dimensional metamaterial structure as ; wherein is the linear thermal expansion coefficient of the three-dimensional mechanical metamaterial structure in the direction is the linear thermal expansion coefficient of the three-dimensional mechanical metamaterial structure in the direction is the linear thermal expansion coefficient of the three-dimensional mechanical metamaterial structure in the direction is the linear thermal expansion coefficient of the three-dimensional mechanical metamaterial structure in the direction is the linear thermal expansion coefficient of the three-dimensional mechanical metamaterial structure in the direction is the linear thermal expansion coefficient of the three-dimensional mechanical metamaterial structure in the direction .

Images