A design method of negative poisson's ratio porous structure based on three-period minimal surface

Abstract

The application discloses a design method of a negative Poisson's ratio porous structure based on a three-period minimal surface, and belongs to the field of computer-aided design, and the specific operation steps are as follows: according to an initial minimal surface function, an extended minimal surface is constructed and solidified; considering the geometric characteristics of the generated porous structure and the buckling mode under the critical load, a problem model of constructing the extended three-period minimal surface with the negative Poisson's ratio is established; then, the problem model is simplified according to the geometric characteristics of the porous structure, and the construction parameters of the minimal surface porous structure with the negative Poisson's ratio are obtained through a step-by-step search method. The application realizes the coupling of the negative Poisson's ratio material and the minimal surface porous structure, two commonly used metamaterials, improves the performance and application range of the material, and can be used for guiding engineering design.

Description

Technical Field

[0001] This invention belongs to the field of computer-aided design and relates to a design method for negative Poisson's ratio porous structures based on a three-period minimal surface, which is applicable to engineering metamaterial design, medical application design and manufacturing, and other fields. Background Technology

[0002] In existing technologies, negative Poisson's ratio porous materials have wide applications in engineering manufacturing, biomedicine, and aerospace due to their inherent unique mechanical properties. Therefore, the development and fabrication of new negative Poisson's ratio materials has always been a research hotspot. Currently, most negative Poisson's ratio structures studied are based on arrays of periodic beams, trusses, or shells, exhibiting strong anisotropy and easy stress concentration. Furthermore, their low internal connectivity leads to limitations in applicability and controllability, restricting their application range. Recently, three-periodic minimal surfaces have attracted widespread attention due to their smooth, interconnected topological structure controlled by functions, as well as their higher hardness and strength compared to similar truss structures. Although many studies have been conducted on the design of various metamaterial structures based on three-periodic minimal surfaces, a complete design method for negative Poisson's ratio porous structures based on three-periodic minimal surfaces has not yet been proposed. Therefore, applying periodic minimal surfaces to the design of negative Poisson's ratio structures and constructing a complete design methodology is a technological gap that urgently needs to be filled in China.

[0003] To achieve the above objectives, a design method for a negative Poisson's ratio porous structure based on a three-period minimal surface is proposed. Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to provide a design method for a negative Poisson's ratio porous structure based on a three-period minimal surface.

[0005] The technical solution of this invention is as follows: This invention discloses a design method for a negative Poisson's ratio porous structure based on a three-period minimum surface, comprising the following steps:

[0006] (1) Construct extended minimum surfaces;

[0007] (2) Extended minimal surface solidification;

[0008] (3) Considering the geometric characteristics of the generated porous structure and the buckling mode under critical load, establish a problem model for constructing an extended three-period minimum surface with negative Poisson's ratio.

[0009] (4) The problem model is simplified based on the geometric characteristics of the porous structure, and the construction parameters of the minimum surface porous structure with negative Poisson ratio are obtained by stepwise search method.

[0010] In step (1), the specific steps for constructing the extended minimal surface are as follows:

[0011] Minimal surface function Based on this, a function for controlling the form is introduced. Design an optimized minimal surface : (1.1)

[0012] in, Represents a three-dimensional vector. x , y , z Each corresponds to its coordinate; This represents a scalar quantity, indicating the value taken on the isosurface. The connection method between different cycles of the surface is controlled, scalar A , B , C By controlling the basic shape of a single-period surface, a surface with more free spatial shape changes is constructed. Other types of surfaces are processed in a similar way, and this type of surface is called an extended three-period minimal surface.

[0013] In step (2), the specific steps of solidifying the extended minimal surface are as follows:

[0014] For a given extended three-period minimum surface equation, the three-dimensional vector The range of values ​​for is the set. : (1.2)

[0015] In the set Given a closed constrained surface The solidified extended three-period minimal surface structure for:

[0016] (1.3).

[0017] In step (3), the specific steps for establishing the problem model of the extended three-period minimum surface with negative Poisson's ratio are as follows:

[0018] Given the basic construction equations of the model, in order for all the articulated ligaments between adjacent periods to buckle so that the structure exhibits a negative Poisson's ratio under critical pressure, the periodic elements should meet the following requirements:

[0019] (a) The connection holes between each periodic unit should be as close to spherical as possible;

[0020] (b) The moment of inertia of the periodic element at the narrowest point along the radial direction of the pore should be less than the moment of inertia of the periodic element at the narrowest point perpendicular to the direction of force.

[0021] (c) The surface remains continuous;

[0022] In mathematics, these constraints can be restated as follows: (1.4)

[0023] in, Indicates the roundness of structural pores. This represents the moment of inertia of the model at the narrowest point along the radial direction of the pores. The moment of inertia represents the point where the model is narrowest, perpendicular to the direction of the force. Represent the second derivative of the surface function; adjust the morphological control coefficients within the construction equations through constraints. A , B , C This is used to change the shape of the surface, so that the structure can adjust the Poisson's ratio of the surface structure while satisfying the basic definition of a minimal surface.

[0024] In step (4), the simplified problem model is expressed as follows:

[0025] (1.5)

[0026] in, Indicating the basic periodic unit in The roundness of the pores projected onto the plane. Indicating the basic periodic unit in The thickness of the beam as projected onto a plane.

[0027] Finally, the surface construction parameters that satisfy formula (1.5) are found by stepwise search method, and then the minimal surface porous structure with negative Poisson ratio is obtained.

[0028] The beneficial effects of this invention are: this invention realizes the coupling of two commonly used metamaterials, negative Poisson's ratio materials and extremely small curved porous structures, which improves the performance and application range of the materials and can be used to guide engineering design. Attached Figure Description

[0029] Figure 1 This is a flowchart illustrating the specific operation of the present invention;

[0030] Figure 2 This is a schematic diagram of the porous structure described in this invention;

[0031] Figure 3 This is a curve showing the Poisson's ratio-strain variation of the porous structure in this invention. Detailed Implementation

[0032] The present invention will be further described in detail below with reference to the embodiments. It should be noted that the scope of protection of the present invention is not limited to the following embodiments. These examples are listed for illustrative purposes only and do not limit the present invention in any way.

[0033] The design method for negative Poisson's ratio porous structures based on three-period minimum surfaces in this example includes the following steps:

[0034] (1) Construct extended minimum surfaces;

[0035] (2) Extended minimal surface solidification;

[0036] (3) Considering the geometric characteristics of the generated porous structure and the buckling mode under critical load, establish a problem model for constructing an extended three-period minimum surface with negative Poisson's ratio.

[0037] (4) The problem model is simplified based on the geometric characteristics of the porous structure, and the construction parameters of the minimum surface porous structure with negative Poisson ratio are obtained by stepwise search method. Example 1

[0038] This example uses the Swartz P minimum surface as an example to construct a negative Poisson's ratio porous structure based on a three-period minimum surface using the method of this invention.

[0039] like Figure 1 The diagram shown is a flowchart of the design method for a negative Poisson's ratio porous structure based on a three-period minimum surface in this example, including the following steps:

[0040] (1) Constructing an extended minimum surface: The specific steps for constructing an extended minimum surface are as follows:

[0041] First, in the Swartz P-minimal surface function Based on this, a function for controlling the form is introduced. Design an extended minimal surface ,in:

[0042] (1.1, 1.2)

[0043] but:

[0044] (1.3)

[0045] (2) Solidification of extended minimal surfaces: The specific steps of solidification of extended minimal surfaces are as follows:

[0046] Let the extended minimum surface function Medium three-dimensional vector The set of values If the range is [-3, 3], then the set Closed cylindrical surface constructed in the middle for:

[0047] (1.4)

[0048] The solidified extended three-period minimal surface structure for: (1.5)

[0049] The generated solid structure is a P-type extended three-period minimal surface porous structure with a radius of 3 and a height of 6;

[0050] (3) Establish a problem model for constructing an extended three-period minimum surface with a negative Poisson's ratio:

[0051] The specific steps for establishing a problem model for constructing an extended three-period minimum surface with a negative Poisson's ratio are as follows:

[0052] Given the basic construction equations of the model, in order for all the articulated ligaments between adjacent periods to buckle so that the structure exhibits a negative Poisson's ratio under critical pressure, the periodic elements should meet the following requirements:

[0053] (a) The connection holes between each periodic unit should be as close to spherical as possible;

[0054] (b) The moment of inertia of the periodic element at the narrowest point along the radial direction of the pore should be less than the moment of inertia of the periodic element at the narrowest point perpendicular to the direction of force.

[0055] (c) The surface remains continuous;

[0056] In mathematics, these constraints are restated as: (1.6)

[0057] in, Indicates the roundness of structural pores. This represents the moment of inertia of the model at the narrowest point along the radial direction of the pores. The moment of inertia represents the point where the model is narrowest, perpendicular to the direction of the force. Represent the second derivative of the surface function; adjust the morphological control coefficients within the construction equations through constraints. A , B , C This is used to change the shape of the surface, so that the structure can adjust the Poisson's ratio of the surface structure while satisfying the basic definition of a minimal surface;

[0058] (4) Simplification and solution of the problem model:

[0059] The specific steps for simplifying the problem model are as follows:

[0060] First, obtain the basic periodic unit inx , y , z The projections in the three planar directions, and thus the problem model described in formula (1.6) can be simplified to:

[0061] (1.7)

[0062] in, Indicating the basic periodic unit in The roundness of the pores projected onto the plane. Indicating the basic periodic unit in The thickness of the beam as projected onto a plane;

[0063] Finally, the surface construction parameters satisfying formula (1.7) are found through a stepwise search method, thereby obtaining a minimal porous surface structure with a negative Poisson's ratio:

[0064] Table 1 shows some of the construction parameters and their corresponding Poisson ratios. A schematic diagram of the corresponding structure is shown below. Figure 2 As shown, the Poisson's ratio-strain variation curve of the corresponding structure is as follows: Figure 3 As shown;

[0065] Table 1 Poisson's ratio of minimally curved porous structures

[0066] .

[0067] This invention achieves the coupling of two commonly used metamaterials: negative Poisson's ratio materials and extremely small curved porous structures, thereby improving the material's performance and application range, and can be used to guide engineering design.

[0068] Finally, it should be understood that the embodiments described in this invention are only used to illustrate the principles of the embodiments of this invention; other variations may also fall within the scope of this invention; correspondingly, the embodiments of this invention are not limited to the embodiments explicitly described and illustrated in this invention.

Claims

1. A design method for a negative Poisson's ratio porous structure based on a three-period minimum surface, characterized in that: The specific operating steps are as follows: (1) Construct extended primary minimal surface functions; (2) Realization of extended minimal surface functions; (3) Based on the geometric characteristics of the generated porous structure and the buckling mode under critical load, a problem model for constructing an extended three-period minimum surface with negative Poisson's ratio is established. The specific operational process for establishing the problem model of the extended three-period minimum surface with negative Poisson's ratio is as follows: Given the basic construction equations of the model, in order for all the articulated ligaments between adjacent periods to buckle so that the structure exhibits a negative Poisson's ratio under critical pressure, its periodic elements should meet the following requirements: a. The connection holes between each periodic unit should be as close to spherical as possible; b. The moment of inertia of the periodic element at its narrowest point along the radial direction of the pore should be less than the moment of inertia of the periodic element at its narrowest point perpendicular to the direction of force. c. The curved surface remains continuous; In mathematics, these constraints are restated as follows: (1.7) in, Indicates the roundness of structural pores. This represents the moment of inertia of the model at the narrowest point along the radial direction of the pores. The moment of inertia represents the point where the model is narrowest, perpendicular to the direction of the force. The second derivative of the extended minimal surface function is represented; the morphological control coefficients within the construction equations are adjusted by constraints. A , B , C This is used to change the shape of the surface, so that the structure can adjust the Poisson's ratio of the surface structure while satisfying the basic definition of a minimal surface; (4) The problem model is simplified based on the geometric characteristics of the porous structure, and the construction parameters of the minimum surface porous structure with negative Poisson ratio are obtained by stepwise search method.

2. The design method for a negative Poisson's ratio porous structure based on a three-period minimal surface according to claim 1, characterized in that: In step (1), the specific operation process for constructing the extended primary minimal surface function is as follows: Minimal surface function Based on this, a function for controlling the form is introduced. Design an extended minimal surface : (1.1); in, Represents a three-dimensional vector. Each corresponds to its coordinate; This represents a scalar quantity, indicating the value taken by the isosurface. The connection method between different cycles of the surface is controlled by scalar. A , B , C By controlling the basic shape of a single-period surface, a surface with more flexible shape changes in space is constructed. Other types of surfaces are processed in a similar way, and this type of surface is called an extended three-period minimal surface.

3. The design method for a negative Poisson's ratio porous structure based on a three-period minimum surface according to claim 2, characterized in that: The minimal surface function The Swartz P-minimum surface is shown in the following equation: (1.2).

4. The design method for a negative Poisson's ratio porous structure based on a three-period minimal surface according to claim 2, characterized in that: Functions that control form As shown in the following formula: (1.3).

5. The design method for a negative Poisson's ratio porous structure based on a three-period minimal surface according to claim 1, characterized in that: In step (2), the specific operation process of materializing the extended minimal surface function is as follows: for a given extended three-period minimal surface equation, the three-dimensional vector The range of values ​​for is the set. : (1.4) In the set Given a closed constrained surface The solidified extended three-period minimal surface structure for: (1.5).

6. The design method for a negative Poisson's ratio porous structure based on a three-period minimal surface according to claim 5, characterized in that: The given closed constraint surface For a radius of The height is The cylindrical surface is shown in the following formula: (1.6).

7. The design method for a negative Poisson's ratio porous structure based on a three-period minimal surface according to claim 1, characterized in that: The simplified problem model in step (4) is expressed as follows: (1.8).

Images