A design method for negative Poisson's ratio structures by simulating three-dimensional buckling modal deformation

Abstract

The present invention discloses a design method for a three-dimensional negative Poisson's ratio structure that simulates three-dimensional buckling modal deformation, comprising: (1) establishing a structural unit formed by orthogonal splicing of multiple lattice elements, arraying and splicing the structural units to form a representative volume unit, and determining the control points and their original coordinates of the representative volume unit; (2) obtaining the three-dimensional buckling deformation mode of the representative volume unit and the deformation coordinates of the control points through analysis; (3) determining the three-dimensional buckling deformation control equation based on the original coordinates and deformation coordinates of the control points; (4) inputting the rotation parameters, lattice element parameters, and array number of the three-dimensional buckling modal deformation, and determining the control point coordinates of the representative volume unit based on the three-dimensional buckling deformation control equation and the rotation parameters; (5) generating a representative volume unit based on the control point coordinates and lattice element parameters of the representative volume unit, and arranging them according to the array number to obtain a three-dimensional negative Poisson's ratio structure, wherein the three-dimensional negative Poisson's ratio structure has a strong structural strength.

Description

Technical Field

[0001] The invention belongs to the field of design and manufacture of porous lattice structures, and in particular relates to a design method of a three-dimensional negative Poisson's ratio structure that simulates three-dimensional buckling modal deformation. Background Art

[0002] With the development of additive manufacturing, porous structures with complex structural features can be printed or manufactured. Negative Poisson's ratio structure is a metamaterial with special properties. When ordinary materials are stretched longitudinally, they shrink laterally; while negative Poisson's ratio structure will expand laterally when stretched longitudinally. Due to its special compression deformation characteristics, negative Poisson's ratio structure is widely used in medical implants, high-sensitivity sensor design and protective devices.

[0003] There are very few negative Poisson's ratio structures in nature, which are generally artificially designed. Most of the designed negative Poisson's ratio structures are porous lattice structures. Among the negative Poisson's ratio structures that have been reported, most are two-dimensional negative Poisson's ratio structures, and there are also some three-dimensional negative Poisson's ratio structures.

[0004] Patent document with application number CN201911308237.5 discloses a combination method of a negative Poisson's ratio structure with three-dimensional characteristics. Any two two-dimensional negative Poisson's ratio structure basic units are overlapped, and the four ring nodes and five ribs are required to be placed in coincidence; one of the two-dimensional negative Poisson's ratio structure basic units is linearly rotated 90° relative to the other two-dimensional negative Poisson's ratio structure basic unit to form an orthogonal three-dimensional basic unit, that is, two two-dimensional chiral negative Poisson's ratio structures are placed orthogonally, and then further repeated on the basis of the three-dimensional basic unit through spatial expansion to form a three-dimensional negative Poisson's ratio structure.

[0005] Patent document with application number CN201810026856.4 discloses an adjustable three-dimensional backhanded negative Poisson's ratio structure and a preparation method thereof. Through the effective combination of rectangular rods and cubic blocks, a three-dimensional negative Poisson's ratio structure can be designed using a two-dimensional negative Poisson's ratio structure.

[0006] There are some areas for improvement in the negative Poisson's ratio structure design methods of the above two patent documents: the structure needs to rely on commercial modeling software, and the design process is relatively cumbersome; the negative Poisson's ratio structure exhibits lower compressive strength during compression. Summary of the invention

[0007] In view of the above, the purpose of the present invention is to provide a three-dimensional negative Poisson's ratio structure design method that simulates three-dimensional buckling modal deformation. The design method can stably realize the design of three-dimensional negative Poisson's ratio structure under different parameter conditions, and the designed three-dimensional negative Poisson's ratio has good structural strength.

[0008] In order to achieve the above-mentioned invention object, the present invention provides the following technical solutions:

[0009] A design method for a three-dimensional negative Poisson's ratio structure simulating three-dimensional buckling modal deformation comprises the following steps:

[0010] Step 1, establishing a structural unit formed by orthogonally splicing a plurality of lattice elements, arraying and splicing the structural units to form a representative volume unit, and determining the control points of the representative volume unit and their original coordinates;

[0011] Step 2, performing three-dimensional buckling modal deformation analysis on the representative volume unit to obtain the three-dimensional buckling deformation mode and the deformation coordinates of the control points;

[0012] Step 3, determining the three-dimensional buckling deformation control equation of the representative volume unit according to the original coordinates and the deformed coordinates of the control points;

[0013] Step 4, inputting the rotation parameters, lattice element parameters and array number of the three-dimensional buckling modal deformation, and determining the control point coordinates of the representative volume unit of the three-dimensional negative Poisson's ratio structure to be designed according to the three-dimensional buckling deformation control equation and the input rotation parameters;

[0014] Step 5, generating representative volume units according to the control point coordinates and lattice element parameters of the representative volume units, arraying the generated representative volume units according to the array number, and obtaining a three-dimensional negative Poisson's ratio structure.

[0015] Preferably, the lattice elements include cylinders, frustums, prisms, pyramids, hexahedrons, etc.; the overall structure formed by six lattice elements orthogonally spliced ​​along six directions of X, Y, Z, -X, -Y, and -Z serves as a structural unit, and a representative volume unit is formed by arraying and splicing the structural units.

[0016] Preferably, in step 1, in the representative volume unit, the control points are divided into central control points, internal control points and external control points according to the splicing status of the control points of the lattice element, wherein the orthogonal splicing points of each structural unit are used as central control points, the splicing points between the structural units are used as internal control points, and the unspliced ​​points on the lattice element are used as external control points.

[0017] Preferably, in step 3, the three-dimensional buckling deformation control equation of the representative volume unit is determined by fitting the original coordinates and the deformed coordinates of the control points as follows:

[0018]

[0019] Where L is the height of the lattice element, s l and hThey are respectively half of the length of the two diagonals of the quadrilateral formed by the internal control points of the four adjacent structural units in the same plane parallel to the coordinate axis in the three-dimensional buckling deformation mode of the representative volume unit, and the quadrilateral is a rhombus;

[0020] According to the three-dimensional buckling deformation control equation, the rotation parameters of the three-dimensional buckling modal deformation are defined as

[0021] Preferably, step 4, according to the three-dimensional buckling deformation control equation and the input rotation parameters And the known L, solve for s l and h , then take the center position of the representative volume unit as the origin, then according to s l and h Determine the coordinates of the internal and external control points of the representative volume unit, and combine the side lengths of the cube formed by all the central control points to satisfy s l +s h , determine the coordinates of the central control point.

[0022] Preferably, step 4, according to the three-dimensional buckling deformation control equation and the input rotation parameters And the known L, solve for s l and h , then take the center position of the representative volume unit as the origin, then according to s l and h Determine the coordinates of the internal control points of the representative volume unit; the side length of the cube formed by combining all the central control points in the representative volume unit is s l +s h , determine the coordinates of the central control point; the length of the rectangle formed by combining the four adjacent external control points in the representative volume unit is 2 (s l +s h ), width (s l +s h ) to determine the coordinates of the external control points.

[0023] Preferably, the designed three-dimensional negative Poisson's ratio structure is used to make medical implants and protective devices.

[0024] Compared with the prior art, the present invention has the following beneficial effects:

[0025] The embodiment provides a design method for a three-dimensional negative Poisson's ratio structure that simulates three-dimensional buckling modal deformation. The three-dimensional buckling modal deformation analysis is performed on the constructed representative volume unit to obtain the deformation law of the representative volume unit, and a porous lattice structure with a three-dimensional negative Poisson's ratio property is designed based on the deformation law. The design method has a good degree of design freedom and can achieve negative Poisson's ratio structure design within a large parameter range. The structural strength, Poisson's ratio, and strain range can be flexibly controlled. The structural strength can be adjusted by changing the lattice element parameters; the strain range and Poisson's ratio can be adjusted by changing the rotation parameter a. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0027] Figure 1 It is a flow chart of a design method of a three-dimensional negative Poisson's ratio structure simulating three-dimensional buckling modal deformation provided by an embodiment;

[0028] Figure 2 is a schematic diagram of control points of a representative volume unit provided in an embodiment;

[0029] Figure 3 It is an orthogonal frustum array and its simulated three-dimensional buckling modal deformation analysis diagram provided by the embodiment;

[0030] Figure 4 is a morphological diagram of three-dimensional buckling negative Poisson's ratio deformation of a representative volume unit provided by an embodiment;

[0031] Figure 5 is a morphological diagram of 3D buckling mixed deformation of a representative volume unit provided by an embodiment;

[0032] Figure 6 The three-dimensional negative Poisson's ratio structure is formed by a representative volume unit with a simulated three-dimensional buckling mode and an array thereof provided in an embodiment;

[0033] Figure 7 The embodiment provides a three-dimensional negative Poisson's ratio structure with a 3D buckling mixed deformation mode;

[0034] Figure 8 is a comparison diagram before and after compression of a three-dimensional negative Poisson's ratio structure entity having a simulated three-dimensional buckling mode provided in an embodiment;

[0035] Fig. 9It is the Poisson's ratio measurement result of the three-dimensional negative Poisson's ratio structure with simulated three-dimensional buckling mode provided by the embodiment.

[0036] Fig.10 is a comparison diagram before and after compression of a three-dimensional negative Poisson's ratio structure entity with a 3D buckling mixed deformation mode provided in an embodiment;

[0037] Fig.11 It is the Poisson's ratio measurement result of the three-dimensional negative Poisson's ratio structure with 3D buckling mixed deformation mode provided by the embodiment. DETAILED DESCRIPTION

[0038] To make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific implementation methods described herein are only used to explain the present invention and do not limit the scope of protection of the present invention.

[0039] In order to design a three-dimensional negative Poisson's ratio structure with high structural strength, an embodiment provides a design method for a three-dimensional negative Poisson's ratio structure that simulates three-dimensional buckling modal deformation. The three-dimensional negative Poisson's ratio structure designed by this design method has high structural strength and can be used to make medical implants, such as tracheal stents, heart stents, etc., and can also be used as protective devices, such as helmets, etc.

[0040] Figure 1 1 is a flow chart of a design method for a three-dimensional negative Poisson's ratio structure that simulates three-dimensional buckling modal deformation provided by an embodiment. Figure 1 As shown, the design method of the three-dimensional negative Poisson's ratio structure provided in the embodiment comprises the following steps:

[0041] Step 1, establish a structural unit formed by orthogonally splicing multiple lattice elements, array and splice the structural units to form a representative volume unit, and determine the control points of the representative volume unit and their original coordinates.

[0042] The structural unit formed by orthogonal splicing of multiple lattice elements passes through a porous structure with an array topology, and buckles and deforms during compression. Under specific porous structure parameters, a three-dimensional negative Poisson's ratio deformation result occurs. Based on this, the embodiment studies the deformation law of the three-dimensional negative Poisson's ratio deformation process of such porous structures, and constructs a three-dimensional negative Poisson's ratio structure using the deformation law of the three-dimensional negative Poisson's ratio deformation.

[0043] In the embodiment, the lattice element is a simple basic structure, which may be a lattice element including a cylinder, a truncated cone, a cone, a prism, a prism, a pyramid, a hexahedron, etc. When constructing a structural unit, the overall structure formed by orthogonally splicing six lattice elements along the six directions of X, Y, Z, -X, -Y, and -Z is used as a structural unit, and a representative volume unit is formed by arraying and splicing the structural units.

[0044] In the embodiment, taking the truncated cone as a lattice element as an example, the construction process of the structural unit is described in detail. The origin is defined as A(0,0,0), and the endpoints along the 6 directions of the coordinate axis are P1(L / 2,0,0), P2(-L / 2,0,0), P3(0,L / 2,0), P4(0,-L / 2,0), P5(0,0,L / 2), P6(0,0,-L / 2), L / 2 is the height of the truncated cone, and truncated cones AP1, AP2, AP3, AP4, AP5, AP6 are created according to the origin and endpoints and the upper and lower radii of the truncated cone. These six truncated cones are orthogonally spliced ​​at the origin to form an orthogonal truncated cone unit. The orthogonal truncated cone unit is used as the basic lattice unit, and the basic lattice unit is arrayed 2×2×2 to form an orthogonal truncated cone volume unit, which is the representative volume unit defined in the embodiment.

[0045] In an embodiment, the first and last points of the lattice element in the length direction are extracted as control points. For example, the center points of the upper and lower planes of the truncated cone are extracted as control points, and the center points of the upper and lower circular planes of the cylinder are extracted as control points. It has been found through research that different control points have different changing rules during three-dimensional negative Poisson's ratio deformation, and it is necessary to classify the control points. Through law summary, it is found that when the number of truncated cones connecting the control points is different, the changing rules are also different. Based on this, in a representative structural unit, according to the state in which the control points of the lattice element are spliced, which can also be understood as the number of truncated cones connecting the control points, the control points are divided into central control points, internal control points and external control points, wherein the orthogonal splicing points of each structural unit are used as central control points, the splicing points between the structural units are used as internal control points, and the unspliced ​​points on the lattice element are used as external control points.

[0046] like Figure 2 As shown in the figure, taking the orthogonal frustum volume unit as an example, the above control point types are explained. The orthogonal splicing point of each orthogonal frustum unit connects 6 frustums, which can be understood as 6 frustums passing through the orthogonal splicing point, and the orthogonal splicing point is the central control point; the splicing point between orthogonal frustum units connects two orthogonal frustum units, which can be understood as 2 orthogonal frustum units passing through the splicing point, and the splicing point is the internal control point; the point on each frustum that does not participate in the splicing can be understood as only 1 frustum passing through the point, and the point is the external control point. Therefore, in the case of Figure 3 In the orthogonal frustum volume unit shown, there are a total of 12 internal control points, 24 external control points, and 8 center control points.

[0047] Step 2: Perform three-dimensional buckling modal deformation analysis on the representative volume unit to obtain the three-dimensional buckling deformation mode and the deformation coordinates of the control points.

[0048] In the embodiment, finite element analysis software is used to perform structural finite element analysis. The finite element analysis software Abaqus can analyze complex solid mechanics and structural mechanics systems, and is particularly capable of handling very large and complex problems and simulating highly nonlinear problems. Therefore, the finite element software Abaqus is used to perform a three-dimensional buckling modal deformation analysis on a representative volume unit. During the analysis, the constructed representative volume unit is imported into the finite element analysis software Abaqus and meshed, and then a longitudinal compression test of the structure is performed, and the buckling analysis module in the finite element analysis software Abaqus is selected to perform a buckling modal analysis, and the buckling modal results of the three-dimensional negative Poisson's ratio deformation are selected from the buckling modal analysis results, such as Figure 3 As shown, the deformation coordinates of each control point can also be obtained.

[0049] Step 3: Determine the three-dimensional buckling deformation control equation of the representative volume unit based on the original coordinates and deformed coordinates of the control points.

[0050] In the embodiment, the three-dimensional buckling deformation control equation of the representative volume unit is determined by fitting the original coordinates and the deformed coordinates of the control points as follows: Where L / 2 is the height of the lattice element. l and h are respectively half the length of the two diagonals of the quadrilateral formed by the internal control points of the four adjacent structural units in the same plane parallel to the coordinate axis in the three-dimensional buckling deformation mode of the representative volume unit; according to the three-dimensional buckling deformation control equation, the rotation parameter of the three-dimensional buckling modal deformation is defined The rotation parameter a indicates the degree of deformation of the designed three-dimensional negative Poisson's ratio structure relative to the original structure, 0≤|a|<1. When |a| is close to 0, the degree of structural deformation is small, and when |a| is close to 1, the degree of structural deformation is large.

[0051] The construction process of the three-dimensional buckling deformation control equation includes: before the orthogonal frustum volume unit is compressed and deformed, a tangent plane Plane1 parallel to the coordinate axis plane is found. There are 4 internal control points, 4 central control points and 12 external control points in the tangent plane Plane1, such as Figure 3 As shown, the four internal control points can form a plane square abcd, and the side length of the square is After the orthogonal frustum volume element is compressed to produce a three-dimensional negative Poisson's ratio deformation mode, such as Figure 4 As shown, these four internal control points will form a tetrahedron abcd in space. After the four internal control points are projected onto the current tangent plane Plane1, the four internal control points projected onto the plane will form a planar rhombus. abcd , plane rhombus abcd The lengths of the two diagonals are 2S respectively. l and 2Sh ; In addition, the side length L of the orthogonal truncated cone unit, that is, the height of the truncated cone is L / 2. In the three-dimensional negative Poisson's ratio deformation process, the internal parameters of the projected plane rhombus satisfy the control equation:

[0052]

[0053] In the representative volume unit, all internal control points satisfy the above control equations during the deformation process. In addition, it is found that after the new volume unit array is formed, since the new volume units are connected through external control points, all external control points representing the new volume unit will be converted into internal control points in the array, and the position change law during the deformation process also satisfies the above control equations.

[0054] The study also found that the position change of the central control point satisfies different change rules. The specific change rules are as follows: in the original representative volume unit, the eight central control points together form a cube. During the three-dimensional negative Poisson's ratio deformation process, the eight central control points can always form a cube, and their side lengths decrease during the deformation process. Based on this transformation law, a tangent plane Plane1 parallel to the coordinate axis plane is made through one of the central control points. In this tangent plane Plane1, the four central control points form a plane square. During the three-dimensional negative Poisson's ratio deformation process, these four central control points are still roughly in the same plane, and they can form a plane square with a side length of s. l +s h ,like Figure 4 shown.

[0055] The study also found that after the representative volume unit is deformed by the simulated 3D buckling mode, the central control point and the internal control point are determined by the above method. The external control point of the representative volume unit after deformation is determined by the control method of the original representative volume unit. This hybrid design method that combines the simulated 3D buckling mode deformation and the original state is named 3D buckling hybrid deformation design. Figure 5 As shown in the figure, there are 24 external control points in the representative volume unit. In the same vertical plane, there are 8 external control points, which can form two planar rectangles respectively. All the planar rectangles formed are equivalent. Specifically, in a planar rectangle dgef formed by 4 external control points, the length of the rectangle is 2(s l +s h ), width (s l +s h ).

[0056] Step 4, input the rotation parameters, lattice element parameters and array number of the three-dimensional buckling modal deformation, and determine the control point coordinates of the representative volume unit of the three-dimensional negative Poisson's ratio structure to be designed based on the three-dimensional buckling deformation control equation and the input rotation parameters.

[0057] In this embodiment, the rotation parameters of the three-dimensional buckling modal deformation are input That is, the value of the rotation parameter a is given. The lattice element parameter is determined according to the lattice element type. The lattice element parameter determines the shape and size of the lattice element. For example, when the lattice element is a truncated cone, the lattice element parameter is two circular radii R and r. The array number n refers to the number of arrays in a single direction, which determines the size of the three-dimensional negative Poisson's ratio structure and is set according to actual conditions.

[0058] In one embodiment, a separate design based on simulated three-dimensional buckling modal deformation is adopted. When a and L are known, according to the three-dimensional buckling deformation control equation and Solve to get sl and sh. When the center of the representative volume unit is chosen as the origin, according to s l and h Determine the coordinates of the internal control points of the representative volume unit, which are: IP 1 (0, s l ,s h ), IP 2 (-s l ,s h ,0),IP 3 (-s h ,0,s l ), IP 4 (0, -s l ,s h ), IP 5 (-s l , -s h ,0),IP 6 (-s h ,0,-s l ), IP 7 (0, s l , -s h ), IP 8 (s l 、s h ,0),IP 9 (s h ,0,s l ), IP 10 (0, -s l , -s h ), IP 11 (s l , -s h ,0),IP 12(s h ,0,-s l ). Since the external control points of the representative volume unit will be converted into internal control points during the array process, according to this rule, we can also use s l and h Determine the coordinates of the external control points of the representative volume unit. When determining the coordinates of the central control point, the side length of the cube formed by combining all the central control points satisfies s l +s h , determine the coordinates of the central control point, which are:

[0059] In another embodiment, based on the deformation law of the three-dimensional negative Poisson's ratio structure of three-dimensional buckling, a hybrid design based on the original state of the simulated three-dimensional buckling modal deformation and the representative volume unit is adopted to improve the compressive strength of the structure and can be seamlessly transitioned during the array process. When a and L are known, according to the three-dimensional buckling deformation control equation and Solve to get s l and h When the center of the representative volume unit is selected as the origin, according to s l and h Determine the coordinates of the internal control points of the representative volume unit. The specific coordinates of the internal control points can refer to the coordinates of the internal control points determined in the individual design based on the simulated three-dimensional buckling modal deformation. When determining the coordinates of the central control points, the side length of the cube formed by combining all the central control points satisfies s l +s h , determine the coordinates of the central control point. The specific coordinates of the central control point can refer to the coordinates of the central control point determined during the individual design based on the simulated three-dimensional buckling modal deformation.

[0060] When determining the external point control coordinates, the length and width of the rectangle formed by the four external control points in the same plane satisfy 2(s l +s h ) and (s l +s h ), determine the external point control coordinates, specifically:

[0061]

[0062] Step 5, generating representative volume units according to the control point coordinates and lattice element parameters of the representative volume units, arraying the generated representative volume units according to the array number, and obtaining a three-dimensional negative Poisson's ratio structure.

[0063] Through research, it is found that the orthogonal truncated cone structure has relatively obvious structural advantages and structural characteristics, including: on the one hand, for the design of three-dimensional negative Poisson's ratio structure, the orthogonal truncated cone structure conforms to the characteristics of large central volume proportion and small edge volume proportion in form. Under appropriate parameters, the three-dimensional negative Poisson's ratio property can be achieved during the compression process, that is, the orthogonal truncated cone structure is easier to achieve three-dimensional negative Poisson's ratio design compared with other structures; on the other hand, the orthogonal truncated cone structure has good structural specific strength and good mechanical properties. Therefore, the lattice element of the embodiment is preferably a truncated cone, and a representative orthogonal truncated cone volume unit is constructed.

[0064] According to the embodiment, after determining the control point coordinates of the representative volume unit, the representative volume unit can be generated by combining the cone parameters R and r. In order to prevent gaps in the representative volume unit at the connection, that is, the internal control point, a sphere with a radius of R is created at the center control point, and a sphere with a radius of r is created at the internal control point.

[0065] When generating representative volume units, you can choose to develop a grid algorithm for basic units based on openvdb. This grid algorithm can realize basic grid modeling of basic units such as spherical and cylindrical structures, generate parameterized representative volume units, and stably perform Boolean operations on basic units to generate grid representative volume units. The representative volume units are arrayed according to the number of arrays to obtain a three-dimensional negative Poisson's ratio structure. The designed three-dimensional negative Poisson's ratio structure is printed by a photocuring printer, and the printing material is a flexible resin, that is, a three-dimensional negative Poisson's ratio structure entity can be obtained.

[0066] Experimental Example 1

[0067] Experimental Example 1 adopts a separate design method based on the simulated three-dimensional buckling modal deformation, with a truncated cone as the lattice element, the height of the truncated cone is set to 5 mm, and the deformation rotation parameter a = 0.17. Under these two parameters, s is determined by solving l and h , and then determine the control point coordinates of the representative orthogonal frustum volume unit, and install the topological relationship in the form of a frustum to connect different endpoints. The radius ratio of the bottom surface to the top surface of the frustum is R / r = 3.25. In addition, the bottom radius of the frustum is R = 1.3mm. The generated orthogonal frustum volume unit is as follows Figure 6 As shown, according to array n=3, the orthogonal frustum volume units are arrayed in 3×3×3 directions along the X, Y, and Z directions respectively, and the obtained orthogonal frustum array structure is a three-dimensional negative Poisson's ratio structure.

[0068] The three-dimensional negative Poisson's ratio structure was output to STL format through the program and transferred to the DLP printer. Flexible resin was used as the printing material and printed through the light-curing printer. After printing, the structure was subjected to compression simulation and experiment on the finite element software and compression testing machine. The compression test process is shown in Figure 8 .

[0069] During the compression process, a camera is used to collect structural deformation images at different strains, and the Poisson's ratio values ​​in different directions in the structure are measured using the images. The experimental values ​​are compared and verified with the Poisson's ratio values ​​obtained by finite element simulation. Fig. 9 , where FEA represents the finite element analysis value, EXP represents the experimental value, and ν xx Represents the value of the Poisson's ratio of the structure along the X-axis, ν yy Indicates the Poisson's ratio of the structure along the Y-axis.

[0070] from Fig. 9 It can be seen that during the compression process, the Poisson's ratio of the structure is below 0, showing a negative Poisson's ratio property. The negative Poisson's ratio is stable between -0.3 and -0.4, proving that it can show good negative Poisson's ratio properties in a larger strain range;

[0071] Experimental Example 2

[0072] Experimental Example 2 adopts a hybrid design based on the original state of simulated three-dimensional buckling modal deformation and representative volume unit. The truncated cone is used as the lattice element, the height of the truncated cone is set to 5 mm, and the deformation rotation parameter a = 0.17. Under these two parameters, s l and h , and then determine the control point coordinates of the representative orthogonal frustum volume unit, and install the topological relationship in the form of a frustum to connect different endpoints. The radius ratio of the bottom surface to the top surface of the frustum is R / r = 3.25. In addition, the bottom radius of the frustum is R = 1.3mm. The generated orthogonal frustum volume unit is then arrayed 3×3×3 along the three directions of X, Y, and Z according to the array n = 3. The orthogonal frustum volume unit is arrayed in 3×3×3 arrays respectively. The obtained orthogonal frustum array structure is a three-dimensional negative Poisson's ratio structure, such as Figure 7 shown.

[0073] The three-dimensional negative Poisson's ratio structure was output to STL format through the program and transferred to the DLP printer. Flexible resin was used as the printing material and printed through the light-curing printer. After printing, the structure was subjected to compression simulation and experiment on the finite element software and compression testing machine. The compression test process is shown in Fig.10 .

[0074] During the compression process, a camera is used to collect structural deformation images at different strains, and the Poisson's ratio values ​​in different directions in the structure are measured using the images. The experimental values ​​are compared and verified with the Poisson's ratio values ​​obtained by finite element simulation. Fig.11 , where FEA represents the finite element analysis value, EXP represents the experimental value, and ν xx Represents the value of the Poisson's ratio of the structure along the X-axis, ν yy Indicates the Poisson's ratio of the structure along the Y-axis.

[0075] from Fig.11 It can be seen that during the compression process, the Poisson's ratio of the structure is below 0, showing a negative Poisson's ratio property. Fig.11 The structure in the compression process can also stabilize the Poisson's ratio at around -0.35, and it has better strength performance.

[0076] The design method of the three-dimensional negative Poisson's ratio structure with three-dimensional buckling modal deformation provided by the above embodiment can stably and effectively design a porous lattice structure with three-dimensional negative Poisson's ratio properties. The design method has a good degree of design freedom and can realize the design of negative Poisson's ratio structure within a large parameter range. The structural strength, Poisson's ratio and strain range can be flexibly controlled. The structural strength can be adjusted by changing the bottom radius of the orthogonal truncated cone structure; the strain range and Poisson's ratio can be adjusted by changing the rotation parameter a.

[0077] The specific implementation methods described above provide a detailed description of the technical solutions and beneficial effects of the present invention. It should be understood that the above is only the most preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, supplements and equivalent substitutions made within the scope of the principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A design method for a three-dimensional negative Poisson's ratio structure simulating three-dimensional buckling modal deformation, characterized in that: The following steps are involved: Step 1, establishing a structural unit formed by orthogonally splicing a plurality of lattice elements, arraying and splicing the structural units to form a representative volume unit, and determining the control points of the representative volume unit and their original coordinates; Step 2, perform three-dimensional buckling modal deformation analysis on the representative volume unit to obtain the three-dimensional buckling deformation mode and the deformation coordinates of the control point; Step 3, determining the three-dimensional buckling deformation control equation of the representative volume unit according to the original coordinates and the deformed coordinates of the control points; Step 4, inputting the rotation parameters, lattice element parameters and array number of the three-dimensional buckling modal deformation, and determining the control point coordinates of the representative volume unit of the three-dimensional negative Poisson's ratio structure to be designed according to the three-dimensional buckling deformation control equation and the input rotation parameters; Step 5, generating representative volume units according to the control point coordinates and lattice element parameters of the representative volume units, arraying the generated representative volume units according to the array number, and obtaining a three-dimensional negative Poisson's ratio structure.

2. The design method of a three-dimensional negative Poisson's ratio structure simulating three-dimensional buckling modal deformation according to claim 1 is characterized in that: The lattice elements include cylinders, frustums, prisms, pyramids, and hexahedrons.

3. The design method of a three-dimensional negative Poisson's ratio structure simulating three-dimensional buckling modal deformation according to claim 1 is characterized in that: The overall structure formed by orthogonally splicing six lattice elements along the six directions of X, Y, Z, -X, -Y, and -Z is used as a structural unit, and a representative volume unit is formed by arraying and splicing the structural units.

4. The design method of a three-dimensional negative Poisson's ratio structure simulating three-dimensional buckling modal deformation according to claim 1 is characterized in that: In step 1, in the representative volume unit, the control points are divided into central control points, internal control points and external control points according to the splicing status of the control points of the lattice element, wherein the orthogonal splicing points of each structural unit are used as central control points, the splicing points between the structural units are used as internal control points, and the unspliced ​​points on the lattice element are used as external control points.

5. The design method of a three-dimensional negative Poisson's ratio structure simulating three-dimensional buckling modal deformation according to claim 4, characterized in that: In step 3, the three-dimensional buckling deformation control equation of the representative volume unit is determined by fitting the original coordinates and deformed coordinates of the control points as follows: Where L is the height of the lattice element, s l and h They are respectively half of the length of the two diagonals of the quadrilateral formed by the internal control points of the four adjacent structural units in the same plane parallel to the coordinate axis in the three-dimensional buckling deformation mode of the representative volume unit, and the quadrilateral is a rhombus; According to the three-dimensional buckling deformation control equation, the rotation parameters of the three-dimensional buckling modal deformation are defined as 6. The design method of a three-dimensional negative Poisson's ratio structure simulating three-dimensional buckling modal deformation according to claim 5, characterized in that: Step 4: Based on the three-dimensional buckling deformation control equation and the input rotation parameters And the known L, solve for s l and h , then take the center position of the representative volume unit as the origin, then according to s l and h Determine the coordinates of the internal and external control points of the representative volume unit, and combine the side lengths of the cube formed by all the central control points to satisfy s l +s h , determine the coordinates of the central control point.

7. The design method of a three-dimensional negative Poisson's ratio structure simulating three-dimensional buckling modal deformation according to claim 5, characterized in that: Step 4: Based on the three-dimensional buckling deformation control equation and the input rotation parameters And the known L, solve for s l and h , then take the center position of the representative volume unit as the origin, then according to s l and h Determine the coordinates of the internal control points of the representative volume unit; the side length of the cube formed by combining all the central control points in the representative volume unit is s l +s h , determine the coordinates of the central control point; the length of the rectangle formed by combining the four adjacent external control points in the representative volume unit is 2 (s l +s h ), width (s l +s h ) to determine the coordinates of the external control points.

8. The design method of a three-dimensional negative Poisson's ratio structure simulating three-dimensional buckling modal deformation according to any one of claims 1 to 7, characterized in that: The designed three-dimensional negative Poisson's ratio structure is used to make medical implants and protective devices.

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