Three-dimensional structure with adjustable Poisson's ratio and coefficient of thermal expansion and its design method

Abstract

The present invention discloses a three-dimensional structure with adjustable Poisson's ratio and coefficient of thermal expansion and its design method. The method includes first selecting different geometric parameters and material combinations of triangular units to design a triangular unit based on three materials, and then using two identical triangular units to form a parallelogram, and constructing a three-dimensional cell based on four identical parallelograms; then arranging the three-dimensional cells periodically along the direction of the horizontal straight rod and mirroring repeatedly along the other two directions to finally obtain a three-dimensional truss structure; then performing mechanical analysis on a three-dimensional cell of the three-dimensional truss structure, and obtaining the equivalent formulas of the elastic parameters and coefficient of thermal expansion of the three-dimensional truss structure through the displacement method and the unit load method, and calculating the corresponding Poisson's ratio and coefficient of thermal expansion based on the equivalent formulas. By selecting reasonable geometric parameters and material combinations, the present invention can achieve a wide range of regulation of the Poisson's ratio and coefficient of thermal expansion of three-dimensional mechanical metamaterials.

Description

Technical Field

[0001] The present invention relates to the technical field of three-dimensional structures, and particularly relates to a three-dimensional structure with adjustable Poisson's ratio and coefficient of thermal expansion and a design method thereof. Background Art

[0002] Negative Poisson's ratio materials expand laterally when stretched and contract laterally when compressed. Due to their unique properties, they have advantages that cannot be compared with other materials in many aspects. Moreover, there is great room for improvement in the physical and mechanical properties such as shear modulus, indentation resistance, and fracture resistance of negative Poisson's ratio materials.

[0003] Negative thermal expansion materials refer to a class of materials that expand anomalously with temperature changes within a certain temperature range and have characteristics opposite to those of general materials with thermal expansion and contraction. By doping and compounding materials with anisotropic expansion coefficients, materials with controllable thermal expansion coefficients or expansion coefficients close to 0 are prepared.

[0004] Similar to negative Poisson's ratio, the coefficient of thermal expansion of negative thermal expansion materials is negative within a certain temperature range. Since natural negative thermal expansion materials are very scarce and their mechanical properties often cannot meet the engineering requirements, scholars have tried to prepare negative thermal expansion materials from two or more positive expansion materials, mainly lightweight materials. Lightweight negative thermal expansion materials can be divided into two categories according to the characteristics of thermal expansion deformation of their microstructures: bending-dominated type and tension-dominated type. The bending-dominated structure relies on the bending deformation of the rods to achieve thermal expansion regulation. The tension-dominated structure has better mechanical properties than the bending-dominated structure because each rod undergoes axial tension and compression deformation.

[0005] Although scholars have done a lot of research on negative Poisson's ratio materials and negative thermal expansion materials, so far, the vast majority of existing materials can only achieve one of negative Poisson's ratio and negative thermal expansion. Only a few scholars have designed materials that can achieve both negative Poisson's ratio and negative thermal expansion. For example, Joseph et al. designed a triangular structure with negative Poisson's ratio and negative thermal expansion. Ai and Gao et al. designed a structure with negative Poisson's ratio and non-positive thermal expansion. Ha et al. designed a structure with controllable thermal expansion and Poisson's ratio close to -1. Fang et al. designed a cellular structure that couples negative thermal expansion and negative Poisson's ratio. However, structures with adjustable Poisson's ratio and coefficient of thermal expansion have not been developed yet. Summary of the Invention

[0006] The first object of the present invention is to overcome the deficiencies of the prior art and provide a design method for a three-dimensional structure with adjustable Poisson's ratio and coefficient of thermal expansion. This method can achieve a wide range of regulation of the Poisson's ratio and coefficient of thermal expansion of three-dimensional mechanical metamaterials by selecting reasonable geometric parameters and material combinations.

[0007] The second object of the present invention is to provide a three-dimensional structure with adjustable Poisson's ratio and coefficient of thermal expansion.

[0008] The third object of the present invention is to provide a computing device.

[0009] The first object of the present invention is achieved by the following technical solutions: A design method for a three-dimensional structure with adjustable Poisson's ratio and coefficient of thermal expansion, comprising the following steps:

[0010] S1. Design a triangular unit, where the longest rod and two diagonal rods of the triangular unit have corresponding rod lengths and are respectively composed of three materials;

[0011] S2. Use two identical triangular units to form a parallelogram, and then construct a three-dimensional cell based on four identical parallelograms;

[0012] S3. Take the direction of one side of the parallelogram at the bottom of the three-dimensional cell as the left-right direction, arrange the three-dimensional cells periodically along this direction, and repeatedly mirror along the front-back direction and up-down direction perpendicular to this direction to finally obtain a three-dimensional truss structure;

[0013] S4. Conduct a mechanical analysis on a three-dimensional cell of the three-dimensional truss structure, and obtain the equivalent formulas of the elastic parameters and coefficient of thermal expansion of the three-dimensional truss structure through the displacement method and the unit load method;

[0014] S5. When designing a three-dimensional structure, select the geometric parameters and material combinations of the triangular unit, construct a three-dimensional structure with corresponding Poisson's ratio and coefficient of thermal expansion according to steps S1 to S3, and calculate the corresponding Poisson's ratio and coefficient of thermal expansion based on the equivalent formulas of the elastic parameters and coefficient of thermal expansion in step S4.

[0015] Preferably, the process of step S4 is specifically as follows:

[0016] Cut out a three-dimensional cell from the three-dimensional truss structure, take the centroid of this three-dimensional cell as the origin O, define the direction of one of the diagonal rods of a triangular unit at the bottom of the three-dimensional cell as the z-axis, establish a Cartesian coordinate system, the y-axis of the Cartesian coordinate system is perpendicular to the z-axis on the horizontal plane, and the x-axis of the Cartesian coordinate system is perpendicular to the z-axis on the vertical plane;

[0017] Apply displacements to the upper and lower surfaces of the three-dimensional cell in the x-axis direction, calculate the displacements generated by the three-dimensional cell in the x, y, and z axis directions, and obtain the equivalent Poisson's ratio and equivalent Young's modulus of the three-dimensional cell based on the displacements;

[0018] Displacements are applied to the front and rear surfaces of the three-dimensional cell in the y-axis direction, and the displacements generated by the three-dimensional cell in the x, y, and z axis directions are calculated. Based on the displacements, the equivalent Poisson's ratio and equivalent Young's modulus of the three-dimensional cell are obtained. According to the deformation symmetry relationship of the cell, the equivalent parameters in the x-axis direction and y-axis direction are the same;

[0019] Displacements are applied to the left and right endpoints of the diagonal bar of the three-dimensional cell in the z-axis direction, and the displacements generated by the three-dimensional cell in the x, y, and z axis directions are calculated. Based on the displacements, the equivalent Poisson's ratio and equivalent Young's modulus of the three-dimensional cell are obtained;

[0020] Under the condition of temperature change, a unit load is applied to the three-dimensional cell, and the displacements generated by the three-dimensional cell in the x, y, and z axis directions are calculated. Based on the displacements and temperature, the equivalent thermal expansion coefficient of the three-dimensional cell is obtained.

[0021] Furthermore, after displacements are respectively applied to the upper and lower surfaces of the cell in the x direction, the front and rear surfaces in the y direction, and the left and right endpoints in the z direction, the equivalent Young's modulus of the cell is:

[0022]

[0023] Among them, E z is the equivalent Young's modulus of the cell in the z direction; E x is the equivalent Young's modulus of the cell in the x direction; E y is the equivalent Young's modulus of the cell in the y direction; Taking the diagonal bar as the z axis as the first diagonal bar and the other diagonal bar of the triangular element as the second diagonal bar, N2 is the axial force of the second diagonal bar; N3 is the axial force of the longest bar; is the included angle between the two diagonal bars; θ is the included angle between the longest bar and the first diagonal bar; u is the distance that the parallelogram at the bottom of the cell moves along the positive x-axis direction; L1 is the length of the first diagonal bar; E1 is the Young's modulus of the first diagonal bar; A1 is four times the cross-sectional area of the first diagonal bar.

[0024] Furthermore, after displacements are simultaneously applied to the upper and lower surfaces of the cell in the x direction, the equivalent formula for Poisson's ratio is obtained as:

[0025]

[0026] Among them, ν xy is the equivalent Poisson's ratio of the cell in the x and y axis directions; ν xz is the equivalent Poisson's ratio of the cell in the x and z axis directions; u is the distance that the parallelogram at the bottom of the cell moves along the positive x-axis direction; is the included angle between the two diagonal bars; θ is the included angle between the longest bar and the first diagonal bar; v is the distance that the parallelogram connecting the upper and lower surfaces moves along the positive y-axis direction; w Bis the distance that the endpoints of the two diagonal bars are simultaneously connected and move in the negative z-axis direction in the parallelogram connecting the upper and lower surfaces; w A is the distance that the endpoints of the longest bar and the second diagonal bar are simultaneously connected and move in the positive z-axis direction in the parallelogram connecting the upper and lower surfaces.

[0027] Furthermore, after simultaneously pulling the unit cell at the left and right endpoints in the z direction, the equivalent formula for Poisson's ratio is obtained as:

[0028]

[0029] ν zx is the equivalent Poisson's ratio of the unit cell in the z and x axis directions; is the included angle between the two diagonal bars; θ is the included angle between the longest bar and the first diagonal bar.

[0030] Furthermore, the equivalent thermal expansion coefficients α x 、α y 、α z of the three-dimensional unit cell in the x, y, and z axis directions are:

[0031]

[0032] wherein, t is the change in temperature; L3 is the length of the longest bar; δ AV is the displacement caused by the temperature change at the endpoint bearing the load; α1 is the thermal expansion coefficient of the first diagonal bar; α2 is the thermal expansion coefficient of the second diagonal bar; α3 is the thermal expansion coefficient of the longest bar; is the included angle between the two diagonal bars; θ is the included angle between the longest bar and the first diagonal bar.

[0033] Furthermore, when θ = 90°, or when 0 < θ < 17°, the Poisson's ratio of the constructed three-dimensional structure is 0.

[0034] Furthermore, when or the thermal expansion coefficients of the constructed three-dimensional structure in the x and y axis directions are 0.

[0035] The second object of the present invention is achieved by the following technical solution: A three-dimensional structure with adjustable Poisson's ratio and thermal expansion coefficient, which is constructed by the design method of the three-dimensional structure with adjustable Poisson's ratio and thermal expansion coefficient described in the first object of the present invention.

[0036] The third object of the present invention is achieved by the following technical solution: A computing device, including a processor and a memory for storing processor-executable programs. When the processor executes the programs stored in the memory, it realizes the design method of the three-dimensional structure with adjustable Poisson's ratio and thermal expansion coefficient described in the first object of the present invention.

[0037] The present invention has the following advantages and effects compared with the prior art:

[0038] (1) The present invention proposes a design method for a three-dimensional structure with adjustable Poisson's ratio and coefficient of thermal expansion. Based on the triangular element of three materials, a three-dimensional structure with adjustable negative Poisson's ratio and coefficient of thermal expansion is designed. For this structure, through reasonable geometric parameters and material combinations, three-dimensional negative Poisson's ratio and bidirectional negative thermal expansion can be achieved, and the adjustment ranges of the Poisson's ratio and coefficient of thermal expansion of the three-dimensional structure are large, and the adjustment method is also simple and convenient, which can provide a reference for the design of structures with both temperature sensitivity and mechanical sensitivity.

[0039] (2) For the three-dimensional structure with adjustable Poisson's ratio and coefficient of thermal expansion constructed by the present invention, the present invention gives the equivalent formulas of Young's modulus, Poisson's ratio and coefficient of thermal expansion, and also calculates the geometric parameter conditions and material combination conditions for achieving zero Poisson's ratio and zero thermal expansion, which is beneficial to the research of high-performance three-dimensional mechanical metamaterials. Brief Description of the Drawings

[0040] Figure 1 It is a schematic diagram for designing a three-dimensional truss structure based on triangular elements. Among them, (a) is a schematic diagram of a parallelogram formed by two triangular elements; (b) is a schematic diagram of a three-dimensional cell; (c) is a schematic diagram of a three-dimensional truss structure composed of four cells.

[0041] Figure 2 It is a schematic diagram of the basic calculation parameters of a three-dimensional cell.

[0042] Figure 3 It is a schematic diagram of the deformation of a three-dimensional cell under the application of displacement.

[0043] Figure 4 It is a schematic diagram of cutting the cell along the direction perpendicular to the x-axis.

[0044] Figure 5 It is a schematic diagram of cutting the cell along the direction perpendicular to the y-axis.

[0045] Figure 6 It is a schematic diagram of cutting the cell along the direction perpendicular to the z-axis.

[0046] Figure 7 It is a schematic diagram of cutting a quarter cell along the z-axis.

[0047] Figure 8 It is a schematic diagram of the basic calculation parameters of the triangular element when the cell realizes negative thermal expansion.

[0048] Figures 9 to 10 It is a schematic diagram of the unit load method for the triangular element when the cell realizes negative thermal expansion.

[0049] Figures 11 to 13 The Poisson's ratio v under the first set of parameters in Embodiment 1 of the present invention xy , v xz , v zx , Young's modulus E x , E z and coefficient of thermal expansion a x , a z Comparison graph of the numerical simulation verification results NR and the formula calculation results AR

[0050] Figures 14 to 16 The Poisson's ratio v under the first set of parameters in Embodiment 1 of the present invention xy , v xz , v zx , Young's modulus E x , E z and coefficient of thermal expansion a x , a z Comparison graph of the numerical simulation verification results NR and the formula calculation results AR

[0051] Figure 17 and Figure 18 are respectively when θ = 90°, Influence schematic diagrams of the structure Poisson's ratio v xy and elastic modulus E x , E y

[0052] Figure 19 and Figure 20 are respectively when θ's influence schematic diagrams of the structure Poisson's ratio v xy and elastic modulus E x , E y

[0053] Figure 21 Schematic diagram of achieving zero thermal expansion in the x-axis and y-axis directions Detailed implementation manners

[0054] The present invention will be further described in detail below in conjunction with embodiments and the accompanying drawings, but the implementation manners of the present invention are not limited thereto.

[0055] Embodiment 1

[0056] This embodiment discloses a design method for a three-dimensional structure with adjustable Poisson's ratio and coefficient of thermal expansion. Through this design method for the three-dimensional structure, various three-dimensional structures can be constructed, such as a three-dimensional zero Poisson's ratio structure, and a three-dimensional structure with zero coefficient of thermal expansion in the x-axis and y-axis directions. The design method includes the following steps:

[0057] ​​S1. Design a triangular unit. The longest rod and the two diagonal rods of the triangular unit have corresponding rod lengths and are made of three materials respectively.

[0058] S2. Use two identical triangular units to form a parallelogram, as shown in Figure (a) of Figure 1 . Then, construct a three-dimensional cell based on four identical parallelograms (AA'D'D, ABCD, BB'C'C, A'B'C'D'), as shown in Figure (b) of Figure 1 and Figure 2 .

[0059] As Figure 2 shown, the cell has three types of rods with different lengths. The first type is one of the diagonal rods AD, A'D', BC, and B'C' of the triangular unit, which is defined as the first diagonal rod with a length of L1 and a cross-sectional area of . The elastic modulus and coefficient of thermal expansion are E1 and α1 respectively. Define the included angle between the two diagonal rods as . For example, define the included angle between the longest rod and the first diagonal rod as θ, such as ∠ACB = θ. The second type is the other diagonal rods BB', B'A', A'A, AB, CD, CC', C'D', D'D of the triangular unit, which are defined as the second diagonal rods with a length of and a cross-sectional area of . The elastic modulus and coefficient of thermal expansion are E2 and α2 respectively. The third type of rod is the longest rod AC, AD', B'C, B'D' of the triangular unit, with a length of and a cross-sectional area of . The elastic modulus and coefficient of thermal expansion are E3 and α3 respectively.

[0060] S3. Take the direction of one side of the parallelogram at the bottom of the three-dimensional cell as the left-right direction, arrange the three-dimensional cells periodically along this direction, and repeatedly mirror along the front-back direction and up-down direction perpendicular to this direction. Finally, obtain a three-dimensional truss structure, such as Figure 1 the three-dimensional truss structure composed of four cells shown in Figure (c) of

[0061] S4. Conduct a mechanical analysis on a three-dimensional cell of the three-dimensional truss structure, and use the displacement method and unit load method to obtain the equivalent formulas for the elastic parameters and coefficient of thermal expansion of the three-dimensional truss structure:

[0062] (1) First, cut out a three-dimensional cell from the three-dimensional truss structure. Take the centroid of this three-dimensional cell as the origin O, define the direction of one of the diagonal rods of a triangular unit at the bottom of this three-dimensional cell as the z-axis, and establish a Cartesian coordinate system. The y-axis of the Cartesian coordinate system is perpendicular to the z-axis on the horizontal plane, and the x-axis of the Cartesian coordinate system is perpendicular to the z-axis on the vertical plane. AsFigure 2 and Figure 3 As shown, the x-axis direction is vertically upward, the y-axis direction points outward, and the z-axis direction is horizontally to the right.

[0063] (2-1) Apply displacements to the upper and lower surfaces of the three-dimensional cell in the x-axis direction. Refer to Figure 3 , calculate the displacements generated by the three-dimensional cell in the x, y, and z-axis directions, and based on the displacements, find the equivalent Poisson's ratio and equivalent Young's modulus of the three-dimensional cell.

[0064] (2-2) Apply displacements to the front and back surfaces of the three-dimensional cell in the y-axis direction. Refer to Figure 3 , calculate the displacements generated by the three-dimensional cell in the x, y, and z-axis directions, and based on the displacements, find the equivalent Poisson's ratio and equivalent Young's modulus of the three-dimensional cell; here, according to the deformation symmetry relationship of the cell, the equivalent parameters in the x-axis direction and the y-axis direction are the same.

[0065] Take the Figure 2 three-dimensional cell to illustrate step (2-2). Use u, v, and w to represent the displacements of points (A, B, C, D, A', B', C', D') along the x, y, and z-axis directions respectively. As Figure 3 shown, the parallelogram BB'C'C moves u in the positive x-axis direction, and the parallelogram AA'D'D moves u in the negative x-axis direction. According to the deformation characteristics of the cell, the parallelogram ABCD moves v in the positive y-axis direction, and the parallelogram A'B'C'D' moves v in the negative y-axis direction. The displacements w of each point along the z-axis direction have the following relationships:

[0066]

[0067] In the formula, w A , w B , w C , w D , w A ', w B ', w C ', w D ' are the displacements of points A, B, C, D, A', B', C', D' along the Z-axis respectively. Among the displacements of each point, assume that u is a known quantity, and w A , w B , w C , w D , w A ', w B ', w C ', w D ' and v are unknown quantities.

[0068] For a three-dimensional cell, a cell has 16 rods, 5 rods with different axial forces: N1 represents the axial force of rods AD, A'D', BC, B'C', N2 represents the axial force of rods AB, B'A', CD, C'D', N'2 represents the axial force of rods A'A, BB', CC', D'D, N3 represents the axial force of rods AC, B'D', and N'3 represents the axial force of rods AD' and B'C. The axial force expressions of these 5 rods are as follows:

[0069]

[0070] like Figure 4 As shown in Figure 2, the cell is cut along the direction perpendicular to the x-axis. Figure 5 As shown, the cell is cut along the direction perpendicular to the y-axis, where the stress σ in the y-direction y = 0. Figure 6 As shown, the cell is cut along the direction perpendicular to the z-axis, where the stress σ in the z-direction z = 0. Figure 7 As shown, a quarter of the cell is cut along the z direction, where the shear stress τ xz =0. y =0,σ z =0, τ xz =0 can be based on Figure 3 The force characteristics and equilibrium conditions of the entire cell are directly obtained.

[0071] In summary, we can get the following equations:

[0072]

[0073] Combining the above equations (3) and the expressions (2) for the axial forces of each rod, we can decouple w A 、w B 、v.

[0074] Therefore, the strain ε x , ε y , ε z It can be expressed as:

[0075]

[0076] Therefore, we can get:

[0077] When displacement is applied to the upper and lower surfaces of the cell in the x direction at the same time, the equivalent formula of Poisson's ratio is:

[0078]

[0079] Among them, ν xy is the equivalent Poisson's ratio of the cell in the x and y axis directions; ν xzis the equivalent Poisson's ratio of the cell in the x and z directions.

[0080] When the cell Figure 4 When the cut is perpendicular to the x-axis, the stress σ in the x-direction is x It is expressed as:

[0081]

[0082] After applying displacements to the upper and lower surfaces of the cell in the x direction and the front and back surfaces in the y direction, the equivalent Young's modulus of the cell is:

[0083]

[0084] Among them, E y is the equivalent Young's modulus of the cell in the y direction; E x is the equivalent Young's modulus of the cell in the x direction.

[0085] (2-3) Apply displacement to the left and right ends of the diagonal rod of the three-dimensional cell in the z-axis direction, see Figure 3 , calculate the displacement of the three-dimensional cell in the x, y, and z directions, and find the equivalent Poisson's ratio and equivalent Young's modulus of the three-dimensional cell based on the displacement.

[0086] Specifically, when pulling the left and right endpoints at the same time Figure 2 After the cell, w A 、w B '、w C 、w D ' is a known quantity, w B 、w D 、w A '、w C ' and u, v are unknown quantities. According to the deformation symmetry relationship of the cell, u=v, N2=N'2, N3=N'3, where τ xz = 0. In summary, we can get the following equations:

[0087]

[0088] Combining the above equations (8) and the expressions (2) of the axial forces of each rod, we can obtain:

[0089]

[0090] Strain ε x , ε z for:

[0091]

[0092] The equivalent Poisson's ratio ν of the cell in the z and x directionszx (i.e., the equivalent formula of Poisson's ratio) is as follows:

[0093]

[0094] As Figure 6 shown, cut the unit cell along the direction perpendicular to the z-axis, and the stress σ in the z-direction z is as follows:

[0095]

[0096] The equivalent Young's modulus E of the unit cell in the z-direction z is as follows:

[0097]

[0098] For orthotropic materials, the following conclusions can also be obtained:

[0099] E z ν xz = E x ν zx (14)

[0100] (3) Under the condition of temperature change, apply a unit load to the three-dimensional unit cell, calculate the displacements generated by the three-dimensional unit cell in the x, y, and z-axis directions, and obtain the equivalent thermal expansion coefficient of the three-dimensional unit cell based on the displacements and temperature.

[0101] Specifically, when the material combinations of the unit cells are different, it is possible to achieve two-way negative thermal expansion. The mechanism of the unit cell to achieve negative thermal expansion is the triangular element, as Figure 8 shown. When the temperature changes by t, first obtain the displacement δ of point A in the vertical direction through the unit load method AV . Apply a unit force K = 1 vertically upward at point A to form Figure 9 the virtual state shown, and the internal forces of each rod (AB, AC, BC) are:

[0102]

[0103] Among them, the displacement δ caused by the temperature change AV is as follows:

[0104]

[0105] In the formula, is the axial force of each rod caused by the unit load, i is the rod number of the i-th rod, and n is the total number of rods in the unit cell structure.

[0106] As Figure 2 shown, according to the deformation symmetry relationship of the unit cell, the equivalent thermal expansion coefficients α in the x-direction and y-direction of the unit cell x 、αy The same. Based on the definition of the coefficient of thermal expansion (the coefficient of thermal expansion is the displacement caused by temperature divided by the original length of the unit cell in a certain direction), formula (17) is obtained:

[0107]

[0108] where t is the change in temperature; L3 is the length of the longest rod; δ AV is the displacement caused by temperature change at the end point bearing the load; α1 is the coefficient of thermal expansion of the first diagonal rod; α2 is the coefficient of thermal expansion of the second diagonal rod; α3 is the coefficient of thermal expansion of the longest rod; is the included angle between the two diagonal rods; θ is the included angle between the longest rod and the first diagonal rod, and L3sinθ is the vertical equivalent height of the unit cell, that is, the original length in the vertical direction.

[0109] Then, when solving for the temperature change t, the horizontal displacement δ BH at point B is applied with a unit force Q = 1 horizontally to the right to form Figure 10 the virtual state shown, and the internal forces of each rod are:

[0110]

[0111] where the displacement δ BH caused by temperature change is:

[0112]

[0113] For the three-dimensional unit cell as Figure 2 shown, its equivalent coefficient of thermal expansion in the z direction is:

[0114]

[0115] Here, L1 is the horizontal equivalent length of the unit cell, that is, the original length in the horizontal direction.

[0116] S5. When a three-dimensional structure needs to be designed, select the geometric parameters and material combinations of the triangular element, construct a three-dimensional structure with the corresponding Poisson's ratio and coefficient of thermal expansion according to steps S1 to S3, and calculate the corresponding Poisson's ratio and coefficient of thermal expansion based on the equivalent formulas of the elastic parameters and coefficient of thermal expansion in step S4.

[0117] This embodiment also verifies the above method through finite element data simulation. The element type used in the numerical simulation is BEAM189. The three-dimensional structure has 8 layers of unit cells in the x-axis and y-axis directions and 30 layers of unit cells in the z-axis direction. Among the three materials of the triangular element, both material one and material two use the material parameters of iron, and the Young's modulus, Poisson's ratio, and coefficient of thermal expansion are respectively: E1 = E2 = 80.65 GPa, ν1 = ν2 = 0.29, α1 = α2 = 1.22×10 -5 / °C. The material parameters of Material 3 using aluminum, the Young's modulus, Poisson's ratio and coefficient of thermal expansion are: E3 = 71.7 GPa, ν3 = 0.33, α3 = 2.32×10 -5 / °C. The cross-sectional areas of the three bars forming the unit cell are taken as A1 = A2 = A3 = 1.5×1.5 mm 2 .

[0118] Here, numerical simulation is carried out in two groups. The first group: Let L1 = 30 mm, L2 = 20 mm, take values of 60°, 70°, 80°, 90°, 100°, 110°, 120°; The second group: Let L2 = 28 mm, where k takes values of 0.5, 0.5714, 0.9286, 1.1429, 1.3571, 1.5714, 1.7857, 2. Through numerical simulation, the Poisson's ratio ν xy , ν xz , ν zx of the structure, the elastic modulus E x , E z , and the coefficient of thermal expansion α x , α z are obtained.

[0119] Finally, the numerical simulation results are compared with the formula calculation results. As Figures 11 to 16 shown is the comparison diagram of the numerical simulation results and the analytical formula results, Figures 11 to 13 which is the result of the first group of data, Figures 14 to 16 and which is the result of the second group of data. Among them, NR represents the numerical simulation result and AR represents the analytical formula result. From Figures 11 to 16 it can be seen that the numerical simulation results are basically in agreement with the formula calculation results. Thus, it can be seen that the equivalent formula in this embodiment can well predict the elastic parameters and coefficient of thermal expansion of the three-dimensional structure constructed in this embodiment. Moreover, the adjustment range of the Poisson's ratio and the coefficient of thermal expansion is relatively large, and the adjustment method is also relatively simple. Just through reasonable geometric parameters and material combinations, the three-dimensional negative Poisson's ratio and bidirectional negative thermal expansion of the structure can be achieved simultaneously.

[0120] In addition, this embodiment also conducts parameter analysis according to the special three-dimensional structure in order to be able to construct a special three-dimensional structure according to the obtained parameter combinations.

[0121] For example, (I) when zero Poisson's ratio design is required, according to the deformation characteristics of the unit cell, if there is zero Poisson's ratio, it must be when θ = 90° or . Therefore, let θ = 90°, and we can get:

[0122]

[0123] When θ = 90°, the data visualization is asFigures 17 to 18 As shown, where the geometric parameters and material combinations are the same as those in the first group of numerical simulations, i.e., E1 = E2 = 80.65 GPa, E3 = 71.7 GPa, L1 = 30 mm, A1 = A2 = A3 = 1.5 × 1.5 mm 2 .

[0124] Let We can obtain:

[0125]

[0126] When the data visualization is as shown in Figures 19 to 20 where the geometric parameters and material combinations are the same as those in the first group of numerical simulations, i.e., E1 = E2 = 80.65 GPa, E3 = 71.7 GPa,

[0127] L1 = 30 mm, A1 = A2 = A3 = 1.5 × 1.5 mm 2 .

[0128] From Figures 17 to 20 it can be seen that when θ = 90°, or 0 < θ < 17°, -0.01 < ν xy < 0, that is, ν xy ≈ ν xz = ν zx = 0, that is, a three-dimensional zero Poisson's ratio structure is constructed.

[0129] (II) When zero thermal expansion design in the x-axis and y-axis directions is required, let α x = 0, and the conditions for achieving zero thermal expansion in the x-axis and y-axis directions are obtained as follows:

[0130]

[0131] Finally, according to formula (23), two special cases for achieving zero thermal expansion in the x-axis and y-axis directions of the three-dimensional structure are obtained:

[0132] Substitute (at this time, the triangular element is an isosceles triangular structure) into formula (23), and we can get:

[0133]

[0134] Substitute (at this time, the triangular element is a right-angled triangular structure) into formula (23), and we can get:

[0135]

[0136] Therefore, when or When this is the case, a three-dimensional structure with zero thermal expansion coefficients in the x-axis and y-axis directions can be constructed by selecting corresponding materials.

[0137] For example, here the material parameters of the first group in numerical simulation are used: α1 = α2 = 1.22×10 -5 / °C, α3 = 2.32×10 -5 / °C. The data visualization of α x < 0, α x = 0, α x > 0 can be obtained. As Figure 21 shown, Figure 21 the abscissa is θ and the ordinate is From Figure 21 it can be clearly seen the θ and x = 0, α x > 0 and α x < 0 cases of magnitudes.

[0138] Embodiment 2

[0139] This embodiment discloses a computing device, including a processor and a memory for storing processor-executable programs. When the processor executes the programs stored in the memory, the design method of the three-dimensional structure with adjustable Poisson's ratio and thermal expansion coefficient described in Embodiment 1 is implemented, specifically as follows:

[0140] S1. Design a triangular unit, where the longest rod and two diagonal rods of the triangular unit have corresponding rod lengths and are made of three materials respectively;

[0141] S2. Use two identical triangular units to form a parallelogram, and then construct a three-dimensional cell based on four identical parallelograms;

[0142] S3. Take the direction of one side of the parallelogram at the bottom of the three-dimensional cell as the left-right direction, arrange the three-dimensional cells periodically along this direction, and repeatedly mirror along the front-back direction and up-down direction perpendicular to this direction to finally obtain a three-dimensional truss structure;

[0143] S4. Conduct a mechanical analysis on a three-dimensional cell of the three-dimensional truss structure, and obtain the equivalent formulas of the elastic parameters and thermal expansion coefficients of the three-dimensional truss structure through the displacement method and the unit load method;

[0144] S5. When a three-dimensional structure needs to be designed, select the geometric parameters and material combinations of the triangular unit, construct a three-dimensional structure with corresponding Poisson's ratio and thermal expansion coefficient according to steps S1 to S3, and calculate the corresponding Poisson's ratio and thermal expansion coefficient based on the equivalent formulas of the elastic parameters and thermal expansion coefficients in step S4.

[0145] The computing device described in this embodiment may be a desktop computer, a laptop computer, a smart phone, a PDA handheld terminal, a tablet computer or other terminal devices with processor functions.

[0146] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications made without departing from the spirit and principle of the present invention shall be equivalent replacement methods and are all included in the protection scope of the present invention.

Claims

1. A design method for a three-dimensional structure with adjustable Poisson's ratio and coefficient of thermal expansion, characterized in that, It includes the following steps: S1. Design a triangular unit, where the longest rod and the two diagonal rods of the triangular unit have corresponding rod lengths and are made of three materials respectively; S2. Use two identical triangular units to form a parallelogram, and then construct a three-dimensional cell based on four identical parallelograms; S3. Take the direction of one side of the parallelogram at the bottom of the three-dimensional cell as the left-right direction, arrange the three-dimensional cells periodically along this direction, and repeatedly mirror along the front-back direction and the up-down direction perpendicular to this direction to finally obtain a three-dimensional truss structure; S4. Conduct a mechanical analysis on a three-dimensional cell of the three-dimensional truss structure, and obtain the equivalent formulas of the elastic parameters and the coefficient of thermal expansion of the three-dimensional truss structure through the displacement method and the unit load method; The process of step S4 is specifically as follows: Cut out a three-dimensional cell from the three-dimensional truss structure, take the centroid of this three-dimensional cell as the origin O, define the direction of one of the diagonal rods of a triangular unit at the bottom of the three-dimensional cell as the z-axis, establish a Cartesian coordinate system, the y-axis of the Cartesian coordinate system is perpendicular to the z-axis on the horizontal plane, and the x-axis of the Cartesian coordinate system is perpendicular to the z-axis on the vertical plane; Apply displacements to the upper and lower surfaces of the three-dimensional cell in the x-axis direction, calculate the displacements generated by the three-dimensional cell in the three directions of the x, y, and z axes, and obtain the equivalent Poisson's ratio and the equivalent Young's modulus of the three-dimensional cell based on the displacements; Apply displacements to the front and back surfaces of the three-dimensional cell in the y-axis direction, calculate the displacements generated by the three-dimensional cell in the three directions of the x, y, and z axes, and obtain the equivalent Poisson's ratio and the equivalent Young's modulus of the three-dimensional cell based on the displacements. According to the deformation symmetry relationship of the cell, the equivalent parameters in the x-axis direction and the y-axis direction are the same; Apply displacements to the left and right endpoints of the diagonal rod of the three-dimensional cell in the z-axis direction, calculate the displacements generated by the three-dimensional cell in the three directions of the x, y, and z axes, and obtain the equivalent Poisson's ratio and the equivalent Young's modulus of the three-dimensional cell based on the displacements; Under the condition of temperature change, apply a unit load to the three-dimensional cell, calculate the displacements generated by the three-dimensional cell in the three directions of the x, y, and z axes, and obtain the equivalent coefficient of thermal expansion of the three-dimensional cell based on the displacements and the temperature; The equivalent thermal expansion coefficients α in the x, y, and z-axis directions of the three-dimensional cell x , α y , α z are as follows: Among them, t is the change in temperature; L3 is the length of the longest rod; δ AV is the displacement caused by temperature change at the end point bearing the load; α1 is the thermal expansion coefficient of the first diagonal rod; α2 is the thermal expansion coefficient of the second diagonal rod; α3 is the thermal expansion coefficient of the longest rod; is the included angle between the two diagonal rods; θ is the included angle between the longest rod and the first diagonal rod; S5. When a three-dimensional structure needs to be designed, select the geometric parameters and material combinations of the triangular unit, construct a three-dimensional structure with corresponding Poisson's ratio and coefficient of thermal expansion according to steps S1 to S3, and calculate the corresponding Poisson's ratio and coefficient of thermal expansion based on the equivalent formulas of the elastic parameters and the coefficient of thermal expansion in step S4.

2. The design method of the three-dimensional structure with adjustable Poisson's ratio and coefficient of thermal expansion according to claim 1, characterized in that After applying displacements to the upper and lower surfaces of the cell in the x direction, the front and back surfaces in the y direction, and the left and right endpoints in the z direction respectively, the equivalent Young's modulus of the cell is: Among them, E z is the equivalent Young's modulus of the unit cell in the z direction; E x is the equivalent Young's modulus of the unit cell in the x direction; E y is the equivalent Young's modulus of the unit cell in the y direction; taking the diagonal bar serving as the z-axis as the first diagonal bar, and the other diagonal bar of the triangular unit as the second diagonal bar, N2 is the axial force of the second diagonal bar; N3 is the axial force of the longest bar; is the included angle between the two diagonal bars; θ is the included angle between the longest bar and the first diagonal bar; u is the distance that the parallelogram at the bottom of the unit cell moves along the positive x-axis; L1 is the length of the first diagonal bar; E1 is the Young's modulus of the first diagonal bar; A1 is four times the cross-sectional area of the first diagonal bar.

3. The design method of the three-dimensional structure with adjustable Poisson's ratio and coefficient of thermal expansion according to claim 1, characterized in that, After applying displacements to the upper and lower surfaces of the cell in the x direction simultaneously, the equivalent formula for Poisson's ratio is: where, ν xy is the equivalent Poisson's ratio of the unit cell in the x and y axis directions; ν xz is the equivalent Poisson's ratio of the unit cell in the x and z axis directions; u is the distance that the parallelogram at the bottom surface of the unit cell moves along the positive x-axis direction; is the included angle between the two diagonal bars; θ is the included angle between the longest bar and the first diagonal bar; v is the distance that the parallelogram connecting the upper and lower surfaces moves along the positive y-axis direction; w B is the distance that the endpoints connecting the two diagonal bars in the parallelogram connecting the upper and lower surfaces move along the negative z-axis direction; w A is the distance that the endpoints connecting the longest bar and the second diagonal bar in the parallelogram connecting the upper and lower surfaces move along the positive z-axis direction.

4. The design method of a three-dimensional structure with adjustable Poisson's ratio and coefficient of thermal expansion according to claim 1, characterized in that, After pulling the cell at the left and right endpoints of the cell in the z direction simultaneously, the equivalent formula for Poisson's ratio is: ν zx is the equivalent Poisson's ratio of the unit cell in the z- and x-axis directions; is the included angle between the two diagonal rods; θ is the included angle between the longest rod and the first diagonal rod.

5. The design method of a three-dimensional structure with adjustable Poisson's ratio and coefficient of thermal expansion according to claim 1, characterized in that When or the Poisson's ratio of the constructed three-dimensional structure is 0.

6. The design method of a three-dimensional structure with adjustable Poisson's ratio and coefficient of thermal expansion according to claim 1, characterized in that, When or the coefficient of thermal expansion of the constructed three-dimensional structure in the x-axis and y-axis directions is 0.

7. A three-dimensional structure with adjustable Poisson's ratio and coefficient of thermal expansion, characterized in that, The three-dimensional structure is constructed by the design method of the three-dimensional structure with adjustable Poisson's ratio and coefficient of thermal expansion according to any one of claims 1 to 6.

8. A computing device, comprising a processor and a memory for storing processor-executable programs, characterized in that, When the processor executes the program stored in the memory, it implements the design method of the three-dimensional structure with adjustable Poisson's ratio and coefficient of thermal expansion described in any one of claims 1 to 6.

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