A heterogeneous metamaterial design method considering zero poisson's ratio and high bearing capacity

Abstract

The application discloses a design method of a heterogeneous superstructure material with zero Poisson's ratio and high bearing capacity. In the linear elasticity theory framework, first, two kinds of cell configurations with theoretically positive and negative Poisson's ratio values are selected based on a structural Poisson's ratio calculation formula of a classical beam theory; then, finite element solutions of the Poisson's ratio and the Young's modulus of the selected cells are calculated; and finally, the two kinds of cells with positive and negative Poisson's ratios are assembled in a column and row arrangement mode according to a given layout rule to obtain a heterogeneous lattice superstructure material with zero Poisson's ratio and high bearing capacity. The application can obtain a heterogeneous superstructure material with zero Poisson's ratio and high bearing capacity through cell assembly design. The heterogeneous lattice superstructure material formed by assembly has stronger deformation resistance and one-way deformation capacity of the zero Poisson's ratio structure, and can provide scheme support for actual engineering design.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of super-light material structure design, and particularly relates to a design method of a heterogeneous super-structure material considering zero Poisson's ratio and high bearing capacity. BACKGROUND

[0002] Research shows that with the decrease of apparent density, the mechanical properties of super-light materials are greatly weakened, which limits the application space of light materials. How to balance the ultra-lightness and high performance of materials is a problem that needs to be solved at present. In the fields of medical equipment, sensors, protective equipment and soft robots, in addition to meeting the requirements of ultra-lightness and high bearing performance, the one-way deformation characteristics of zero Poisson's ratio structure are also required, that is, no lateral shrinkage occurs under uniaxial compression.

[0003] Lattice materials are widely used due to their material distribution regularity, structure designability, material functionality, cross-scale, light weight and other characteristics. Lattice materials are periodic structural materials composed of nodes and connecting rod elements between nodes. The cell configuration is similar to the lattice structure (material) of crystal materials. By periodically arranging the cells on the mesoscopic level, a repeated periodic macroscopic configuration is obtained, thereby obtaining a new functional material.

[0004] Research shows that the mechanical properties of macroscopic lattice materials are largely dependent on the cell configuration and the distribution of internal pores, so by designing the representative volume element (RVE) of the lattice structure, the mechanical properties of the material can be controlled to obtain high bearing capacity and one-way deformation of zero Poisson's ratio structure.

[0005] The current main research direction of lattice materials mainly focuses on the homogeneous materials composed of single cells, for example: the positive and negative Poisson's ratio of the homogeneous lattice material is adjusted by carefully designing the configuration of the cell, and the enhancement design of the torsional properties and bearing properties of the material is completed by establishing the relationship between the geometric parameters of the cell configuration and the material properties based on the guidance of the classical theory. These optimizations of cell configuration greatly limit the performance design space of lattice materials, and it is difficult to meet the needs of different fields for ultra-light, high bearing and zero Poisson's ratio. The heterogeneous lattice structure formed by the combination of multiple cells can produce extremely diverse lattice configurations, greatly expanding the design space of lattice materials, and fully exerting the excellent potential of lattice materials in bearing performance. However, there is no design method for obtaining a heterogeneous super-structure material with zero Poisson's ratio and high bearing capacity by combining cells at home and abroad, and there is a lack of theoretical guidance when designing multiple cell combinations, making it difficult to find a cell configuration design and reasonable combination method that can balance zero Poisson's ratio and high bearing capacity. Therefore, it is necessary to establish a design method to guide the construction of a heterogeneous super-structure material that balances zero Poisson's ratio and high bearing capacity to meet the specific needs of different application fields for structural bearing performance. SUMMARY

[0006] In order to overcome the above-mentioned shortcomings of the prior art, the purpose of the present application is to provide a heterogeneous super-structure material design method that balances zero Poisson's ratio and high bearing capacity, and the assembled heterogeneous lattice super-structure material has stronger resistance to deformation and one-way deformation ability of zero Poisson's ratio structure, which can provide scheme support for engineering application.

[0007] In order to achieve the above requirements, the technical scheme adopted by the present application is as follows:

[0008] A heterogeneous super-structure material design method that balances zero Poisson's ratio and high bearing capacity, under the framework of linear elasticity theory, first selects two cell configurations with theoretically positive and negative Poisson's ratio values based on the structural Poisson's ratio calculation formula of the classical beam theory, then calculates the finite element solution of the Poisson's ratio and Young's modulus of the selected cells, and then assembles the two cells with positive and negative Poisson's ratio in a column and row arrangement according to the given layout rule, to obtain a heterogeneous lattice super-structure material that balances zero Poisson's ratio and high bearing capacity.

[0009] A heterogeneous super-structure material design method that balances zero Poisson's ratio and high bearing capacity, comprising the following steps:

[0010] 1) Selection of cells:

[0011] The connection between the designed cells is through the bar, the tensile or compressive load is transmitted between the cells through the connection, and then the deformation is generated, and the Young's modulus and Poisson's ratio of the lattice structure are obtained by calculating the elastic relationship between the load and the deformation and the mutual relationship between the deformations in different directions; Based on the classical beam theory structure Poisson's ratio calculation formula, the cell configuration with positive and negative Poisson's ratio is obtained in theory.

[0012] 2) Finite element solution of cell mechanical properties:

[0013] First, the quasi-static tensile or compression test boundary conditions are applied to the cell, that is, a uniaxial force is applied to one side of the cell, and a full fixed constraint is applied to the other side, and then the periodic boundary conditions are applied to the cell on the basis of the boundary conditions, and the boundary condition setting is completed; The regional node is located at the midpoint of the four boundaries, and is represented by a, b, c and d in anticlockwise direction respectively, and the regional number is represented by its position (i, j) in RVE, that is, the region located in the ith row and jth column, therefore, the periodic boundary condition is expressed as:

[0014]

[0015]

[0016]

[0017]

[0018] In the formula: i, j represent the position of the cell in RVE, that is, the cell located in the ith row and jth column, M and N represent the number of rows and columns of the cells in RVE respectively, u represents displacement, u ax represents the x direction displacement of cell a node; L x represents the total length of RVE in x direction, L y represents the total length of RVE in y direction, ε x represents the strain of RVE in x direction, ε y represents the strain of RVE in y direction;

[0019] The calculation results including the average displacement of the cell boundary and the support reaction force are obtained by solving the physical field through finite element analysis, and then the equivalent Young's modulus and Poisson's ratio of the cell are calculated; The mathematical expression of the calculation method of the structure Young's modulus E in finite element analysis is:

[0020] E = σ / ε (2)

[0021] Wherein, E is the Young's modulus of the structure, σ is the stress of the structure, and ε is the strain of the structure;

[0022] The ratio of the sum of the support reaction force of the loaded surface ∑F to the action area A is used to calculate the stress of the structure, that is:

[0023]

[0024] Equivalent Young's modulus of the structure Equal to the Young's modulus E of the structure and the Young's modulus E of the bulk material s The ratio, that is:

[0025]

[0026] The mathematical expression for calculating the Poisson's ratio of a structure in finite element analysis is:

[0027] The strain in the y-direction of the overall RVE structure is ε. y The strain in the x-direction is ε. x For the overall RVE structure, the Poisson's ratio v represents the deformation in the y direction caused by loading in the x direction. xy for:

[0028] ν xy =-ε y / ε x (5)

[0029] 3) Design of RVE configuration for heterogeneous lattice metamaterials:

[0030] Based on the given assembly rules, using two types of cells with positive and negative Poisson ratios, and based on the mechanical properties and dimensional parameters of the cells, the RVE configuration of the heterogeneous lattice metamaterial is designed to obtain a heterogeneous lattice metamaterial that balances zero Poisson ratio and high load-bearing capacity.

[0031] The assembly rules are as follows:

[0032]

[0033] Where N represents the number of columns of cells in the RVE, L jx Represents the length of the unit cell in column j ( Figure 2 L), v jyx The Poisson's ratio value represents the unit cell of column j when loaded in the y-direction;

[0034] If only two cells with positive and negative Poisson ratios are used for assembly according to a given layout rule, the ratio of the number of cells with positive and negative Poisson ratios in the RVE is expressed as:

[0035]

[0036] Where n1 represents the number of positive cell columns in the RVE, n2 represents the number of negative cell columns in the RVE, lxa represents the length of the positive cell, lxb represents the length of the negative cell, and v yxa v represents the Poisson's ratio when a positive cell is loaded in the y-direction. yxbPoisson's ratio of the negative cell when the y direction is loaded;

[0037] 4) verification of mechanical properties of the heterogeneous lattice metamaterial:

[0038] The finite element analysis method of applying periodic boundary conditions is used to calculate the Young's modulus and Poisson's ratio of the assembled heterogeneous lattice metamaterial, to determine whether the material performance meets the requirements, if it meets the requirements, the RVE configuration of the heterogeneous lattice metamaterial and the corresponding mechanical properties are output; if it does not meet the requirements, two positive and negative Poisson's ratio cells are selected again, and then steps 2), 3) and 4) are repeated until the requirements are met.

[0039] The beneficial effects of the present application are:

[0040] (1) The present application uses different cells with positive and negative Poisson's ratio to combine to obtain a heterogeneous lattice structure, which greatly expands the design space of lattice materials;

[0041] (2) The present application establishes a design method of a heterogeneous lattice metamaterial assembled by multiple cells, which can guide the design of a heterogeneous metamaterial with zero Poisson's ratio and high bearing capacity. Compared with traditional lattice materials, this heterogeneous metamaterial has zero Poisson's ratio characteristics, and the bearing capacity is also greatly improved. BRIEF DESCRIPTION OF DRAWINGS

[0042] Figure 1 is a flowchart of the present application.

[0043] Figure 2 is a cell configuration diagram of an embodiment of the present application.

[0044] Figure 3 is a four-cell connection diagram of an embodiment of the present application.

[0045] Figure 4 is an RVE configuration diagram of a heterogeneous lattice metamaterial obtained by assembling cells with positive and negative Poisson's ratio at different proportions. DETAILED DESCRIPTION

[0046] In order to better illustrate the technical solutions, objects and advantages of the present application, the present application will be further described below in combination with the drawings and embodiments.

[0047] Referring to Figure 1 A design method of a heterogeneous metamaterial with zero Poisson's ratio and high bearing capacity, comprising the following steps:

[0048] 1) Selection of cells:

[0049] The designed cells are connected by bars, and the tensile or compressive load is transmitted between the cells through the connection, thereby generating deformation. The Young's modulus and Poisson's ratio of the lattice structure can be obtained by calculating the elastic relationship between the load and the deformation and the mutual relationship between the deformations in different directions. Based on the formula for calculating the structure Poisson's ratio in the classical beam theory, the cell configuration with theoretically positive and negative Poisson's ratio is obtained.

[0050] As shown in the drawings, two kinds of cells with positive and negative Poisson's ratio are designed in the embodiment, and each kind of cell has two cells. In order to ensure that the cells can be assembled in a column arrangement, the cell width H is 6.00 mm, the wall thickness t is 0.1 mm, the stress in the thickness direction is ignored, and the other specific dimensions are as follows: positive cell 1: α = 170°; L = 6.00 mm; b = 2.50 mm; positive cell 2: θ = 20.47°; l = 2.70 mm; l1 = 3.10 mm; L = 7.57 mm; h = 5.90 mm; negative cell 1: α = 9.90°; L = 6.00 mm; b = 2.50 mm; negative cell 2: θ = 13.84°; l = 4.00 mm; l1 = 2.99 mm; L = 6.34 mm; h = 5.90 mm. Figure 2 Based on the classical beam theory, the theoretical solution calculation formula of the Poisson's ratio of the isotropic cell is obtained as follows:

[0051]

[0052] In the formula: v is the Poisson's ratio of the isotropic cell; α is the angle value of the isotropic cell;

[0053] Based on the classical beam theory, the theoretical solution calculation formula of the Poisson's ratio of the anisotropic cell is as follows:

[0054]

[0055]

[0056] In the formula: l1 and l are the length values of different parts of the anisotropic cell; θ is the angle value of the anisotropic cell; ν yx represents the Poisson's ratio of the anisotropic cell when loaded in the y direction; ν xy represents the Poisson's ratio of the anisotropic cell when loaded in the x direction.

[0057] 2) Finite element solution for calculating the mechanical properties (Young's modulus and Poisson's ratio) of the cell:

[0058] First, the quasi-static tensile or compression test boundary conditions are applied to the cell, that is, a uniaxial force is applied to one side of the cell, and a fixed constraint is applied to the other side. Then, the periodic boundary conditions are applied to the cell on the basis of the boundary conditions, the boundary condition setting is completed, and then the finite element solution is carried out. As Figure 3 ​As shown, the region nodes are located at the midpoints of the four boundaries, and are denoted by a, b, c, and d respectively in a counterclockwise direction. The region number is represented by its position (i,j) in the RVE, that is, the region located in the i-th row and j-th column. Therefore, the periodic boundary condition can be expressed as:

[0059]

[0060] In the formula: i,j represent the position of the cell in the RVE, i.e., located in the i-th row and j-th column; M and N represent the row number and column number of the cell in the RVE, respectively; u represents the displacement. ax For example, u ax L represents the x-direction displacement of node a in cell a; x L represents the total length of the RVE in the x-direction. y ε represents the total length of the RVE in the y-direction. x ε represents the strain in the x-direction of the RVE. y The strain in the y-direction represents the RVE;

[0061] The physical field is solved by finite element analysis to obtain calculation results, including the average displacement and support reaction force of the cell boundary, and then the equivalent Young's modulus and Poisson's ratio of the cell are calculated. The mathematical expression for the calculation method of the Young's modulus E of the structure in finite element analysis is as follows:

[0062] E=σ / ε (4)

[0063] In the formula, E is the Young's modulus of the structure, σ is the structural stress, and ε is the structural strain. Since the structure is subjected to small strain, ε is taken as 0.001.

[0064] Since structural stress cannot be directly measured in finite element analysis, the ratio of the sum of the support reactions ∑F to the area A is used to calculate the structural stress, i.e.:

[0065]

[0066] Equivalent Young's modulus of the structure Equal to the Young's modulus E of the structure and the Young's modulus E of the bulk material s The ratio, that is:

[0067]

[0068] The mathematical expression for calculating the Poisson's ratio of a structure in finite element analysis is: the strain in the y-direction of the overall RVE structure is ε. y The strain in the x-direction is ε. x For the overall RVE structure, the Poisson's ratio v represents the deformation in the y direction caused by loading in the x direction. xy for:

[0069] ν xy = -ε y / ε x (7)

[0070] The positive and negative Poisson's ratio cell mechanical properties and key size parameters obtained by finite element analysis calculation are shown in Table 1:

[0071] Table 1

[0072]

[0073] 3) Design of RVE configuration of heterogeneous lattice metamaterial:

[0074] According to the given assembly rule, taking the assembly of positive cell 1 and negative cell 1 as an example, Therefore, the number of positive and negative Poisson's ratio cells in each row of the lattice RVE is assembled in the proportion of 8:9, and a heterogeneous lattice metamaterial RVE configuration (configuration IV) is obtained, which takes into account zero Poisson's ratio and high bearing capacity. Positive cell 1 and negative cell 2 are paired respectively, and then assembled according to the given layout rule, a total of four such configurations, and the specific assembly configuration is shown in Figure 4 , (in the figure, configurations I-IV are the RVE configurations of the heterogeneous lattice metamaterial assembled by positive cell 2 and negative cell 1, positive cell 2 and negative cell 2, positive cell 1 and negative cell 2, and positive cell 1 and negative cell 1, respectively).

[0075] 4) Simulation of design results of heterogeneous lattice metamaterial:

[0076] The finite element analysis method of applying periodic boundary conditions is used to calculate the Young's modulus and Poisson's ratio of the assembled heterogeneous lattice metamaterial, and the rationality of the design method is verified. Specifically, the configuration uses plane 182 elements, the real constant is used to define the thickness of the plane element, which is set to r=0.1mm, the element is meshed by quadrilateral mesh, the mesh size is 0.02mm, the left end of the structure is fixedly constrained, the right end of the structure is subjected to a displacement load with a strain size ε=0.001, and then the periodic boundary condition is applied to the structure. Then, statics solving is performed; the results of finite element analysis on the above four assembly configurations are shown in Table 2:

[0077] Table 2

[0078]

[0079] From the data in Table 2, the Poisson's ratios of the four assembled configurations are close to zero, and compared with the mechanical properties of the constituent cells in Table 1, it is found that the equivalent Young's modulus values of the assembled configurations are significantly improved compared with the constituent cells, and the equivalent Young's modulus of configuration III is improved by 74 times compared with the equivalent Young's modulus of the constituent cell (compared with the cell with larger equivalent Young's modulus in the constituent cell), which proves the effectiveness of the present application.

[0080] The above is the specific steps of the present application, which does not constitute any limitation on the protection scope of the present application; any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A design method for heterogeneous metamaterials that balances zero Poisson's ratio and high load-bearing capacity, characterized in that: Within the framework of linear elasticity theory, based on the structural Poisson's ratio calculation formula of classical beam theory, two cell configurations with theoretically positive and negative Poisson's ratios are selected. Then, the finite element solutions of the selected cell Poisson's ratio and Young's modulus are calculated. Finally, the two cell configurations with positive and negative Poisson's ratios are assembled in a column arrangement according to a given layout rule to obtain a heterogeneous lattice metamaterial that balances zero Poisson's ratio and high load-bearing capacity. Includes the following steps: 1) Selection of cell units: The cells are connected by rods. Tensile or compressive loads are transmitted between cells through the connections, resulting in deformation. By calculating the elastic relationship between load and deformation, as well as the relationship between deformations in different directions, the Young's modulus and Poisson's ratio of the lattice structure are obtained. Based on the classical beam theory formula for calculating Poisson's ratio, cell configurations with theoretically positive and negative Poisson's ratios are obtained. 2) Finite element solution for calculating the mechanical properties of the cell: First, apply quasi-static tensile or compressive test boundary conditions to the cell, that is, apply a uniaxial force to one side of the cell and apply a fixed constraint to the other side. Then, apply periodic boundary conditions to the cell based on these boundary conditions to complete the boundary condition setting. The physical field is solved by finite element analysis to obtain the calculation results, including the average displacement and support reaction force of the cell boundary, and then the equivalent Young's modulus and Poisson's ratio of the cell are calculated. The structural stress is calculated using the ratio of the sum of the support reactions on the loaded surface ∑F to the area A of action. Equivalent Young's modulus of the structure Equal to the Young's modulus E of the structure and the Young's modulus E of the bulk material s The ratio; 3) Design of RVE configuration for heterogeneous lattice metamaterials: Based on the given assembly rules, using two types of cells with positive and negative Poisson ratios, and based on the mechanical properties and dimensional parameters of the cells, the RVE configuration of the heterogeneous lattice metamaterial is designed to obtain a heterogeneous lattice metamaterial that balances zero Poisson ratio and high load-bearing capacity. Step 3) The assembly pattern is as follows: Where N represents the number of cell columns in the RVE, L jx v represents the unit cell length of the j-th column. jyx The Poisson's ratio value represents the unit cell of column j when loaded in the y-direction; If only two cells with positive and negative Poisson ratios are used for assembly according to a given layout rule, the ratio of the number of cells with positive and negative Poisson ratios in the RVE is expressed as: Where n1 represents the number of positive cell columns in the RVE, n2 represents the number of negative cell columns in the RVE, lxa represents the length of the positive cell, lxb represents the length of the negative cell, and v yxa v represents the Poisson's ratio when a positive cell is loaded in the y-direction. yxb Poisson's ratio represents the value of a negative cell under load in the y-direction. 4) Verification of the mechanical properties of heterogeneous lattice metamaterials: The Young's modulus and Poisson's ratio of the assembled heterogeneous lattice metamaterial are calculated using the finite element analysis method with applied periodic boundary conditions. The material's performance is then assessed to determine if it meets the requirements. If it does, the RVE configuration and corresponding mechanical properties of the heterogeneous lattice metamaterial are output. If it does not meet the requirements, two positive and negative Poisson's ratio cells are selected, and steps 2), 3), and 4) are repeated until the requirements are met.

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