Equivalent mechanical performance analysis method of dual-phase TPMS lattice structure and application of equivalent mechanical performance analysis method

Abstract

The invention discloses an equivalent mechanical performance analysis method of a dual-phase TPMS lattice structure and application of the equivalent mechanical performance analysis method, and belongs to the technical field of material structures. Two materials in the two-phase TPMS lattice structure are equivalent to one material through an equivalent theory method, a shell unit can be used for establishing a model for calculation when a single material is used for simulation, and only one layer of unit is arranged on the thickness of the curved surface wall of the shell model, so that the number of model units is greatly reduced, and the cost is reduced. The coupling effect between the two materials does not need to be considered, so that the calculation efficiency can be improved by performing simulation calculation, and the effectiveness of the simulation calculation is verified; according to the method, the equivalent calculation method of the composite material plate is creatively applied to the curved surface of the structure, the calculation speed and efficiency are greatly improved on the premise that the calculation and analysis accuracy is guaranteed, compared with a common analysis and calculation method using entity units for modeling, the calculation duration is shortened by 95.32%, and the method has important application prospects.

Description

Technical Field

[0001] The present invention belongs to the technical field of material structure, and in particular relates to an equivalent mechanical performance analysis method of a two-phase TPMS lattice structure and an application thereof. Background Art

[0002] In the modern engineering field, the speed and efficiency of analytical calculations is an important issue. Researchers have been committed to improving the efficiency of actual engineering, reducing the time cost of analytical calculations, shortening the R&D cycle, and improving the quality of analytical calculations through advanced computing technologies and methods.

[0003] In the material structure design, combining the dual-phase with the TPMS lattice structure can obtain better mechanical properties. When analyzing the mechanical properties of the dual-phase TPMS lattice structure, the general analysis and calculation method first establishes a solid mesh model of the dual-phase TPMS lattice structure, then assigns material properties to the locations of the two materials respectively, and then couples the four layers of materials together through constraints to perform numerical simulation. Such analysis and calculation has good accuracy, but the overall structure of the multi-cell array contains a large amount of mesh volume, and due to the dual-phase design, the structure has two materials in thickness. Therefore, under the general calculation method, more meshes need to be divided in the thickness direction than a single material to ensure the accuracy of the calculation, which leads to a significant increase in the number of meshes, resulting in low efficiency and long time for the mechanical performance analysis of the dual-phase TPMS lattice structure. It occupies more computing resources and is difficult to meet the needs of actual engineering. Therefore, the mechanical performance analysis method of the dual-phase TPMS lattice structure still needs to be developed and broken through. Summary of the invention

[0004] The purpose of the present invention is to provide an equivalent mechanical performance analysis method of a two-phase TPMS lattice structure and its application, which greatly improves the calculation speed and efficiency while ensuring the accuracy of the calculation and analysis.

[0005] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0006] The present invention provides an equivalent mechanical performance analysis method for a dual-phase TPMS lattice structure, and the specific steps include:

[0007] S1. Select two materials, soft phase material and hard phase material, for dual-phase design, and perform dog-bone tensile tests on the selected materials to obtain their dog-bone tensile engineering stress-strain curves, thereby obtaining material performance parameters: stiffness E, Poisson's ratio ν, yield stress σ Y , and calculate the stiffness matrix of the two materials respectively to obtain the stiffness matrix coefficient;

[0008] S2. The two materials are equivalent to one material according to the equivalent theory, and the stiffness matrix coefficients of the equivalent material are calculated based on the stiffness matrix coefficients of the two materials obtained in step S1, and then the engineering constants are obtained; at the same time, the effective mass density and yield stress of the equivalent material are calculated;

[0009] S3. Generate the basic surface configuration of the TPMS lattice structure based on the mathematical control equation of the three-period minimal surface, then establish the surface model of the TPMS structure in the finite element software, divide it into shell meshes and assign corresponding thicknesses to obtain a shell model, and use the equivalent material parameters obtained in step S2: engineering constants, effective mass density and yield stress as inputs to perform quasi-static compression numerical simulation to obtain the mechanical response of the structure, analyze its deformation mode and stress-strain curve during the quasi-static compression process, and calculate its related mechanical properties.

[0010] According to the above scheme, in step S1, the soft phase material is thermoplastic polyurethane (TPU) material.

[0011] According to the above scheme, in step S1, the hard phase material is polylactic acid (PLA) material.

[0012] The soft phase material has a buffering and energy absorbing function, while the hard phase material has a load-bearing and supporting function.

[0013] According to the above scheme, in step S1, the volume ratio of the soft phase material and the hard phase material is 1:1.

[0014] According to the above scheme, in step S1, a dog-bone tensile test is performed on the selected material, specifically: a uniaxial tensile test is performed on a universal testing machine, and the universal testing machine is equipped with a computer control and data acquisition system, so that force and displacement data can be automatically obtained; wherein the dog-bone tensile engineering stress-strain curve is obtained through the force-displacement curve, thereby obtaining the material performance parameters: stiffness E, Poisson's ratio ν, yield stress σ Y .

[0015] According to the above scheme, in step S1, the stiffness matrix of the material is calculated by the following formula:

[0016]

[0017] According to the above scheme, Represent the stiffness matrix coefficients of the soft phase material and the hard phase material, respectively, v t 、v p Respectively represent the volume fractions of the soft phase material and the hard phase material. The stiffness matrix coefficient of the equivalent material after the two materials are equivalent to one material is calculated by the following formula:

[0018]

[0019]

[0020] After obtaining the stiffness matrix from the stiffness matrix coefficient, the flexibility matrix is ​​obtained by inverting the stiffness matrix, S nn is the flexibility matrix coefficient, and the engineering constant is calculated by the following formula:

[0021]

[0022] Among them, E 1 、E 2 、E 3 are the elastic moduli of the material in the 1st, 2nd and 3rd principal elastic directions respectively; ν ij The negative value of the ratio of the strain in the i direction to the strain in the j direction when there is only a positive stress in the j direction without other stress components is called Poisson's ratio; G 23 , G 31 , G 12 They are the shear elastic moduli in the 2-3, 3-1, and 1-2 planes respectively.

[0023] According to the above scheme, the effective mass density and yield stress are calculated by the following formula:

[0024]

[0025] in, are the effective mass density and yield stress of the equivalent material, ρ p , t are the mass densities of the hard phase material and the soft phase material, σ Y p , σ Y t are the yield stresses of the hard phase material and the soft phase material, respectively, v p 、v t are the volume fractions of the hard phase material and the soft phase material, respectively.

[0026] According to the above scheme, the basic surface configuration of the three-dimensional TPMS lattice structure generated based on the mathematical control equation of the three-periodic minimal surface is specifically:

[0027] Select the Gyroid surface, whose mathematical control equation is:

[0028] f Gyroid (x,y,z)=sin(x)cos(y)+sin(z)cos(x)+sin(y)cos(z)=0

[0029] In the formula for a three-periodic minimal surface, x, y, and z usually represent coordinates in three-dimensional space. Specifically, these coordinates define the position of each point on the surface;

[0030] According to actual needs, the size, thickness and array quantity of the minimal surface unit cell are determined, and the software Matlab is used for drawing and modeling to obtain the basic surface configuration of the three-dimensional TPMS lattice structure.

[0031] Provided is an application of an equivalent mechanical performance analysis method of the above-mentioned two-phase TPMS lattice structure in analyzing and calculating mechanical properties in the field of material structure.

[0032] The beneficial effects of the present invention are as follows:

[0033] The present invention provides an equivalent mechanical performance analysis method for a two-phase TPMS lattice structure, which equates two materials in the two-phase TPMS lattice structure to one material through an equivalent theoretical method. When a single material is used for simulation, a shell unit can be used to establish a model for calculation. The shell model has only one layer of units on the thickness of the curved wall, which greatly reduces the number of model units and does not need to consider the coupling effect between the two materials. Therefore, the simulation calculation can improve its calculation efficiency and verify its effectiveness. The present invention innovatively applies the equivalent calculation method of the composite material plate to the curved surface of this structure, greatly improving the calculation speed and efficiency while ensuring the accuracy of the calculation analysis. Compared with the general analysis and calculation method using solid unit modeling, the calculation time is reduced by 95.32%, which has important application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 Flow chart of the equivalent mechanical performance analysis method of the dual-phase TPMS lattice structure in an embodiment of the present invention.

[0035] Figure 2 It is a surface model of the TPMS lattice structure in the embodiment of the present invention.

[0036] Figure 3 Schematic diagram of two material filling methods for the dual-phase TPMS lattice structure in an embodiment of the present invention.

[0037] Figure 4 It is a comparison chart of mechanical properties in the embodiments of the present invention. DETAILED DESCRIPTION

[0038] The following is a further description of the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings and specific embodiments. It can be understood that the specific embodiments described herein are only used to explain the present invention, rather than to limit the present invention. It should also be noted that, for ease of description, only the parts related to the present invention are shown in the accompanying drawings, rather than all of the contents.

[0039] The embodiments of the present invention are described in detail below in conjunction with the accompanying drawings.

[0040] Example 1

[0041] 1) Select two materials for dual-phase design, and perform dog-bone tensile test on the selected materials. After obtaining their performance curves, calculate the stiffness matrices of the two materials respectively.

[0042] Based on application requirements, the soft phase material of the two materials is selected as thermoplastic polyurethane (TPU), and the hard phase material is polylactic acid (PLA), and the volume ratio of the two materials is 1:1.

[0043] In order to obtain the material parameters related to the mechanical properties of the soft phase material and the hard phase material, a uniaxial tensile test was carried out on a universal testing machine equipped with a computer control and data acquisition system, so that the force and displacement data can be automatically obtained. The tensile engineering stress-strain curve of the dog bone is obtained through the force-displacement curve, and the material performance parameters obtained are: For TPU material, the stiffness E t =59.6Mpa, Poisson's ratio ν t =0.4, yield stress σ Y t =6.4Mpa; for PLA material, stiffness E p =1390Mpa, Poisson's ratio ν p =0.4, yield stress σ Y p =44Mpa.

[0044] The stiffness matrix of the material is then calculated using the following formula:

[0045]

[0046] Then the stiffness matrix of TPU material is:

[0047]

[0048] Then the stiffness matrix of PLA material is:

[0049]

[0050] 2) The soft phase material and the hard phase material are equivalent to one material according to the equivalent theory, and the equivalent material performance is calculated;

[0051] Represent the stiffness matrix coefficients of the soft phase material and the hard phase material, v t 、v p They respectively represent the volume fractions of the soft phase material and the hard phase material, both of which are 50% here. The stiffness matrix coefficient of the equivalent material after the two materials are equivalent to one material is calculated by the following formula:

[0052]

[0053]

[0054] The stiffness matrix is ​​obtained from the stiffness matrix coefficients:

[0055]

[0056] The flexibility matrix is ​​obtained by inverting the stiffness matrix, S nn is the flexibility matrix coefficient:

[0057]

[0058] The engineering constant is calculated by the following formula:

[0059]

[0060] Among them, E 1 、E 2 、E 3 are the elastic moduli of the material in the 1st, 2nd and 3rd principal elastic directions respectively; ν ij The negative value of the ratio of the strain in the i direction to the strain in the j direction when there is only a positive stress in the j direction without other stress components is called Poisson's ratio; G 23 , G 31 , G 12 They are the shear elastic moduli in the 2-3, 3-1, and 1-2 planes respectively.

[0061] Effective mass density With yield stress It is calculated by the following formula:

[0062]

[0063] Among them, ρ p , t are the mass densities of the two materials, σ Y p , σ Y t are the yield stresses of the two materials, v p 、v t are the volume fractions of the two materials respectively.

[0064] 3) Generate the basic surface configuration of the TPMS lattice structure based on the mathematical control equation of the three-periodic minimal surface, and use equivalent material parameters to perform finite element model simulation on the model; specifically:

[0065] Select the Gyroid surface, whose mathematical control equation is:

[0066] f Gyroid (x,y,z)=sin(x)cos(y)+sin(z)cos(x)+sin(y)cos(z)=0

[0067] In the formula for a three-periodic minimal surface, x, y, and z usually represent coordinates in three-dimensional space. Specifically, these coordinates define the location of each point on the surface.

[0068] According to actual needs, the size of the minimal surface unit cell is determined to be 12.5 mm, the thickness is 2.4 mm, and the number of arrays is 4*4*4 in the XYZ directions. Matlab is used for drawing and modeling to obtain the basic surface configuration of the three-dimensional TPMS lattice structure.

[0069] like Figure 2 As shown, a surface model of the TPMS lattice structure is established in the finite element software. The surface model is a two-dimensional surface structure without thickness. It is divided into shell meshes and given corresponding thickness to obtain a shell model. Since the model is a two-dimensional shell structure and has no thickness in the normal direction of the surface, the number of meshes in the model is relatively small. The equivalent material performance parameters obtained in step 2: engineering constants, effective mass density and yield stress are used as inputs to perform a quasi-static compression numerical simulation. The model has a fast calculation speed and the calculation time is 2.5 hours. The mechanical response of the structure can be obtained through simulation, and its deformation mode and stress-strain curve during the quasi-static compression process can be analyzed, and its related mechanical properties can be calculated. The relevant calculation results are shown in the following table. Figure 4 shown.

[0070] This equivalent mechanical performance analysis and calculation method of Example 1 was compared and verified with the experimental and general analysis and calculation methods;

[0071] 1) The specific steps of the experiment of the dual-phase structure of Example 1 are:

[0072] The material filling method of the structure is to divide the basic surface configuration of the TPMS lattice structure with the determined thickness in step 3 into 4 equal parts along the surface thickness direction, and alternately fill the soft phase and hard phase materials to obtain a dual-phase TPMS lattice structure as shown in FIG. Figure 3 As shown. The sample was prepared by FFF (fused filament fabrication) printing technology and printed using a dual-nozzle printer. The left and right nozzles of the printer simultaneously print different materials, and finally a dual-phase TPMS lattice structure sample can be manufactured.

[0073] The obtained samples were tested for performance, specifically: the quasi-static compression test was performed on a universal testing machine with a certain loading speed. The engineering stress of the configuration was calculated based on the compression load data obtained by the sensor, while the engineering strain was calculated based on the original displacement data of the indenter; its stress-strain curve and the calculation results of related mechanical properties are shown in Figure 4 shown.

[0074] 2) The calculation steps of the general analysis and calculation method of the dual-phase structure of Example 1 are as follows:

[0075] The entity model of the dual-phase TPMS lattice structure is established, and the entity mesh is divided into the entity mesh. Since the model has four material layers, the mesh needs to be divided layer by layer to ensure the calculation accuracy, so the number of entity meshes divided into the model is relatively large. The material properties are assigned to the locations of the two materials respectively, and the four layers of materials are coupled together through constraints to perform quasi-static compression numerical simulation. The calculation time is 53.4 hours. The mechanical response of the structure can be obtained through simulation, and its deformation mode and stress-strain curve during the quasi-static compression process can be analyzed, and its related mechanical properties can be calculated. The relevant calculation results are as follows: Figure 4 shown.

[0076] The results of the equivalent mechanical performance analysis and calculation method calculated in step 3 are compared with the above experimental results and the results of the general analysis and calculation method and verified as follows:

[0077] like Figure 4 As shown, from the comparison of the obtained stress-strain curves, it can be seen that the general analysis and calculation method is accurate, and the simulation results of the equivalent mechanical performance analysis method are close to the experimental results. The relative error of the specific energy absorption calculated by the equivalent mechanical performance analysis method and the experimental results is 3.24%, and the relative error of the specific Young's modulus is 1.71%, which can verify the accuracy of this method.

[0078] Comparing the computational efficiency of this equivalent mechanical performance analysis method with that of the general analysis and calculation method, the number of grids of the equivalent mechanical performance analysis method and the general analysis and calculation method are 245253 and 4325688 respectively, which is a 94.33% reduction in the number of grids of this method. The calculation time is 2.5h and 53.4h respectively, which is a 95.32% reduction in the calculation time. This verifies the high efficiency of this method.

[0079] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for analyzing the equivalent mechanical performance of a two-phase TPMS lattice structure, characterized in that: The specific steps include: S1. Select two materials, soft phase material and hard phase material, for dual-phase design, and perform dog-bone tensile tests on the selected materials to obtain their dog-bone tensile engineering stress-strain curves, thereby obtaining material performance parameters: stiffness E, Poisson's ratio ν and yield stress σ Y , and calculate the stiffness matrix of the two materials respectively to obtain the stiffness matrix coefficient; S2. The two materials are equivalent to one material according to the equivalent theory, and the stiffness matrix coefficients of the equivalent material are calculated based on the stiffness matrix coefficients of the two materials obtained in step S1, and then the engineering constants are obtained; at the same time, the effective mass density and yield stress of the equivalent material are calculated; S3. Generate the basic surface configuration of the TPMS lattice structure based on the mathematical control equation of the three-period minimal surface, then establish the surface model of the TPMS structure in the finite element software, divide it into shell meshes and assign corresponding thicknesses to obtain a shell model, and use the equivalent material parameters obtained in step S2: engineering constants, effective mass density and yield stress as inputs to perform quasi-static compression numerical simulation to obtain the mechanical response of the structure, analyze its deformation mode and stress-strain curve during the quasi-static compression process, and calculate its related mechanical properties.

2. The equivalent mechanical performance analysis method according to claim 1, characterized in that: In the step S1, the soft phase material is thermoplastic polyurethane.

3. The equivalent mechanical performance analysis method according to claim 1, characterized in that: In the step S1, the hard phase material is polylactic acid.

4. The equivalent mechanical performance analysis method according to claim 1, characterized in that: In the step S1, the volume ratio of the soft phase material to the hard phase material is 1:

1.

5. The equivalent mechanical performance analysis method according to claim 1, characterized in that: In step S1, a dog-bone tensile test is performed on the selected material, specifically: a uniaxial tensile test is performed on a universal testing machine, and the universal testing machine is equipped with a computer control and data acquisition system, so that force and displacement data can be automatically obtained; wherein the dog-bone tensile engineering stress-strain curve is obtained through the force-displacement curve, thereby obtaining the material performance parameters: stiffness E, Poisson's ratio ν, yield stress σ Y .

6. The equivalent mechanical performance analysis method according to claim 1, characterized in that: In step S1, the stiffness matrix of the material is calculated by the following formula:

7. The equivalent mechanical performance analysis method according to claim 1, characterized in that: Represent the stiffness matrix coefficients of the soft phase material and the hard phase material, respectively, v t 、v p Respectively represent the volume fractions of the soft phase material and the hard phase material. The stiffness matrix coefficient of the equivalent material after the two materials are equivalent to one material is calculated by the following formula: After obtaining the stiffness matrix from the stiffness matrix coefficient, the flexibility matrix is ​​obtained by inverting the stiffness matrix, S nn is the flexibility matrix coefficient, and the engineering constant is calculated by the following formula: Among them, E1, E2, and E3 are the elastic moduli of the material in the 1st, 2nd, and 3rd elastic principal directions respectively; ν ij The negative value of the ratio of the strain in the i direction to the strain in the j direction when there is only a positive stress in the j direction without other stress components is called Poisson's ratio; G 23 , G 31 , G 12 They are the shear elastic moduli in the 2-3, 3-1, and 1-2 planes respectively.

8. The equivalent mechanical performance analysis method according to claim 1, characterized in that: The effective mass density and yield stress are calculated by the following formula: in, are the effective mass density and yield stress of the equivalent material, ρ p , t are the mass densities of the hard phase material and the soft phase material, σ Y p , σ Y t are the yield stresses of the hard phase material and the soft phase material, respectively, v p 、v t are the volume fractions of the hard phase material and the soft phase material, respectively.

9. The equivalent mechanical performance analysis method according to claim 1, characterized in that: The basic surface configuration of the three-dimensional TPMS lattice structure generated based on the mathematical control equation of the three-periodic minimal surface is as follows: Select the Gyroid surface, whose mathematical control equation is: F Gyroid (x,y,z)=sin(x)cos(y)+sin(z)cos(x)+sin(y)cos(z)=0 According to actual needs, the size, thickness and array quantity of the minimal surface unit cell are determined, and the software Matlab is used for drawing and modeling to obtain the basic surface configuration of the three-dimensional TPMS lattice structure.

10. An application of the equivalent mechanical performance analysis method of the dual-phase TPMS lattice structure according to any one of claims 1 to 9 in analyzing and calculating mechanical properties in the field of material structure.

Images