An equivalent mechanical performance analysis method for a dual-phase TPMS lattice structure and its application

Abstract

This invention discloses an equivalent mechanical performance analysis method for a biphase TPMS lattice structure and its application, belonging to the field of materials structure technology. This invention treats the two materials in a biphase TPMS lattice structure as a single material using equivalent theory. Since shell elements can be used to build the model for calculation when simulating with a single material, and the shell model has only one layer of elements on the curved wall thickness, the number of model elements is greatly reduced, and the coupling effect between the two materials does not need to be considered. Therefore, the simulation calculation efficiency is improved, and its effectiveness has been verified. This invention innovatively applies the equivalent calculation method of composite material plates to the curved surface of this structure, significantly improving the calculation speed and efficiency while ensuring the accuracy of the calculation analysis. Compared with the general analysis calculation method using solid element modeling, the calculation time is reduced by 95.32%, showing significant application prospects.

Description

Technical Field

[0001] This invention belongs to the field of materials structure technology, specifically relating to an equivalent mechanical performance analysis method for a two-phase TPMS lattice structure and its application. Background Technology

[0002] In modern engineering, the speed and efficiency of analytical calculations are important issues. Researchers have been working to improve the efficiency of practical engineering, reduce the time cost of analytical calculations, shorten the research and development cycle, and improve the quality of analytical calculations through advanced computing technologies and methods.

[0003] In material structure design, combining biphase and TPMS lattice structures can achieve better mechanical properties. General analytical methods for analyzing the mechanical properties of biphase TPMS lattice structures first establish a solid mesh model of the structure, then assign material properties to the locations of the two materials, and finally couple the four layers together through constraints for numerical simulation. This method offers good accuracy, but the large mesh volume inherent in multi-cell array structures, coupled with the presence of two materials in the thickness due to the biphase design, necessitates a significantly larger mesh in the thickness direction compared to single-material structures to ensure accuracy. This substantial increase in mesh count leads to low efficiency, long computation time, and high computational resource consumption in the mechanical property analysis of biphase TPMS lattice structures, making it difficult to meet the needs of practical engineering. Therefore, the analysis methods for the mechanical properties of biphase TPMS lattice structures still require further development and breakthroughs. Summary of the Invention

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

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0006] This invention provides a method for analyzing the equivalent mechanical properties of a two-phase TPMS lattice structure, the specific steps of which include:

[0007] S1. Two-phase design was carried out using both soft and hard phase materials. Tensile tests were conducted on dog bone components for each material to obtain their stress-strain curves. From this, the material property parameters were obtained: stiffness E, Poisson's ratio ν, and yield stress σ. Y Then, the stiffness matrices of the two materials were calculated separately, and the stiffness matrix coefficients were obtained.

[0008] S2. Using the equivalence theory, the two materials are equivalent to one material. Based on the stiffness matrix coefficients of the two materials obtained in step S1, the stiffness matrix coefficients of the equivalent material are calculated, 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. Based on the three-period minimal surface mathematical control equation, the basic surface configuration of the TPMS lattice structure is generated. Then, the surface model of the TPMS structure is established in the finite element software, divided into shell meshes with corresponding thicknesses to obtain the shell model. The equivalent material parameters obtained in step S2, namely engineering constants, effective mass density and yield stress, are used as inputs to perform quasi-static compression numerical simulation to obtain the mechanical response of the structure. The deformation mode and stress-strain curve during the quasi-static compression process are analyzed, and its relevant mechanical properties are calculated.

[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).

[0012] Soft phase materials have a buffering and energy absorption function, while hard phase materials have 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 equipped with a computer control and data acquisition system, which can automatically obtain force and displacement data. The stress-strain curve of the dog bone tensile test is obtained from the force-displacement curve, thereby obtaining the material performance parameters: stiffness E, Poisson's ratio ν, and yield stress σ. Y .

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

[0016]

[0017] According to the above plan, V represents the stiffness matrix coefficients of the soft phase material and the hard phase material, respectively. t v p These represent the volume fractions of the soft phase material and the hard phase material, respectively. The stiffness matrix coefficients of the equivalent material after converting two materials into one are calculated using the following formula:

[0018]

[0019]

[0020] After obtaining the stiffness matrix from the stiffness matrix coefficients, the flexibility matrix is ​​obtained by inverting the stiffness matrix, S. nn For the compliance matrix coefficients, the engineering constants are calculated using the following formula:

[0021]

[0022] Wherein, E1, E2, and E3 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 strain in direction i to strain in direction j when only a normal stress is applied in direction j without other stress components is called Poisson's ratio; G 23 , G 31 , G 12 These are the shear moduli in the planes 2-3, 3-1, and 1-2, respectively.

[0023] According to the above scheme, the effective mass density and yield stress can be calculated using the following formulas:

[0024]

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

[0026] According to the above scheme, the basic surface configuration for generating the three-dimensional TPMS lattice structure based on the mathematical governing equations of the three-period minimal surface is as follows:

[0027] Choosing a Gyroid-type surface, its mathematical governing equations are:

[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-period minimal surface, x, y, and z typically represent coordinates in three-dimensional space. Specifically, these coordinates define the position of each point on the surface;

[0030] Based on actual needs, the size, thickness, and array number of the minimal surface unit cell are determined, and the basic surface configuration of the three-dimensional TPMS lattice structure is obtained by using the software Matlab for drawing and modeling.

[0031] This paper provides an application of the equivalent mechanical property analysis method for the above-mentioned two-phase TPMS lattice structure in the field of material structure analysis and computation of mechanical properties.

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

[0033] This invention provides an equivalent mechanical performance analysis method for a two-phase TPMS lattice structure. The two materials in the two-phase TPMS lattice structure are equivalently represented as a single material using equivalent theory. Since shell elements can be used to build the model for calculation when simulating with a single material, and the shell model has only one layer of elements on the curved wall thickness, the number of model elements is greatly reduced. Furthermore, the coupling effect between the two materials does not need to be considered, thus improving the computational efficiency of the simulation calculation, and its effectiveness has been verified. This invention innovatively applies the equivalent calculation method of composite material plates to the curved surface of this structure, significantly improving the calculation speed and efficiency while ensuring the accuracy of the calculation analysis. Compared with general analysis methods using solid element modeling, the calculation time is reduced by 95.32%, demonstrating significant application potential. Attached Figure Description

[0034] Figure 1 This is a flowchart of the equivalent mechanical performance analysis method for the biphase TPMS lattice structure in an embodiment of the present invention.

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

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

[0037] Figure 4 This is a comparison diagram of mechanical properties in an embodiment of the present invention. Detailed Implementation

[0038] The technical solutions of the embodiments of the present invention will be further described below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely for explaining the present invention and are not intended to limit the present invention. Furthermore, it should be noted that, for ease of description, only the parts related to the present invention are shown in the accompanying drawings, and not all of them.

[0039] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0040] Example 1

[0041] 1) Select two materials for two-phase design, and conduct tensile tests on dog bone parts for the selected materials. After obtaining their performance curves, calculate the stiffness matrix of the two materials respectively.

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

[0043] To obtain the relevant material parameters for the mechanical properties of soft-phase and hard-phase materials, uniaxial tensile tests were performed on a universal testing machine equipped with a computer control and data acquisition system, which could automatically obtain force and displacement data. The stress-strain curve of the dog bone component was derived from the force-displacement curve, and the resulting material property parameters were: for TPU material, stiffness E... t =59.6 MPa, Poisson's ratio ν t =0.4, yield stress σ Y t =6.4 MPa; For PLA material, stiffness E p =1390 MPa, Poisson's ratio ν p =0.4, yield stress σ Y p =44 MPa.

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

[0045]

[0046] The stiffness matrix of TPU material is as follows:

[0047]

[0048] The stiffness matrix of PLA material is as follows:

[0049]

[0050] 2) Using the equivalence theory, soft phase materials and hard phase materials are equivalent to one material, and the properties of the equivalent material are calculated.

[0051] V represents the stiffness matrix coefficients of the soft phase material and the hard phase material, respectively. t v p These represent the volume fractions of the soft phase material and the hard phase material, respectively, both of which are 50% here. The stiffness matrix coefficients of the equivalent material after converting two materials into one are calculated using the following formula:

[0052]

[0053]

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

[0055]

[0056] Inverting the stiffness matrix yields the flexibility matrix, S nn For the coefficients of the compliance matrix:

[0057]

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

[0059]

[0060] Wherein, E1, E2, and E3 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 strain in direction i to strain in direction j when only a normal stress is applied in direction j without other stress components is called Poisson's ratio; G 23 , G 31 , G 12 These are the shear moduli in the planes 2-3, 3-1, and 1-2, respectively.

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

[0062]

[0063] Where, ρ p ρ t These are the mass densities of the two materials, σ Y p σ Y t The yield stresses of the two materials are v and v, respectively. p v t These represent the volume fractions of the two materials, respectively.

[0064] 3) The basic surface configuration of the TPMS lattice structure is generated based on the mathematical governing equations of the three-period minimal surface, and the model is simulated using the finite element method with equivalent material parameters; specifically:

[0065] Choosing a Gyroid-type surface, its mathematical governing equations are:

[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-period minimal surface, x, y, and z typically represent coordinates in three-dimensional space. Specifically, these coordinates define the position of each point on the surface.

[0068] Based on actual needs, the size of the minimal surface unit cell was determined to be 12.5 mm, the thickness to be 2.4 mm, and the array number to be 4*4*4 in the XYZ direction. Matlab was used to draw and model 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 was established in the finite element method (FEM) software. This surface model is a two-dimensional surface structure without thickness. It was divided into a shell mesh with corresponding thickness to obtain a shell model. Since this model is a two-dimensional shell structure with no thickness in the normal direction of the surface, the number of meshes in this model is relatively small. The equivalent material property parameters obtained in step 2—engineering constants, effective mass density, and yield stress—were used as inputs for a quasi-static compression numerical simulation. This model has a relatively fast calculation speed, with a calculation time of 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. Its relevant mechanical properties can be calculated, and the relevant calculation results are as follows: Figure 4 As shown.

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

[0071] 1) The specific steps of the experiment for the biphasic structure in Example 1 are as follows:

[0072] The material filling method for this structure involves dividing the basic curved surface configuration of the TPMS lattice structure, whose thickness was determined in step 3, into four equal parts along the surface thickness direction, and alternately filling it with soft and hard phase materials to obtain a two-phase TPMS lattice structure, as shown below. Figure 3 As shown, samples were prepared using FFF (Fused Filament Fabrication) printing technology, and printed using a dual-nozzle printer. The left and right nozzles of this printer simultaneously print different materials, ultimately producing a two-phase TPMS lattice structure sample.

[0073] The obtained samples underwent performance testing, specifically: a quasi-static compression test was conducted on a universal testing machine at a set loading speed. The engineering stress of the configuration was calculated based on the compressive load data obtained from the sensor, while the engineering strain was calculated based on the original displacement data of the indenter; its stress-strain curve and related mechanical property calculation results are as follows: Figure 4 As shown.

[0074] 2) The calculation steps of the general analytical calculation method for the two-phase structure as in Example 1 are as follows:

[0075] A solid model of the two-phase TPMS lattice structure was established, and the model was meshed. Since the model has four material layers, layer-by-layer meshing was necessary to ensure computational accuracy, resulting in a large number of solid meshes. Material properties were assigned to the locations of the two materials, and the four material layers were coupled together through constraints for quasi-static compression numerical simulation, which took 53.4 hours. The simulation yielded the mechanical response of the structure, allowing analysis of its deformation modes and stress-strain curves during quasi-static compression, and calculation of its relevant mechanical properties. The relevant calculation results are as follows: Figure 4 As shown.

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

[0077] like Figure 4 As shown, the comparison of the obtained stress-strain curves shows 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 verifies 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 for the equivalent mechanical performance analysis method is 245,253 and 4,325,688 respectively. Compared with the general analysis and calculation method, the number of grids for this method is reduced by 94.33%, and the computation time is 2.5h and 53.4h respectively. Compared with the general analysis and calculation method, the computation time for this method is reduced by 95.32%, which verifies the high efficiency of this method.

[0079] The above are merely 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 within the protection scope of the present invention.

Claims

1. A method for analyzing the equivalent mechanical properties of a two-phase TPMS lattice structure, characterized in that, The specific steps include: S1. Two-phase design was performed using both soft and hard phase materials. Tensile tests were conducted on dog-bone components for each material. Specifically, uniaxial tensile tests were performed on a universal testing machine equipped with a computer control and data acquisition system to automatically obtain force and displacement data. The stress-strain curve of the dog-bone component was derived from the force-displacement curve, thus obtaining the material performance parameters: stiffness. Poisson's ratio and yield stress The stiffness matrices of the two materials were calculated separately to obtain the stiffness matrix coefficients; where: the soft phase material is thermoplastic polyurethane, the hard phase material is polylactic acid, and the volume ratio of the soft phase material to the hard phase material is 1:1; S2. Using the equivalence theory, the two materials are equivalent to one material. Based on the stiffness matrix coefficients of the two materials obtained in step S1, the stiffness matrix coefficients of the equivalent material are calculated, 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. Based on the three-period minimal surface mathematical control equation, the basic surface configuration of the TPMS lattice structure is generated. Then, the surface model of the TPMS structure is established in the finite element software, divided into shell meshes with corresponding thicknesses to obtain the shell model. The equivalent material parameters obtained in step S2, namely engineering constants, effective mass density and yield stress, are used as inputs to perform quasi-static compression numerical simulation to obtain the mechanical response of the structure. The deformation mode and stress-strain curve during the quasi-static compression process are analyzed, and its relevant mechanical properties are calculated.

2. The equivalent mechanical performance analysis method according to claim 1, characterized in that, In step S1, the stiffness matrix of the material is calculated using the following formula: 。 3. The equivalent mechanical performance analysis method according to claim 1, characterized in that, , These represent the stiffness matrix coefficients for the soft phase material and the hard phase material, respectively. , These represent the volume fractions of the soft phase material and the hard phase material, respectively. The stiffness matrix coefficients of the equivalent material after converting two materials into one are calculated using the following formula: After obtaining the stiffness matrix from the stiffness matrix coefficients, the flexibility matrix is ​​obtained by inverting the stiffness matrix. For the compliance matrix coefficients, the engineering constants are calculated using the following formula: ， ， ； ， ， ； ， ， ； in, , , These are the elastic moduli of the material in the 1st, 2nd, and 3rd principal elastic directions, respectively; The negative value of the ratio of strain in direction i to strain in direction j when a normal stress is applied only in direction j without other stress components is called Poisson's ratio. , , These are the shear moduli in the planes 2-3, 3-1, and 1-2, respectively.

4. The equivalent mechanical performance analysis method according to claim 1, characterized in that, The effective mass density and yield stress are calculated using the following formulas: in, , These are the effective mass density and yield stress of the equivalent material, respectively. , The mass densities are those of the hard phase material and the soft phase material, respectively. , These represent the yield stresses of the hard-phase material and the soft-phase material, respectively. , These represent the volume fractions of the hard phase material and the soft phase material, respectively.

5. The equivalent mechanical performance analysis method according to claim 1, characterized in that, The basic surface configuration for generating a three-dimensional TPMS lattice structure based on the mathematical governing equations of a three-period minimal surface is as follows: Choosing a Gyroid-type surface, its mathematical governing equations are: Based on actual needs, the size, thickness, and array number of the minimal surface unit cell are determined, and the basic surface configuration of the three-dimensional TPMS lattice structure is obtained by using the software Matlab for drawing and modeling.

6. The application of the equivalent mechanical property analysis method of the two-phase TPMS lattice structure according to any one of claims 1-5 in the field of material structure analysis and computation of mechanical properties.

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