Multi-scale Modeling and Simulation Method for a Porous Composite Material

Abstract

The present invention relates to a multi-scale modeling and simulation method for a porous composite material, comprising the following steps: S1. Establish a multi-particle model for each interface in the composite material according to the material composition of the composite material; S2. Select a potential function capable of describing the interaction between atoms in the system, and perform systematic relaxation, thermodynamic, and kinetic analyses on the multi-particle model by using the molecular dynamics method; S3. Calculate and obtain the mechanical and thermal properties related to each interface in the composite material by using the molecular dynamics method; S4. Establish a representative volume element model for the composite material; S5. Perform finite element analysis on the representative volume element. Compared with the prior art, the present invention can be used for simulation studies on the relationship between the micro-structure and physical properties of porous composite materials under different working conditions, such as exploring the effects of interface strength, interface thermal conductivity, pores, particle sizes, distributions, and contents on parameters such as the thermal conductivity, elastic modulus, yield strength, stress distribution, and conductivity of the composite material.

Description

Technical Field

[0001] The present invention relates to the field of analysis of porous composites, and particularly to a multi-scale modeling and simulation method for porous composites. Background Art

[0002] Porous composites use porous materials as supports and modify or load other functional substances, integrating the advantages of inorganic materials and organic polymer materials. They are a new type of material with excellent performance and are increasingly widely used in catalysts, electrochemistry, biomedicine, etc.

[0003] The membrane electrode is one of the core components of a proton exchange membrane fuel cell and is a typical porous composite. It consists of a Pt catalyst, a carbon carrier, and an ionomer. Among them, the catalyst particles are the reaction active devices, the carbon carrier plays a role in supporting the catalyst, and the ionomer serves as the matrix and transports the protons generated by the reaction; the pores are also important features of the membrane electrode structure and play an important role in transporting reaction gases and water. The multi-phase interface including the matrix, functional particles, pores, etc. is an important place for such porous composites to exert their performance. The quality of the interface performance and the delamination, cracks, etc. of the interface directly affect the performance of the material.

[0004] However, restricted by the complex microstructure of most porous materials such as membrane electrodes and the limitations of microscopic interface characterization methods, it is difficult to establish the relationship between the microstructure, microscopic interface and material properties through experiments. Computer simulation technology can accurately predict the relationship between the microscopic model and macroscopic properties of materials, providing guidance for material optimization design and has become an important part of materials science research.

[0005] Currently, some researchers have applied the finite element method to analyze the structure and properties of some composites. For example, in the paper "Numerical investigation of delamination onset and propagation in catalyst layers of PEM fuel cells under hygrothermal cycles" published by Yixiang Zhang et al., a microscopic model of the catalyst layer was established, and the finite element analysis was used to calculate some mechanical behaviors of the catalyst layer under hygrothermal loads, which can reflect the relationship between the mesoscopic structure and macroscopic mechanical behavior of the material to a certain extent. However, its disadvantage is that it is limited to the mesoscopic scale, lacking microscopic aspects such as the prediction of microscopic interface properties, and the setting of interface contact properties is mainly estimated, so the accuracy is relatively low.

[0006] Therefore, to accurately predict the mechanical, thermal and other related properties of porous composites, it is urgent to develop a multi-scale research method that can accurately calculate the microscopic interface properties of materials, make up for the lack of material properties in finite element simulations, build a bridge between the microscopic and mesoscopic scales, and finally accurately predict the macroscopic properties. Summary of the Invention

[0007] The purpose of the present invention is to provide a multi-scale modeling and simulation method for porous composites to overcome the defects existing in the above-mentioned prior art.

[0008] The purpose of the present invention can be achieved by the following technical solutions:

[0009] Starting from molecular dynamics, the present invention calculates and obtains the microscopic properties of materials in terms of mechanics and thermotics, which are difficult to characterize experimentally. On this basis, a representative volume element model of the material is established to build a bridge between the microscopic and mesoscopic scales. Finally, the relationship between the microscopic structure and macroscopic properties of the material is established through finite element analysis. The specific solutions are as follows:

[0010] A multi-scale modeling and simulation method for porous composites, the method comprising the following steps:

[0011] S1. According to the material composition of the composite material, establish a multi-particle model for each interface in the composite material;

[0012] S2. Select a potential function that can describe the interaction between atoms in the system, and use the molecular dynamics method to perform system relaxation and thermodynamic and kinetic analyses on the multi-particle model;

[0013] S3. Calculate and obtain the mechanical and thermal related properties of each interface in the composite material through the molecular dynamics method;

[0014] S4. Make model assumptions and geometric settings for the composite material, establish a representative volume element model, and the interface properties of the model are provided by the molecular dynamics results;

[0015] S5. Perform finite element analysis on the representative volume element.

[0016] Further, step S1 includes the following specific steps:

[0017] S101. According to the molecular formulas of each phase, establish multi-particle models respectively;

[0018] S102. Combine the multi-particle models that make up the interface, describe the interaction force between interface atoms with van der Waals forces, and the model spacing during combination shall not be less than the distance range of covalent bond interaction between atoms.

[0019] Further, the parameters of the system relaxation in step S2 include annealing, energy minimization, isothermal isobaric ensemble temperature control conditions, and neighbor list.

[0020] Further, when calculating in step S3, the system is divided into n layers, and the interfacial layer is at least separately divided into one layer, and the corresponding thermodynamic quantities and other properties at the interface are calculated.

[0021] Further, in step S3, the interfacial mechanical properties include tensile strength and shear strength.

[0022] Further, the specific method for calculating the interfacial thermal conductivity is as follows: The system is divided into n layers (n = 20, 40, 80, etc.), the middle layer is set as the heat source, and a constant heat flux P is applied; the two end layers of the system are set as the cold sources, and the same heat flux P is removed, keeping the total energy of the system unchanged. After the heat transfer reaches stability, the temperature of each layer is statistically analyzed, and the interfacial thermal conductivity is calculated according to the temperature difference of the interfacial layer. The formula for the thermal conductivity is:

[0023]

[0024] where A is the interfacial contact area, dT / dz is the temperature gradient in the heat transfer direction, and k is the thermal conductivity.

[0025] Further, in step S4, in the representative volume element model, the pores, matrix phase, inclusion phase, and interface phase of the porous composite material, where the thickness of the interface phase is assumed to be 0, and the interface properties are given through contact properties.

[0026] Further, step S4 includes the following specific steps:

[0027] S1001. Set the matrix phase, inclusion phase, interface phase, and pores in 3D modeling software. Set the matrix phase as a square structure, and set the inclusion phase and pores as circles.

[0028] S1002. Establish a matrix phase model. Use Boolean subtraction to remove a circle with a diameter equal to the size of the pore at the center coordinates of the pore in the matrix phase to obtain a hole. Similarly, use Boolean subtraction to remove a circle equal to the size of the inclusion phase, and insert the inclusion phase in the excavated circular area.

[0029] S1003. Set the periodic boundary conditions according to the following formula:

[0030] u r -u l = u1 - u0 (2)

[0031] u t -u b = u2 - u0 (3)

[0032] u3 - u2 = u1 - u0 (4)

[0033] where ut and u b and u l and u r are the displacements of points on the upper, lower, left, and right boundaries of the square, respectively, and u0, u1, u2, and u3 are the displacements of the four vertices of the lower left, lower right, upper left, and upper right, respectively;

[0034] S1004. Establish the contact between the inclusion phase and the matrix phase, and endow the interface phase with properties such as the interface strength and interface thermal conductivity obtained from molecular dynamics calculations.

[0035] Compared with the prior art, the present invention has the following advantages:

[0036] (1) Based on the actual microstructure and mechanical properties of the material, the present invention first establishes a multi-particle model of the porous composite material, calculates the thermal and mechanical properties of various interfaces at the atomic and molecular scales, and uses them for the setting of interface properties in the representative volume element. Finally, through the finite element analysis method, the relationship between the microstructure and macroscopic properties of the composite material is established, which will provide a model reference for optimizing the microstructure and properties of the porous composite material;

[0037] (2) The present invention can be used for the simulation study of the relationship between the microstructure and physical properties of the porous composite material under different working conditions, such as the influence laws of interface strength, interface thermal conductivity, pores, particle sizes, distribution, and content on parameters such as the thermal conductivity, elastic modulus, yield strength, internal stress distribution, and conductivity of the composite material. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 is the flow chart of the method of the present invention;

[0039] Figure 2 is the schematic diagram of the multi-particle model of graphene / Nafion in the embodiment;

[0040] Figure 3 is the schematic diagram of calculating the interface tensile strength by the molecular dynamics method in the embodiment;

[0041] Figure 4 is the schematic diagram of the interaction force-separation distance curve during the stretching process in the embodiment;

[0042] Figure 5 is the schematic diagram of the principle of calculating the interface thermal conductivity in the embodiment;

[0043] Figure 6 is the temperature distribution diagram obtained after the heat transfer reaches equilibrium in the embodiment;

[0044] Figure 7 is the representative volume element (RVE) model established in the embodiment;

[0045] Figure 8 Property settings for interface contact of the RVE model in the embodiment

[0046] Figure 9 Stress nephogram and stress-strain curve of the RVE under tension in the embodiment

[0047] Figure 10 Temperature distribution nephogram of the RVE after heat transfer stabilization in the embodiment Detailed implementation mode

[0048] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented on the premise of the technical solution of the present invention, and detailed implementation manners and specific operation processes are given, but the protection scope of the present invention is not limited to the following embodiments.

[0049] Embodiment

[0050] A multi-scale modeling and simulation method for a porous composite material, as Figure 1 , the method includes the following steps:

[0051] S1. According to the material composition of the composite material, establish multi-particle models of each interface in the composite material;

[0052] S2. Select a potential function that can describe the interaction between atoms in the system, and use the molecular dynamics method to perform system relaxation and thermodynamic and kinetic analyses on the multi-particle model;

[0053] S3. Calculate and obtain the mechanical and thermal properties related to each interface in the composite material through the molecular dynamics method;

[0054] S4. Make model assumptions and geometric settings for the composite material, establish a representative volume element model, and the interface properties of the model are provided by the molecular dynamics results;

[0055] S5. Perform finite element analysis on the representative volume element.

[0056] In step S1, when establishing the multi-particle model of the composite material, first establish multi-particle models according to the molecular formulas of each phase, as Figure 2 the models established respectively are the Nafion polymer (a) and graphene (b) models; then combine the two multi-particle models that make up the interface, and describe the interaction force between atoms on both sides of the interface with van der Waals forces. When combining, the distance between the two models shall not be less than the distance range of covalent bond interaction between atoms. The multi-particle model for calculating interface properties is as Figure 2 (c) shown.

[0057] In step S2, a potential function that can accurately describe the interactions between atoms in the system is selected. In this example, the selected potential function is UFF (Universal Force Field), which can describe the interactions between almost all atoms in the periodic table. During relaxation, energy optimization, annealing, and equilibrium constraints in the isothermal isobaric ensemble are included for the system. Among them, conjugate gradient method is used for energy optimization, and the iteration stops when the energy change between two adjacent iteration steps divided by the total energy is less than 10 -4 or the magnitude of the global force vector is less than 10 -6 ; Annealing is 5 cycles of heating from 300K to 600K and then cooling from 600K to 300K at a pressure of one atmosphere, with a step size of 1fs and 0.4ns for each cycle.

[0058] In step S3, the tensile strength, shear strength, and interfacial thermal conductivity of the graphene / Nafion molecular interface are calculated. The calculation of tensile strength and shear strength includes the following steps:

[0059] A. Apply a constant loading speed V of 0.3 Å / fs to the entire graphene molecule in the direction away from the Nafion molecule, and track the interfacial distance and interaction force between graphene and Nafion during the stretching process, as Figure 3 shown;

[0060] B. Separate until the interaction force is completely 0, and make a curve of interaction force - separation distance. Take the maximum force as the force required to completely separate the interface, as Figure 4 shown;

[0061] C. Divide the maximum force by the contact area to obtain the tensile strength;

[0062] For the shear process, just change the direction of the velocity load to the shear direction.

[0063] The calculation of thermal conductivity includes the following steps:

[0064] a. Divide the system into 20 layers, with at least one layer separated for the interface layer alone;

[0065] b. Set the middle layer as the heat source and apply a constant heat P; set the two end layers of the system as cold sources and remove the same heat P, keeping the total energy of the system unchanged until the heat transfer reaches stability, as Figure 5 shown;

[0066] c. Statistically analyze the temperature of each layer, and obtain dT / dz based on the temperature difference of the interface layer, as Figure 6 shown, and calculate the interfacial thermal conductivity according to formula (1).

[0067] The establishment of the representative volume element model (RVE) in step S4 includes the following steps:

[0068] S1001. Set the matrix phase Nafion, inclusion phase Pt / C, and pores in 3D modeling software. Set the matrix phase to a square structure and the inclusion phase and pores to circular shapes.

[0069] S1002. Establish a matrix phase model with dimensions of 100 nm × 100 nm. At the center coordinates of the pores in the matrix phase, successively remove circles with a diameter of 30 nm using Boolean subtraction operations to obtain the pores. Similarly, remove circles with a diameter of 20 nm using Boolean subtraction operations and insert the inclusion phase in the circular area with a diameter of 20 nm that has been removed. Finally, form 5 holes and 4 Pt / C particles, as Figure 7 shown. The structural parameter settings of the RVE model are shown in Table 1.

[0070] Table 1 Structural parameter settings of the RVE model

[0071]

[0072] S1003. Set the periodic boundary conditions according to equations (2), (3), and (4);

[0073] S1004. Establish the contact between the inclusion phase and the matrix phase. Select the inclusion phase as the master surface and the matrix phase as the slave surface, and adjust the initial contact tolerance to 0.1 to ensure complete contact between the inclusion and the matrix. Assign properties such as the interface strength and interface thermal conductivity obtained from molecular dynamics calculations to the interface contact, as Figure 8 shown.

[0074] In step S5, calculate the elastic modulus of the representative volume element as follows:

[0075] The assigned material properties are shown in Table 2;

[0076] Table 2 Material properties

[0077]

[0078] Select the static analysis step with automatic step size control and a minimum step size of 10 -5 s;

[0079] Perform mesh division: Set the element size of the four sides of the matrix phase to 0.5, the element size at the contact between the matrix and the holes and the inclusion phase to 0.3. The element shape is a 2D quadrilateral, and use the central axis algorithm to automatically divide the mesh. Set the element size of the inclusion phase to 0.5, slightly larger than the element size at the contact, and the shape is a 2D tetrahedron, and use the wavefront method to automatically divide the mesh.

[0080] Finally, apply a displacement load of 10 nm in both the X and Y directions to the RVE model, solve the problem, and output the stress-strain curve through the post-processing module ( Figure 9a) and the stress nephogram ( Figure 9 as shown in b and 9c).

[0081] By analyzing the stress-strain curve, it can be known that the elastic modulus of the RVE model is 91.3 MPa. The initial stress continuously increases with the increase of strain, and the stress is mainly concentrated at the pore edge; when the strain reaches 0.142 ( Figure 9 c), there is a sudden drop in stress. It can be seen from the stress nephogram that this sudden drop is caused by the interface detachment between the inclusion phase and the matrix phase. At this time, the stress is mainly concentrated at the crack tip of the interface, and the crack continuously expands. This can provide a reference for the optimal design of porous composites and the research on the interface separation mechanism.

[0082] In step S5, to calculate the thermal conductivity of the representative volume element, only need to change the element type to a heat transfer element, change the load to a temperature load, set the left boundary to 80 °C, set the right boundary to 25 °C, and perform heat transfer simulation. Finally, the temperature distribution nephogram is as Figure 10 shown. It can be seen that due to the large thermal resistance at the interface, there is a large temperature difference at the junction of the inclusion phase and the matrix phase. In the actual process, due to the difference in the coefficient of thermal expansion, stress residues may be formed at the interface, which is more likely to cause interface separation in the actual stress-bearing engineering. Finally, the thermal conductivity of the model is calculated to be 0.101 W / (m·K) according to the steady-state heat flux.

[0083] In summary, the method of the present invention starting from molecular dynamics combined with finite element analysis provides a model reference for the interface separation mechanism and the interface heat transfer process at the micro-nano level. The established model can reflect the influence of the molecular interface strength and interface thermal conductivity of porous composites on interface separation, heat transfer and other behaviors, which is helpful to improve the design and processing technology of composites. It provides a model reference for the microstructure and thermodynamic properties of a series of materials that are difficult to analyze by experimental methods, saves experimental resources, provides convenience for research, and reduces research costs.

[0084] The present invention can be used for the simulation research on the relationship between the microstructure and physical properties of porous composites under different working conditions, such as the influence laws of interface strength, interface thermal conductivity, pores, particle sizes, distributions and contents on parameters such as the thermal conductivity, elastic modulus, yield strength, internal stress distribution and conductivity of composites.

[0085] The above is only a preferred embodiment of the present invention, and it is not a limitation of the present invention in other forms. Any person skilled in the art may use the disclosed technical content to make changes or modifications into equivalent embodiments with equivalent changes. However, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention without departing from the technical solution content of the present invention still belong to the protection scope of the technical solution of the present invention.

Claims

1. A multi-scale modeling and simulation method for a porous composite material, characterized in that, The method includes the following steps: S1. Establish a multi-particle model of each interface in the composite material according to the material composition of the composite material; S2. Select a potential function that can describe the interaction between atoms in the system, and use the molecular dynamics method to perform system relaxation, thermodynamic, and kinetic analyses on the multi-particle model; S3. Calculate the mechanical and thermal properties of each interface in the composite material through the molecular dynamics method; S4. Make model assumptions and geometric settings for the composite material, establish a representative volume element model, and the interface properties of the model are provided by the molecular dynamics results; S5. Perform finite element analysis on the representative volume element; Among them, in step S4, in the representative volume element model, the pores, matrix phase, inclusion phase, and interface phase of the porous composite material, where the thickness of the interface phase is assumed to be 0, and the interface properties are assigned through contact properties; Step S4 also includes the following specific steps: S1001. Set the matrix phase, inclusion phase, interface phase, and pores in 3D modeling software, set the matrix phase as a square structure, and set the inclusion phase and pores as circles; S1002. Establish a matrix phase model, use Boolean subtraction operation to remove a circle with a diameter equal to the pore size at the center coordinates of the pores in the matrix phase to obtain holes; similarly, use Boolean subtraction operation to remove a circle equal to the size of the inclusion phase, and insert the inclusion phase in the excavated circular area; S1003. Set the periodic boundary conditions according to the following formula: u r -u l = u1 - u0 (2) u t -u b = u2 - u0 (3) u3 - u2 = u1 - u0 (4) where u t , u b , u l , u r are the displacements of the points on the upper, lower, left, and right boundaries of the square, respectively, and u0, u1, u2, and u3 are the displacements of the four vertices at the lower left, lower right, upper left, and upper right, respectively; S1004. Establish the contact between the inclusion phase and the matrix phase, and assign the interface strength and interface thermal conductivity properties obtained from molecular dynamics calculations to the interface phase.

2. The multi-scale modeling and simulation method of a porous composite material according to claim 1, characterized in that Step S1 includes the following specific steps: S101. Establish multi-particle models respectively according to the atomic and molecular structures, sizes, and contents of each phase; S102. Combine the multi-particle models that make up the interface, describe the interaction forces between interface atoms with van der Waals forces, and the model spacing during combination shall not be less than the distance range of covalent bond interaction between atoms.

3. A multi-scale modeling and simulation method for a porous composite material according to claim 1, characterized in that, The parameters of the system relaxation described in step S2 include annealing, energy minimization, isothermal and isobaric ensemble temperature control conditions, and neighbor list.

4. A multi-scale modeling and simulation method for a porous composite material according to claim 1, characterized in that During the calculation in step S3, divide the system into n layers, and at least divide the interface layer into a single layer, and calculate the corresponding thermodynamic quantities and other properties at the interface.

5. A multi-scale modeling and simulation method for a porous composite material according to claim 1, characterized in that In step S3, the interface mechanical properties include tensile strength, shear strength, and the corresponding interface separation distance.

6. A multi-scale modeling and simulation method for a porous composite material according to claim 5, characterized in that, The specific method for calculating the interface mechanical properties is: apply a constant velocity load to the molecules on one side of the interface, calculate the interaction forces between the two sides of the molecules, separate until the interaction forces are completely 0, and make an interaction force-separation distance curve, and use the maximum force as the force required to completely separate the interface.

7. A multi-scale modeling and simulation method for a porous composite material according to claim 1, characterized in that In step S3, the interface thermal properties include interface thermal conductivity.

8. A multi-scale modeling and simulation method for a porous composite material according to claim 7, characterized in that The specific method for calculating the interface thermal conductivity is: divide the system into n layers, set the middle layer as the heat source, and apply a constant heat flux P; set the two end layers of the system as cold sources, remove the same amount of heat P, and keep the total energy of the system unchanged. After the heat transfer reaches stability, count the temperature of each layer, and calculate the interface thermal conductivity according to the temperature difference of the interface layer. The thermal conductivity calculation formula is: Where A is the interfacial contact area, dT / dz is the temperature gradient in the heat transfer direction, and k is the thermal conductivity.

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