Simulation method for adjusting mechanical property of solid electrolyte on surface of silicon negative electrode of lithium ion battery

Abstract

The invention provides a simulation method for adjusting the mechanical property of a solid electrolyte on the surface of a silicon negative electrode of a lithium ion battery. The method comprises the steps that S1, an SEI model is constructed, an atomic model constructed by software is adopted for simulation, and the construction process of the interface SEI membrane model on the surface of the silicon negative electrode of the lithium ion battery sequentially comprises the steps of constructing a silicon-based electrode material model, constructing an electrolyte solvent model and constructing an SEI membrane model; s2, performing molecular dynamics simulation by selecting a potential function; s3, carrying out mechanical property testing by determining the thickness of the SEI film and measuring the Young modulus of the SEI film model and the bulk modulus of the SEI film model; the mechanical property of the SEI film on the surface of the silicon negative electrode can be researched by using a molecular dynamics simulation method.

Description

Technical Field

[0001] The invention relates to the technical field of lithium ion battery performance optimization, in particular to a method for simulating mechanical properties of a solid electrolyte on a silicon negative electrode surface of a lithium ion battery. Background Art

[0002] Lithium-ion batteries are divided into negative electrode, positive electrode and electrolyte. During the initial reaction, a layer of material will be produced on the surface of the negative electrode, which is usually called solid electrolyte interface (SEI). This layer of solid electrolyte greatly affects the service life and safety of lithium-ion batteries. Especially for silicon negative electrode, during the battery charging and discharging process, the silicon negative electrode will continuously embed and extract lithium atoms, resulting in a volume change of up to 400% of the silicon negative electrode, and the SEI film will be destroyed, thereby forming a new SEI film, further reducing the cycle life of lithium-ion batteries. Most of the current research focuses on the composition of the SEI film and the role of salts, solvents and additives in the formation and subsequent evolution of the SEI film. There are relatively few mechanical measurements of the SEI film. The research methods of interfacial SEI film mainly include experimental and simulation methods. In the experiment, the SEI film needs to be peeled off from the electrode for operation, which will reduce the accuracy of the test to a certain extent. Due to the limitations of experimental technical methods, computer simulation technology is increasingly being introduced into the study of SEI film, providing structural evolution and electrochemical information. In recent years, the Reactive Force Field (ReaxFF) has emerged, which can simulate the evolution of SEI film structure and composition, making the molecular dynamics simulation (MD) SEI film generation method more credible.

[0003] Currently, no one has conducted a simulation of the mechanical properties of the SEI film on the surface of the silicon negative electrode, or even a simulation of the SEI formation process on the surface of the silicon negative electrode.

[0004] The present invention proposes a simulation scheme for studying the mechanical properties of the SEI film generated by using silicon as the negative electrode of a lithium-ion battery and different solvents as electrolytes. The scheme described in the present invention mainly studies the effects of different solvent types, the concentration of silicon embedded lithium ions, externally applied electric fields and temperatures on the mechanical properties of the SEI film. Summary of the invention

[0005] The present invention proposes a simulation method for regulating the mechanical properties of a solid electrolyte on the surface of a silicon negative electrode of a lithium-ion battery, and can use a molecular dynamics simulation method to study the mechanical properties of a SEI film on the surface of a silicon negative electrode.

[0006] The present invention adopts the following technical solutions.

[0007] A simulation method for regulating the mechanical properties of a solid electrolyte on a silicon negative electrode surface of a lithium-ion battery, the method comprising the following steps:

[0008] Step S1, constructing a SEI model, using an atomic model constructed by software to simulate, the process of constructing an interface SEI film model on the surface of a silicon negative electrode of a lithium-ion battery, sequentially includes constructing a silicon-based electrode material model, constructing an electrolyte solvent model, and constructing a SEI film model;

[0009] Step S2, performing molecular dynamics simulation by selecting a potential function;

[0010] Step S3: Conduct mechanical property testing by determining the SEI film thickness, the SEI film model Young's modulus, and the SEI film model bulk modulus.

[0011] In step S1, the atomic model is constructed using Material Studio software.

[0012] When constructing a silicon-based electrode material model in step S1, the method is specifically as follows:

[0013] First build The box uses periodic boundary conditions p in the x and y directions and contraction boundary conditions s in the z direction. The area is set as a silicon block; the silicon block is set to contain 1152 silicon atoms, and the bottom The height of the silicon atoms is fixed, and the box is in the z direction. The area is filled with Li ion solution;

[0014] The silicon block and the Li ion solution were energy minimized using the conjugate gradient method, the simulation ensemble used the NVT ensemble, and then the Nose-Hoover heat bath method was used for relaxation;

[0015] When the simulation process needs to be accelerated, the equilibrium temperature is set to 1000K, the time for the two to relax separately is set to 10ps, the time step is set to 0.2fs, and then the initial lithium silicon model is output; on this basis, the initial model is still heated according to the above temperature control method, the simulation time is set to 200ps, and the z direction of the simulation result is intercepted from 0 to Li x The Si model is used as the silicon-based electrode material for subsequent simulation analysis; the final silicon-based electrode material contains 2215 lithium atoms and 559 silicon atoms, and the overall silicon-based battery material is approximately Li4Si.

[0016] Step S1: When constructing the electrolyte solvent model, the method is specifically as follows: assuming that the electrolyte solvent molecules used in the lithium-ion battery are ethylene carbonate C3H4O3 abbreviated as EC, dimethyl carbonate C3H6O3 abbreviated as DMC, propylene carbonate C4H6O3 abbreviated as PC, ethyl methyl carbonate C4H8O3 abbreviated as EMC, diethyl carbonate C5H6O3 abbreviated as DEC, 10 O6 or a mixture of one or more; when modeling, Material Studio software is first used to construct a single electrolyte solvent molecule, and then its built-in COMPASS force field is used to optimize the molecular configurations of EC, DMC, and PC to minimize their energy, and then LAMMPS (Large-scale Atomic / Molecular Massively Parallel Simulator) software is used to build a box, and a specified number of solvent molecules are randomly filled into the box; finally, the conjugate gradient method is used to relax and minimize the energy of the electrolyte solvent model, and then it is balanced under the NVT ensemble, with periodic boundary conditions p in the x and y directions and contractile boundary conditions s in the z direction, and a Nose-Hoover heat bath is used for temperature control, and the initial temperature and equilibrium temperature are both set to 500K.

[0017] In step S1, when constructing the SEI film model, the method is specifically as follows: the silicon-based electrode model and the electrolyte solvent model are merged under a suitable reaction force field, and a modeling process is set. During the merging, the lithium ions in the silicon-based electrode react with the solvent to generate a SEI film; the modeling process is set to be carried out under the isothermal and isobaric ensemble NPT, and the Nose-Hoover hot bath method is used for temperature control. The initial temperature is set to 500K, and the simulation relaxation time is set to 100ps.

[0018] In step S2, the potential function is used to set the motion mode of each atom in the model and to set the way of building chemical bonds between atoms; the ReaxFF reaction force field applicable to the atomic system is used as the potential function of the simulation, and the ReaxFF reaction force field is a force field that has been verified to correctly describe the reduction reaction between the electrolyte and the electrode material.

[0019] In step S3, when determining the SEI film thickness, the method is as follows: assuming that the surface of the SEI film generated by the lithium-ion battery is uneven, in order to quantify it, the average value of the z coordinates of the top 5% silicon atoms is used as the lower boundary of the SEI film, and the average value of the z coordinates of the top 5% lithium atoms is used as the upper boundary condition of the SEI film. At this time, the film thickness is the difference between the upper and lower boundaries.

[0020] In step S3, when measuring the Young's modulus of the SEI film model and the bulk modulus of the SEI film model, the method is: after determining the upper and lower boundaries of the SEI film, the stabilized SEI film model is cut out, and a mechanical tensile test is performed on it to measure its Young's modulus and bulk modulus.

[0021] When conducting the tensile test, the three directions of x, y, and z are all set as periodic boundary conditions p, the conjugate gradient method is used for energy minimization, the Nose-Hoover heat bath method is used for temperature control, the equilibrium temperature is set to 300K, and it is set under the NPT ensemble condition; when measuring Young's modulus, the time step is 0.25fs, the equilibrium time is set to 50ps, the stretching rate is set to 1%ps-1, and the strain is set to 25%. When measuring the bulk modulus, tensile strains are applied along the three directions of x, y, and z axes, and the strain is set to a small deformation of 2%, so the stretching rate is set to 0.1%ps-1, the time step is set to 0.1fs, and the equilibrium time is set to 50ps.

[0022] In step S3, when measuring the SEI film model Young's modulus and the SEI film model bulk modulus,

[0023] Young's modulus = stress / strain, that is, E = δ1 / ε1;

[0024] Bulk modulus: Among them C ij is the elastic coefficient, that is, a small deformation of 2% is applied to the SEI film in each direction to obtain the ratio of the stress value to the strain value after deformation. Where:

[0025]

[0026] δ 11 represents the normal stress along the x-axis, ε 11 represents the strain of SEI film in the x-axis direction. 11 , C 22 and C 33 They represent the elastic constants of the x, y, and z axes respectively. The solution method is the same as that of C 11 The same; and C 12 , C 13 , C 23 represents the elastic constants along the xy, xz, and yz directions, and the solution is as follows:

[0027]

[0028] ε 12 =ε 11 +ε 22

[0029] ε 12 represents shear strain, ε12 and ε 23 Obtained using the same method.

[0030] The present invention relates to the study of the mechanical properties of the SEI film on the surface of the silicon negative electrode of a lithium ion battery. It is the first time that a molecular dynamics simulation method is used to study the mechanical properties of the SEI film on the surface of the silicon negative electrode. The present invention proposes a simulation method for the generation of the SEI film on the surface of the silicon negative electrode of a lithium ion battery, proposes to calculate the mechanical properties of the SEI film on the surface of the silicon negative electrode by simulation, and proposes that the mechanical properties of the SEI film can be optimized by adjusting the reaction temperature, electric field strength, lithium insertion degree of the silicon negative electrode and the type of mixed solvent in the primary reaction of the lithium ion battery. Through the scheme described in the present invention, the mechanical properties of the SEI film can be adjusted by adjusting the type of solvent, applying an external electric field, the reaction temperature and the lithium insertion degree of the silicon negative electrode, thereby optimizing the battery design. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0032] Attached Figure 1 It is a schematic diagram of the effect of different lithiation degrees of silicon-based materials on the mechanical properties of SEI film in the present invention (taking PC+DEC electrolyte solvent as an example);

[0033] Attached Figure 2 This is a schematic diagram of the effect of electric field strength on the tensile mechanical properties of the SEI film in the present invention (taking PC+DEC electrolyte solvent as an example):

[0034] Attached Figure 3 This is a schematic diagram of the model usage in the process of determining the Young's modulus and bulk modulus of the SEI film. DETAILED DESCRIPTION

[0035] As shown in the figure, a simulation method for adjusting the mechanical properties of a solid electrolyte on the surface of a silicon negative electrode of a lithium-ion battery comprises the following steps:

[0036] Step S1, constructing a SEI model, using an atomic model constructed by software to simulate, the process of constructing an interface SEI film model on the surface of a silicon negative electrode of a lithium-ion battery, sequentially includes constructing a silicon-based electrode material model, constructing an electrolyte solvent model, and constructing a SEI film model;

[0037] Step S2, performing molecular dynamics simulation by selecting a potential function;

[0038] Step S3: Conduct mechanical property testing by determining the SEI film thickness, the SEI film model Young's modulus, and the SEI film model bulk modulus.

[0039] In step S1, the atomic model is constructed using Material Studio software.

[0040] When constructing a silicon-based electrode material model in step S1, the method is specifically as follows:

[0041] First build The box uses periodic boundary conditions p in the x and y directions and contraction boundary conditions s in the z direction. The area is set as a silicon block; the silicon block is set to contain 1152 silicon atoms, and the bottom The height of the silicon atoms is fixed, and the box is in the z direction. The area is filled with Li ion solution;

[0042] The silicon block and the Li ion solution were energy minimized using the conjugate gradient method, the simulation ensemble used the NVT ensemble, and then the Nose-Hoover heat bath method was used for relaxation;

[0043] When the simulation process needs to be accelerated, the equilibrium temperature is set to 1000K, the time for the two to relax separately is set to 10ps, the time step is set to 0.2fs, and then the initial lithium silicon model is output; on this basis, the initial model is still heated according to the above temperature control method, the simulation time is set to 200ps, and the z direction of the simulation result is intercepted from 0 to Li x The Si model is used as the silicon-based electrode material for subsequent simulation analysis; the final silicon-based electrode material contains 2215 lithium atoms and 559 silicon atoms, and the overall silicon-based battery material is approximately Li4Si.

[0044] Step S1: When constructing the electrolyte solvent model, the method is specifically as follows: assuming that the electrolyte solvent molecules used in the lithium-ion battery are ethylene carbonate C3H4O3 abbreviated as EC, dimethyl carbonate C3H6O3 abbreviated as DMC, propylene carbonate C4H6O3 abbreviated as PC, ethyl methyl carbonate C4H8O3 abbreviated as EMC, diethyl carbonate C5H6O3 abbreviated as DEC, 10O6 or a mixture of one or more; when modeling, Material Studio software is first used to construct a single electrolyte solvent molecule, and then its built-in COMPASS force field is used to optimize the molecular configurations of EC, DMC, and PC to minimize their energy, and then LAMMPS (Large-scale Atomic / Molecular Massively Parallel Simulator) software is used to build a box, and a specified number of solvent molecules are randomly filled into the box; finally, the conjugate gradient method is used to relax and minimize the energy of the electrolyte solvent model, and then it is balanced under the NVT ensemble, with periodic boundary conditions p in the x and y directions and contractile boundary conditions s in the z direction, and a Nose-Hoover heat bath is used for temperature control, and the initial temperature and equilibrium temperature are both set to 500K.

[0045] In step S1, when constructing the SEI film model, the method is specifically as follows: the silicon-based electrode model and the electrolyte solvent model are merged under a suitable reaction force field, and a modeling process is set. During the merging, the lithium ions in the silicon-based electrode react with the solvent to generate a SEI film; the modeling process is set to be carried out under the isothermal and isobaric ensemble NPT, and the Nose-Hoover hot bath method is used for temperature control. The initial temperature is set to 500K, and the simulation relaxation time is set to 100ps.

[0046] In step S2, the potential function is used to set the motion mode of each atom in the model and to set the way of building chemical bonds between atoms; the ReaxFF reaction force field applicable to the atomic system is used as the potential function of the simulation, and the ReaxFF reaction force field is a force field that has been verified to correctly describe the reduction reaction between the electrolyte and the electrode material.

[0047] In step S3, when determining the SEI film thickness, the method is as follows: assuming that the surface of the SEI film generated by the lithium-ion battery is uneven, in order to quantify it, the average value of the z coordinates of the top 5% silicon atoms is used as the lower boundary of the SEI film, and the average value of the z coordinates of the top 5% lithium atoms is used as the upper boundary condition of the SEI film. At this time, the film thickness is the difference between the upper and lower boundaries.

[0048] In step S3, when measuring the Young's modulus of the SEI film model and the bulk modulus of the SEI film model, the method is: after determining the upper and lower boundaries of the SEI film, the stabilized SEI film model is cut out, and a mechanical tensile test is performed on it to measure its Young's modulus and bulk modulus.

[0049] When conducting the tensile test, the three directions of x, y, and z are all set as periodic boundary conditions p, the conjugate gradient method is used for energy minimization, the Nose-Hoover heat bath method is used for temperature control, the equilibrium temperature is set to 300K, and it is set under the NPT ensemble condition; when measuring Young's modulus, the time step is 0.25fs, the equilibrium time is set to 50ps, the stretching rate is set to 1%ps-1, and the strain is set to 25%. When measuring the bulk modulus, tensile strains are applied along the three directions of x, y, and z axes, and the strain is set to a small deformation of 2%, so the stretching rate is set to 0.1%ps-1, the time step is set to 0.1fs, and the equilibrium time is set to 50ps.

[0050] In step S3, when measuring the SEI film model Young's modulus and the SEI film model bulk modulus,

[0051] Young's modulus = stress / strain, that is, E = δ1 / ε1;

[0052] Bulk modulus: Among them C ij is the elastic coefficient, that is, a small deformation of 2% is applied to the SEI film in each direction to obtain the ratio of the stress value to the strain value after deformation. Where:

[0053]

[0054] δ 11 represents the normal stress along the x-axis, ε 11 represents the strain of SEI film in the x-axis direction. 11 , C 22 and C 33 They represent the elastic constants of the x, y, and z axes respectively. The solution method is the same as that of C 11 The same; and C 12 , C 13 , C 23 represents the elastic constants along the xy, xz, and yz directions, and the solution is as follows:

[0055]

[0056] ε 12 =ε 11 +ε 22

[0057] ε 12 represents shear strain, ε 12 and ε 23 Obtained using the same method.

[0058] Example:

[0059] In this example, when the required computing resources (servers, workstations, etc.) are large, only the application of mainstream electrolyte solvent types in lithium-ion batteries can be considered; only amorphous silicon is used for simulation of the negative electrode to reduce the requirements for computing resources.

[0060] The process of this example is: 1. construct a silicon-based electrode; 2. construct an electrolyte solvent; 3. generate a SEI film; 4. extract the SEI film and obtain its film thickness; 5. perform a mechanical tensile test on the SEI; 6. determine its Young's modulus and bulk modulus.

[0061] In this example, when constructing the electrolyte solvent model in step S1, 5 groups of different electrolyte models are constructed, and the volume ratio of each part of the mixed solvent in the box is 1:1.

[0062] As shown in the following table

[0063]

[0064] In this example, in step S2, the potential function developed by Yun is selected.

[0065] In step S3, according to the mechanical property determination method of this example, the mechanical properties of the SEI film generated at different lithium insertion concentrations are calculated. The influence of the degree of lithiumization of the silicon negative electrode on the mechanical properties of the SEI is shown in the following table;

[0066]

[0067] According to the mechanical property determination method of this example, the mechanical properties of the SEI film generated under different electric field strengths are calculated. The influence of the applied electric field on the mechanical properties of the SEI film is shown in the following table;

[0068]

Claims

1. A simulation method for adjusting the mechanical properties of solid electrolyte on the surface of silicon negative electrode of lithium-ion battery, characterized by: The method comprises the following steps: Step S1, constructing a SEI model, using an atomic model constructed by software to simulate, the process of constructing an interface SEI film model on the surface of a silicon negative electrode of a lithium-ion battery, sequentially includes constructing a silicon-based electrode material model, constructing an electrolyte solvent model, and constructing a SEI film model; Step S2, performing molecular dynamics simulation by selecting a potential function; Step S3: Conduct mechanical property testing by determining the SEI film thickness, the SEI film model Young's modulus, and the SEI film model bulk modulus.

2. The method for simulating mechanical properties of solid electrolyte on the surface of silicon negative electrode of lithium ion battery according to claim 1, characterized in that: In step S1, the atomic model is constructed using Material Studio software.

3. The method for simulating mechanical properties of solid electrolyte on the surface of silicon negative electrode of lithium ion battery according to claim 2, characterized in that: When constructing a silicon-based electrode material model in step S1, the method is specifically as follows: First build The box uses periodic boundary conditions p in the x and y directions and contraction boundary conditions s in the z direction. The area is set as a silicon block; the silicon block is set to contain 1152 silicon atoms, and the bottom The height of the silicon atoms is fixed, and the box is in the z direction. The area is filled with Li ion solution; The silicon block and the Li ion solution were energy minimized using the conjugate gradient method, the simulation ensemble used the NVT ensemble, and then the Nose-Hoover heat bath method was used for relaxation; When the simulation process needs to be accelerated, the equilibrium temperature is set to 1000K, the time for the two to relax separately is set to 10ps, the time step is set to 0.2fs, and then the initial lithium silicon model is output; on this basis, the initial model is still heated according to the above temperature control method, the simulation time is set to 200ps, and the z direction of the simulation result is intercepted from 0 to Li x The Si model is used as the silicon-based electrode material for subsequent simulation analysis; the final silicon-based electrode material contains 2215 lithium atoms and 559 silicon atoms, and the overall silicon-based battery material is approximately Li4Si.

4. The method for simulating mechanical properties of solid electrolyte on the surface of silicon negative electrode of lithium ion battery according to claim 2, characterized in that: Step S1: When constructing the electrolyte solvent model, the method is specifically as follows: assuming that the electrolyte solvent molecules used in the lithium-ion battery are ethylene carbonate C3H4O3 abbreviated as EC, dimethyl carbonate C3H6O3 abbreviated as DMC, propylene carbonate C4H6O3 abbreviated as PC, ethyl methyl carbonate C4H8O3 abbreviated as EMC, diethyl carbonate C5H6O3 abbreviated as DEC, 10 O6 or a mixture of one or more of them; when modeling, Material Studio software is first used to construct a single electrolyte solvent molecule, and then its built-in COMPASS force field is used to optimize the molecular configurations of EC, DMC, and PC to minimize their energy, and then LAMMPS software is used to build a box, and a specified number of solvent molecules are randomly filled into the box; finally, the conjugate gradient method is used to relax and minimize the energy of the electrolyte solvent model, and then it is balanced under the NVT ensemble, with periodic boundary conditions p in the x and y directions and contractile boundary conditions s in the z direction, and a Nose-Hoover heat bath is used for temperature control, and the initial temperature and equilibrium temperature are both set to 500K.

5. The method for simulating mechanical properties of solid electrolyte on the surface of silicon negative electrode of lithium ion battery according to claim 2, characterized in that: In step S1, when constructing the SEI film model, the method is specifically as follows: the silicon-based electrode model and the electrolyte solvent model are merged under a suitable reaction force field, and a modeling process is set. During the merging, the lithium ions in the silicon-based electrode react with the solvent to generate a SEI film; the modeling process is set to be carried out under the isothermal and isobaric ensemble NPT, and the Nose-Hoover hot bath method is used for temperature control. The initial temperature is set to 500K, and the simulation relaxation time is set to 100ps.

6. The method for simulating mechanical properties of solid electrolyte on the surface of silicon negative electrode of lithium ion battery according to claim 2, characterized in that: In step S2, the potential function is used to set the motion mode of each atom in the model and to set the way of building chemical bonds between atoms; the ReaxFF reaction force field applicable to the atomic system is used as the potential function of the simulation, and the ReaxFF reaction force field is a force field that has been verified to correctly describe the reduction reaction between the electrolyte and the electrode material.

7. The method for simulating mechanical properties of solid electrolyte on the surface of silicon negative electrode of lithium ion battery according to claim 2, characterized in that: In step S3, when determining the SEI film thickness, the method is as follows: assuming that the surface of the SEI film generated by the lithium-ion battery is uneven, in order to quantify it, the average value of the z coordinates of the top 5% silicon atoms is used as the lower boundary of the SEI film, and the average value of the z coordinates of the top 5% lithium atoms is used as the upper boundary condition of the SEI film. At this time, the film thickness is the difference between the upper and lower boundaries.

8. The method for simulating mechanical properties of solid electrolyte on the surface of silicon negative electrode of lithium ion battery according to claim 2, characterized in that: In step S3, when measuring the Young's modulus of the SEI film model and the bulk modulus of the SEI film model, the method is: after determining the upper and lower boundaries of the SEI film, the stabilized SEI film model is cut out, and a mechanical tensile test is performed on it to measure its Young's modulus and bulk modulus.

9. The method for simulating mechanical properties of solid electrolyte on the surface of silicon negative electrode of lithium ion battery according to claim 8, characterized in that: When conducting the tensile test, the three directions of x, y, and z are all set as periodic boundary conditions p, the conjugate gradient method is used for energy minimization, the Nose-Hoover heat bath method is used for temperature control, the equilibrium temperature is set to 300K, and it is set under NPT ensemble conditions; when measuring Young's modulus, the time step is 0.25fs, the equilibrium time is set to 50ps, the stretching rate is set to 1%ps-1, and the strain is set to 25%; when measuring the bulk modulus, tensile strains are applied along the x, y, and z axes respectively, and the strain is set to a small deformation of 2%, so the stretching rate is set to 0.1%ps-1, the time step is set to 0.1fs, and the equilibrium time is set to 50ps.

10. The method for simulating mechanical properties of solid electrolyte on the surface of silicon negative electrode of lithium ion battery according to claim 9, characterized in that: In step S3, when measuring the SEI film model Young's modulus and the SEI film model bulk modulus, Young's modulus = stress / strain, that is, E = δ1 / ε1; Bulk modulus: Among them j is the elastic coefficient, that is, a small deformation of 2% is applied to the SEI film in each direction to obtain the ratio of the stress value to the strain value after deformation; where: δ 11 represents the normal stress along the x-axis, ε 11 represents the strain of SEI film in the x-axis direction; C 11 , C 22 and C 33 They represent the elastic constants of the x, y, and z axes respectively. The solution method is the same as that of C 11 The same; and C 12 , C 13 , C 23 represents the elastic constants along the xy, xz, and yz directions, and the solution is as follows: E12=ε11+ε22 ε 12 represents shear strain, ε 12 and ε 23 Obtained using the same method.

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