Multi-scale method for simulating mechanical and thermodynamic properties of particle reinforced biological composite material

Abstract

The invention relates to multi-scale modeling and mechanical and thermodynamic property simulation of a particle reinforced biological composite material, and belongs to the crossing field of biology, material science and computer simulation. The method specifically comprises the following steps: constructing a polyether-ether-ketone (PEEK) high-molecular polymer and a graphene reinforced composite material model thereof through a cross-linking algorithm under a microscopic scale, and simulating and calculating the mechanical and thermodynamic properties of the model by adopting molecular dynamics; in the microscopic scale, constructing a representative volume element model of the microstructure artificial skeleton, inputting property parameters calculated by molecular dynamics into a microscopic model, and calculating microscopic mechanical and thermodynamic properties of the model by adopting a substance point method; and inputting the property parameters obtained under the microscale into the macroscopic model, and calculating the overall macromechanical and thermodynamic behavior response of the material by adopting a finite element method. According to the method, mechanical and thermodynamic responses of the biological composite material are finally simulated through transmission of property parameters of different scales, and theoretical support is provided for research and formula design of the particle reinforced biological composite material.

Description

Technical Field

[0001] The present invention relates to the field of multi-scale modeling of biocomposite materials and multi-scale simulation of mechanical and thermodynamic properties, and belongs to the interdisciplinary field of biology, materials science, computer simulation, etc. Background Art

[0002] In biomedicine, PEEK is an ideal choice for orthopedic implants because its mechanical properties are close to the modulus of human cortical bone, and it has excellent biocompatibility and does not cause toxicity or mutagenic effects. PEEK can also be combined with reinforcing agents such as carbon fiber and alumina to form a stronger composite material, making it an excellent choice to replace titanium alloy as an orthopedic surgical material. Although PEEK and its composites have performed well in experimental studies, their micromechanical and thermodynamic mechanisms have not yet been fully clarified, especially in terms of material parameters after particle reinforcement modification design. There are few reports in the existing literature, so a theoretical method is needed to calculate the properties of the modified material to clarify the micromechanism of the material and provide a reliable basis for designing different biocomposite materials.

[0003] With the advancement of computer technology, new opportunities have emerged in theoretical research in materials science. Numerical simulation, as an equally important tool as experimental tools, helps researchers gain a deeper understanding of material properties and behaviors. However, since materials exhibit different properties at different scales, computational methods at each scale have their limitations. At the microscopic scale, molecular dynamics (MD) [1] It can accurately describe the interaction between molecules, chemical bonding and interface effects, and reveal basic physical and chemical properties such as bonding energy, diffusion behavior and thermodynamic stability. However, due to the large amount of calculation, MD is usually limited to the simulation of systems within the nanoscale space and nanosecond time frame. At the microscopic scale, the material point method (MPM) [2] Combined with representative volume element (RVE) analysis, the internal structure evolution of the material and its impact on performance can be simulated, which is especially suitable for large deformation and complex nonlinear material behavior. Although MPM enhances the ability to capture geometric changes through a dual grid system, it also increases algorithm complexity and numerical instability, resulting in higher computational requirements and longer simulation time. At the macro scale, the finite element method (FEM) [3]Used to predict the overall mechanical behavior of materials, including stress-strain distribution, fracture mechanism and fatigue performance. The accuracy of FEM depends on the parameters provided by experimental data or empirical models. For new materials, accurate simulation becomes difficult due to the lack of key parameters. In order to fully utilize the advantages of various methods and overcome the limitations of single-scale simulation, cross-scale modeling has become a trend. This method integrates simulation results at different scales, provides a comprehensive perspective from atoms to macro, optimizes the design process, improves the efficiency of new material development, reduces experimental losses, saves resources, and provides strong support for materials science and engineering research. Current multi-scale research is mostly based on molecular dynamics simulation and finite element models, which have a large span and cannot clearly deal with the interface contact problems caused by discontinuities between materials in finite elements.

[0004] Therefore, the present invention proposes a multi-scale simulation calculation method for the mechanical and thermodynamic properties of particle-reinforced biocomposite materials. Starting from the molecular scale of the chemical structure, density functional theory and molecular dynamics simulation are used to calculate the property parameters of the molecular unit cell at the microscopic scale, which are brought into the representative volume element at the mesoscopic scale, and the multi-phase contact criteria of the traction law and the friction law between the multi-phase materials are set. The thermodynamic properties of the multi-phase biocomposite material are calculated using the material point method, and finally brought into the three-dimensional finite element geometric model at the macroscopic scale to observe the thermodynamic behavior response of the overall biomaterial. This multi-scale calculation method transforms the discontinuity problem existing in the finite element into the calculation of the material point method at the mesoscopic scale, and for PEEK (polyetheretherketone) composite materials containing a small amount of graphene modification, we adopt the concept of homogenization treatment, simplify the material modeling process, and effectively transform the discontinuity problems at different scales into continuum problems for solution, which provides a strong theoretical basis for material design or material modification, and can reduce experimental resource loss and reduce R&D costs. Summary of the invention

[0005] The purpose of the present invention is to provide a method for multi-scale simulation of the mechanical behavior of a multi-scale composite material model based on the microstructure of a particle-reinforced biocomposite material, starting from the molecular scale of the chemical structure, going deeper step by step, from microscopic scale molecular simulation, to the mesoscopic scale material point method, and finally to the macroscopic scale finite element, spanning multiple continuous scales, and connecting the same materials at different scales through the transfer of key parameters. This method of sequential multi-scale numerical simulation calculation provides a theoretical basis for material design or material modification, which can reduce the loss of experimental resources and reduce research and development costs.

[0006] To achieve the above purpose, the present invention proposes a multi-scale simulation calculation method for the mechanical and thermodynamic properties of particle-reinforced biocomposite materials. The technical solution of the present invention is as follows:

[0007] A multi-scale simulation calculation method for mechanical and thermodynamic properties of particle-reinforced biocomposite materials, comprising the following steps:

[0008] Step 1: Using density functional theory to optimize the structure of single component difluorobenzophenone, hydroquinone and other chemical small molecules in the composite material to obtain their stable structure;

[0009] Step 2: According to the chemical synthesis reaction, a dynamic cross-linking algorithm is used to connect difluorobenzophenone and hydroquinone to construct a PEEK amorphous unit cell model, and then different amounts of graphene are added to construct an amorphous unit cell model of a particle-reinforced PEEK-based composite material;

[0010] Step 3, calculation of material properties at microscopic scale: molecular dynamics (MD) simulation is performed on the unit cell model of PEEK and its composite materials in step 2 to solve the mechanical and thermodynamic properties of the unit cell of PEEK and its composite materials;

[0011] Step 4, establishing a representative volume element model of biocomposite materials such as artificial bones at a mesoscopic scale, wherein the microstructure of the mesoscopic model is composed of hydroxyapatite (HA) particles filled with different proportions of PEEK and its composite materials in step 2, and there is an explicit interface between the HA particles and the PEEK matrix, and a multiphase contact model including traction law and friction law is set to describe the explicit interface;

[0012] Step 5, calculation of material properties at the mesoscale: the mechanical and thermodynamic property parameters obtained by MD in step 3 are input into the mesoscale representative volume element biocomposite material model established in step 4, and numerical simulation is performed using the material point method according to the multiphase contact model established in step 4 to calculate the mechanical and thermodynamic properties of the composite material composed of PEEK (including graphene particle reinforced PEEK) and HA particles at the mesoscale;

[0013] Step 6, construct a model of a biomedical composite material based on a continuous medium at a macro scale, input the mechanical and thermodynamic property parameters of the biocomposite material including an explicit interface at a micro scale obtained in step 5 to define boundary conditions and constraints, and use the finite element method to calculate the mechanical and thermodynamic responses at a macro scale;

[0014] Furthermore, the step 1 includes constructing three small molecules of difluorobenzophenone, hydroquinone, and graphene, and optimizing their structures using density functional theory to obtain a stable monomer molecular structure.

[0015] Furthermore, the step 2 includes establishing a polymer PEEK model and a PEEK-based composite material unit cell model after adding graphene in different mass ratios. The unit cell model of the polymer PEEK and its composite material is constructed by using a dynamic crosslinking algorithm, setting the chemical active sites R1 and R2 of the difluorobenzophenone molecule and the hydroquinone molecule, setting the maximum cutoff radius to determine whether crosslinking occurs, forming a PEEK-based molecular unit cell model, and then adding different amounts of graphene molecules to construct a particle-reinforced PEEK-based composite material amorphous unit cell model.

[0016] Furthermore, step 3 includes relaxing the crystal structure obtained in step 2, and using molecular dynamics simulation to calculate the thermodynamic properties of the PEEK-based material including thermal conductivity, isobaric heat capacity, thermal expansion coefficient, and mechanical properties including elastic modulus, Poisson's ratio, and friction coefficient.

[0017] Furthermore, step 4 includes, based on real biocomposites, using a filling model, randomly generating non-intersecting circular HA particles of different particle sizes in a representative volume element model, filling the PEEK-based polymer composite material outside the hydroxyapatite (HA), and setting a pressure head for applying a load in the model to form a final biocomposite model.

[0018] Furthermore, step 5 includes setting contact criteria between multiphase materials according to the representative volume element model of the biocomposite material constructed in step 4, describing the interface relationship between different materials by Coulomb friction, bringing in the material parameters calculated at the microscopic scale in step 3, using the material point method, and performing numerical simulation by uniaxial compression, and obtaining the mechanical properties of different materials by simulating a variety of different situations, including equivalent stress, equivalent strain, and equivalent Young's modulus.

[0019] Furthermore, step 6 includes constructing a corresponding finite element three-dimensional geometric model based on the scenario of a real medical biocomposite material, bringing in the parameters calculated by the material point method in step 5, constructing a parameter model and using it in the finite element model, defining loads and boundary conditions and constraints, using a solver to solve the operation, and observing changes in its mechanical behavior.

[0020] The advantages and beneficial effects of the present invention are as follows:

[0021] (1) The present invention provides a nano-micro-meso-macro continuous multi-scale numerical simulation method for studying the thermodynamic properties of biocomposite materials.

[0022] (2) During the simulation process, each level is connected through key parameters. The lower-level simulation parameters are presented by the upper-level simulation after calculation, rather than directly using empirical models or existing experimental values. This method achieves the connection between different scales.

[0023] (3) The material is constructed based on the molecular structure, and a dynamic cross-linking algorithm is used to construct the polymer PEEK instead of directly constructing the polymer chain, eliminating human errors.

[0024] (4) The properties of PEEK are enhanced by adding graphene in different mass ratios. The properties of PEEK material are calculated after homogenization at the microscale, which provides a modeling idea for modified materials.

[0025] (5) The problem of multi-material discontinuities in the finite element method is scaled to the microscopic scale material point method for solution. The properties of the graphene-modified PEEK composite material in the material point method model are then scaled to the microscopic scale dynamic simulation for calculation. The discontinuities at different scales are converted into continuums for processing, which optimizes the simulation model, reduces the complexity of the calculation, and saves calculation time. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 The present invention is a flow chart of a multi-scale method for simulating the mechanical and thermodynamic properties of particle-reinforced biocomposite materials.

[0027] Figure 2 Microscopic molecular models: (a) difluorobenzophenone molecular structure, (b) hydroquinone molecular structure, and (c) nanographene molecular structure.

[0028] Figure 3 To demonstrate the active sites of the cross-linking algorithm and the unit cell effect after cross-linking, (a) difluorobenzophenone and hydroquinone active sites R1 and R2, (b) PEEK unit cell structure after cross-linking (c) molecular unit cell structure after adding nanographene.

[0029] Figure 4 Fitting curve of thermal expansion coefficient of PEEK.

[0030] Figure 5 Friction model of PEEK-based composite materials. (a) is the friction model of HA and PEEK, and (b) is the control group, using the friction model of PEEK and Fe.

[0031] Figure 6 This is a representative volume element model of a biocomposite material mixed with PEEK-based materials and HA at the mesoscale. Figure (a) is an image of HA under a polymer in real life, and Figure (b) is a representative volume element model constructed for material point method calculation.

[0032] Figure 7 This is the curve of equivalent stress changing with time for PEEK-based biocomposite models with different graphene contents at a compression speed of 30 mm / s.

[0033] Figure 8 This is the equivalent Young's modulus curve of composite material models with different graphene contents and different HA area ratios under a compression speed of 30 mm / s.

[0034] Fig. 9 The temperature change curve of PEEK-based biocomposite models with different graphene contents at a compression speed of 30 mm / s.

[0035] Fig.10 This is the 3D geometric model diagram of the finite element three-dimensional artificial bone.

[0036] Fig.11 Schematic diagram of multi-scale model construction of the present invention DETAILED DESCRIPTION

[0037] The following will be combined with the accompanying drawings to describe the implementation case technical method of the present invention in detail. The described embodiment is only a part of the embodiment of the present invention.

[0038] The following description takes polyetheretherketone (PEEK) polymer and PEEK-based composite material modified by adding nanographene molecules as examples.

[0039] See also Figure 1 The present invention provides a multi-scale simulation calculation method for mechanical and thermodynamic properties of particle-reinforced biocomposite materials, comprising the following steps:

[0040] Step 1: According to the chemical reaction process, use molecular simulation software to construct the corresponding small molecule monomer, and use density functional theory (DFT) simulation on the constructed small molecule monomer to optimize and stabilize its structure.

[0041] 101. Firstly, the monomer small molecule model was constructed by taking difluorobenzophenone and hydroquinone, the raw materials of PEEK polymer synthesis process commonly used in industry, as the objects.

[0042] 102. Construct nanographene molecules for modification using single-layer nanographene.

[0043] 103. Density functional theory (DFT) calculations are used for the above three small molecules to adjust the atomic positions in the molecules and find a structure with the lowest total energy, that is, a stable structure after optimization. Figure 2 is a small molecule model after density functional optimization, ( Figure 2 (a)) is a difluorobenzophenone molecule, ( Figure 2 (b)) is a hydroquinone molecule, ( Figure 2 (c)) is a nanographene molecule.

[0044] Step 2: Use dynamic cross-linking to construct a PEEK polymer unit cell and a unit cell model modified by adding different mass fractions of graphene molecules.

[0045] 201. Setting chemically active sites of difluorobenzophenone molecules and hydroquinone molecules to determine whether cross-linking occurs. Figure 3 (a) are the chemically active atoms R1 and R2 of the difluorobenzophenone molecule and hydroquinone molecule, respectively.

[0046] 202. 149 difluorobenzophenone and hydroquinone molecules are encapsulated in a periodic amorphous unit cell. The unit cell modified with graphene is a unit cell that combines and encapsulates 149 difluorobenzophenone and hydroquinone as well as nanographene molecules with calculated mass fractions of 1%, 3%, and 5%.

[0047] 203. Dynamic cross-linking is performed on the encapsulated unit cell. The specific process is to perform dynamic simulation under the NPT ensemble with the temperature set to 593K, the temperature of industrial synthetic PEEK. During the simulation, the distance between the active atoms R1 and R2 is determined, and the cutoff radius is set to 7, that is, a bond is formed when the distance between the active atoms R1 and R2 is less than the cutoff radius. After multiple NPT simulations and bonding, the cross-linking degree of difluorobenzophenone and hydroquinone molecules in the unit cell finally reaches about 80%.

[0048] 204. The cross-linking degree is measured by determining the ratio of functional groups. In this case, the ratio of the number of R2 groups that have participated in the cross-linking reaction to the initial total amount is calculated. (Figure (3b)) is the PEEK unit cell structure after cross-linking, and (Figure (3c)) is the molecular unit cell structure after adding nanographene.

[0049] 205. The constructed PEEK unit cell model and PEEK-based composite material model were relaxed using molecular dynamics simulation software to obtain the amorphous unit cell conformation after complete relaxation. The density of each unit cell after final equilibrium is shown in Table 1.

[0050] Table 1 Density of unit cell model of PEEK-based composite materials

[0051]

[0052] The unit cells of PEEK, 1% graphene composite material, 3% graphene composite material, and 5% graphene composite material are 1.2883, 1.2917, 1.3393, and 1.3613ρ(g·cm -3 ), where the density of PEEK is similar to Solvay [4]The density used in the experiment is 1.30ρ(g·cm -3 ), which proves that the simulation results are reliable and can be used as a reference.

[0053] Step 3: Perform molecular dynamics simulation on the unit cell conformation after relaxation to calculate its thermal and mechanical properties at the microscopic scale, where the thermal properties include thermal conductivity, isobaric heat capacity, and thermal expansion coefficient, and the mechanical properties include Young's modulus, bulk modulus, shear modulus, Poisson's ratio, and friction coefficient.

[0054] 301. Calculate the thermal conductivity of the unit cell after relaxation in step 2. The calculation process uses the RNEMD (reverse perturbation nonequilibrium molecular dynamics, RNEMD) proposed by Müller-Plathe. [5] Methods The graphene / PEEK nanocomposite was simulated and calculated. The RNEMD method generates heat flow by exchanging particle velocities in different regions. We divide the molecular model into N regions of equal width along the z direction, define the middle region as the hot bath region, and only set the left end as the cold bath region due to periodic boundary conditions. The temperature of each region is obtained by statistically averaging the temperatures of all atoms in the region. The atomic temperature in the region is calculated as follows:

[0055]

[0056] Where m i is the atomic mass, v i is the speed, k b is the Boltzmann constant. In the process of velocity exchange, the velocities of atoms of the same mass need to be exchanged to keep the total momentum, total kinetic energy and total energy unchanged. The simulation calculation results are shown in Table 2

[0057] Table 2 Thermal conductivity of PEEK-based composites

[0058]

[0059] As the mass fraction of graphene increases, the thermal conductivity of the material gradually increases. This is because the thermal conductivity of graphene is high, which effectively improves the properties of PEEK-based composites and improves the thermal properties of PEEK materials. The theoretically calculated value of 0.3254 is consistent with that of Huang Suling et al. [6] The experimental value of 0.3334 is also relatively close, which reflects the rationality and reliability of the theoretical calculation.

[0060] 302. Heat capacity refers to the amount of heat absorbed or released by a substance per unit mass when the temperature changes. It reflects the ability of a substance to store heat during temperature changes. Usually, the heat capacity of a substance can be further calculated by calculating the change in energy with temperature. This scheme uses the calculation method of isobaric heat capacity, which is calculated as follows:

[0061]

[0062] Where m is the mass of the substance, ΔE represents the change in energy during the heating process, and ΔT represents the change in temperature.

[0063] By using the NVT ensemble in the molecular simulation software, the system was heated from 300K to 500K, then simulated using the NPT ensemble, and finally the NVT ensemble was used to reach equilibrium. The integration results were substituted into the formula to calculate the isobaric heat capacity as shown in Table 3:

[0064] Table 3 Isobaric heat capacity of PEEK-based composites

[0065]

[0066] When graphene is added to PEEK, it forms an efficient heat conduction network, thereby improving the overall thermal conductivity of the composite. However, due to the low specific heat capacity of graphene itself, the total specific heat capacity of the composite decreases with the increase of graphene content. It can also be seen from the trend in the table that with the addition of graphene, the specific heat capacity decreases, and the simulated PEEK isobaric heat capacity of 1.4556 is consistent with that of Li Jixin et al. [7] The experimental value of 1.4522 is also very close, which verifies the rationality of the theory.

[0067] 303. Thermal expansion is usually a phenomenon in which the volume or length of a material changes with increasing temperature. This phenomenon is usually characterized by the thermal expansion coefficient. In industry, the average linear thermal expansion coefficient is usually used to represent the thermal expansion characteristics of a material. For isotropic solids or liquids, the linear thermal expansion coefficient of the material can also be calculated using volume expansion. The conversion relationship can be expressed as the formula:

[0068]

[0069] Where L0 represents the initial length, ΔL represents the change in length during the temperature change, and ΔT is the change in temperature. For the molecular simulation process, the thermal expansion coefficient is calculated using the cycle method. The temperature is gradually increased from 300K to 500K. The cycle process is first simulated by the NPT ensemble for 1000ps, and then the NVT is used to simulate 500ps to reach equilibrium. Then, the volume change with temperature is calculated by increasing the temperature by 20K each time. Finally, it is substituted into the formula for fitting calculation. The fitting curve is as follows: Figure 4 , Figure 4 The volume of the PEEK unit cell changes with temperature. The calculation results of the volume expansion coefficient are shown in Table 4:

[0070] Table 4 Thermal expansion coefficient of PEEK-based composites

[0071]

[0072] Graphene itself has a very low thermal expansion coefficient, almost close to zero. This means that it hardly changes in size when the temperature changes. Therefore, adding graphene to PEEK can effectively limit the thermal expansion of the PEEK matrix, thereby reducing the thermal expansion coefficient of the entire composite material. As can be seen from Table 4, as the content of graphene increases, the thermal expansion coefficient also decreases. The Pearson correlation coefficients of the curve fitting are all above 0.9, indicating that the fitting effect is good and consistent with Li Jia et al. [8] By comparing the experimental values, it is found that the gap is small and the theoretical research is more convincing.

[0073] 304. The mechanical properties are approximately solved by the Voigt-Reuss upper and lower limit method. The Voigt upper limit calculation formula for the shear modulus and bulk modulus is as follows:

[0074]

[0075]

[0076] In molecular dynamics, the PEEK base is simulated and calculated by uniaxial stretching, and its trajectory information is analyzed. The shear modulus and bulk modulus values ​​are fitted according to the stress-strain. The Young's modulus and Poisson's ratio are calculated by the shear modulus and bulk modulus. The calculation formulas of Young's modulus and Poisson's ratio are as follows:

[0077]

[0078]

[0079] The final calculation results are shown in Table 5 below:

[0080] Table 5 Young's modulus, Poisson's ratio and shear modulus of PEEK-based composites

[0081]

[0082] From the data in Table 5, it can be seen that with the addition of graphene, the modulus of the material increases, that is, the rigidity of the material increases, and it can better resist deformation. [9] The difference in experimental values ​​is also small, and Pisani WA[9] The theoretical calculated value is also quite close.

[0083] 305. The friction coefficient is usually a dimensionless constant used to describe the friction between two different materials. Its usual calculation formula is:

[0084]

[0085] Among them, F f Represents friction force, and N represents positive pressure. Experimentally, an object is usually placed on a sliding surface, and a sliding force is applied. The friction coefficient is obtained by measuring the ratio of the force that maintains sliding and the positive pressure. Here, we use the friction between HA and PEEK to obtain its friction coefficient. The model is constructed as follows: Figure 5 As shown, (a) represents the friction model between HA and PEEK, the HA layer is slid, and the friction force and positive pressure ratio between them are calculated to obtain the friction coefficient, (b) is the control group, using Fe and PEEK to rub, to simulate the friction between steel and PEEK under the experimental equipment, the composition of steel is 90% iron. The final calculation results are shown in Table 6 below:

[0086]

[0087] By comparing the simulated value of PEEK and Fe (0.439) with the experimental value, it is found that the simulated value is

[10] The experimental values ​​are in the range of 0.303-0.482, indicating that the model is feasible. HA is introduced into the simulation experiment, and the friction coefficients of the materials are 0.3292, 0.2986, 0.2977, and 0.2792, respectively. With the addition of graphene, the friction coefficient decreases. This is because graphene has a low friction coefficient and acts as a lubricant inside the material.

[0088] Step 4: Based on the real biocomposite model, a representative volume element model of the biocomposite at the microscopic scale is established, and the microstructure of the model is composed of the PEEK-based polymer and hydroxyapatite in step 2.

[0089] 401. The polymer PEEK-based composite material is homogenized, that is, the added graphene particles are homogenized into the PEEK-based polymer as a filler and coated outside the HA. This homogenization idea is in the

[11] It has been confirmed in experimental verification and can be used in theoretical research.

[0090] 402. HA particles of different diameters are randomly generated in the mold. The model effect is as follows Figure 6, where (a) is an image of HA under polymer in real conditions, and (b) is a representative volume element model constructed for material point method calculation. The rigid indenter is placed on the left side of the model to simulate the applied load.

[0091] For the representative volume element model constructed, the diameter of the circle is changed to simulate the effect of different HA area ratios on the overall biocomposite material.

[0092] Step 5. According to the representative volume element model of the biocomposite material constructed in step 4, the contact criteria between the multiphase materials are set, the interface relationship between different materials is described by Coulomb friction, the material parameters calculated at the microscopic scale in step 3 are brought in, the material point method is used, and the uniaxial compression method is used for numerical simulation. Through a variety of different situations, the mechanical properties of different materials in different situations are obtained, including equivalent stress, equivalent strain, and equivalent Young's modulus.

[0093] 501. For the model in step 4, apply a load from left to right, apply a speed of 30 mm / ms to the rigid indenter part at the left end, simulate the PEKK-based composite materials with different graphene contents, and simulate the models with different HA area ratios, and the total time is set to 2 ms.

[0094] The simulation results are as follows Figure 7 As shown, Figure 7 (a) shows the variation of equivalent stress with equivalent strain for models with different graphene contents. At this time, the HA area accounts for 40%. It can be seen that with the increase of graphene content, the slope of the ratio curve between equivalent stress and equivalent strain increases. Similarly, Figure (b) shows that with the increase of the area ratio of HA particles, the slope of the ratio curve between equivalent stress and equivalent strain also increases. The model used in this model is the PEEK model, that is, the model without adding graphene. This slope reflects the change of the equivalent Young's modulus, that is, the increase in the rigidity of the material.

[0095] 502. The ratio of the above equivalent stress to equivalent strain is fitted, and its slope reflects the equivalent Young's modulus of the material. The specific results are as follows: Figure 8 As shown, Figure 8 (a) is the change of the equivalent Young's modulus of the model with different graphene contents and HA area accounting for 40%. Figure 8 (b) shows the changes in the equivalent Young's modulus of the model with different HA area ratios and the coating material being PEEK. It can be seen intuitively that with the addition of graphene content and the increase in the HA area ratio, the equivalent Young's modulus increases and the material rigidity increases. From the value in the figure, it can be seen that it gradually increases from 6.5 GPa. The Young's modulus of these biocomposites is similar to that of our human cortical bone 7-20 GPa, and can be considered for use as artificial bone materials.

[0096] 503. The temperature change of the material is simulated and studied. By observing the situation of each frame, it is found that the overall material change range is small, but there are local high temperatures during the calculation process. By taking points to study the local high temperatures, taking the material point M700 of the model as an example, Figure (9) shows the temperature change of the material point M700 under different HA area ratios. As the area of ​​HA increases, the temperature of the material point tends to decrease, that is, as the HA increases, the local high temperature tends to be alleviated.

[0097] Step 6: Based on the scenario of real medical biocomposite materials, construct the corresponding finite element three-dimensional geometric model, select medical artificial bones as the research object, and construct a bone 3D finite element model. Bring in the parameters calculated by the material point method in step 5, build a parameter model and use it in the finite element model, define the load and boundary conditions and constraints, and use the solver to solve the operation.

[0098] 601. Based on the real appearance of the artificial bone, a 3D bone model is constructed in the finite element software Comsol. The specific model is shown in Figure (10). The 3D finite element model is constructed by imitating the appearance of the tibia.

[0099] For the model in Figure (10), we conducted simulation research by adding loads on the surface. The load sizes were 1, 2, and 3 times the normal human body weight to simulate standing, climbing stairs, and running.

[0100] 603. For the model in Figure (10), boundary conditions, we only apply a boundary constraint on the upper side. The overall mesh is adjusted to be finer in the finite element simulation software Comsol. The final simulation situation is that as the load increases, it is gradually transferred upward from the applied surface, and increases with the increase of load. Probes are set at the positions of probes 1 and 2 in Figure (10) to record the mechanical conditions of the model.

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[0112]

[11] Xue L, Borodin O, Smith GD, et al.Micromechanics simulations oftheviscoelastic properties of highly filled composites by the material pointmethod(MPM)[J].Modelling and Simulation in Materials Science andEngineering,2006,14(4):703. The above contents are only embodiments of the present invention. The common sense such as the known specific structures and characteristics in the scheme is not described in detail here. The ordinary technicians in the relevant field know all the common technical knowledge in the technical field to which the invention belongs before the application date or the priority date, can obtain all the existing technologies in the field, and have the ability to apply the conventional experimental means before the date. The ordinary technicians in the relevant field can improve and implement this scheme in combination with their own abilities under the enlightenment given by this application. Some typical known structures or known methods should not become obstacles for ordinary technicians in the relevant field to implement this application. It should be pointed out that for those skilled in the art, without departing from the structure of the present invention, several deformations and improvements can be made, which should also be regarded as the protection scope of the present invention, which will not affect the effect of the implementation of the present invention and the practicality of the patent. The protection scope required by this application shall be based on the content of its claims, and the specific implementation methods and other records in the specification can be used to explain the content of the claims.

Claims

1. A multi-scale simulation method for the mechanical and thermodynamic properties of particle-reinforced biocomposites, characterized in that: The following steps are involved: Step 1: Using density functional theory to optimize the structure of single component difluorobenzophenone, hydroquinone and other chemical small molecules in the composite material to obtain their stable structure; Step 2: According to the chemical synthesis reaction, a dynamic cross-linking algorithm is used to connect difluorobenzophenone and hydroquinone to construct a PEEK amorphous unit cell model, and then different amounts of graphene are added to construct an amorphous unit cell model of a particle-reinforced PEEK-based composite material; Step 3, calculation of material properties at a microscopic scale: molecular dynamics (MD) simulation is performed on the PEEK and its composite unit cell model in step 2 to solve the mechanical and thermodynamic properties of the PEEK and its composite unit cell; Step 4, establishing a representative volume element model of biocomposite materials such as artificial bones at a mesoscopic scale, wherein the microstructure of the mesoscopic model is composed of hydroxyapatite (HA) particles filled with different proportions of PEEK and its composite materials in step 2, and there is an explicit interface between the HA particles and the PEEK matrix, and a multiphase contact model including traction law and friction law is set to describe the explicit interface; Step 5, calculation of material properties at the mesoscale: input the mechanical and thermodynamic property parameters obtained by MD in step 3 into the mesoscale representative volume element biocomposite material model established in step 4, and perform numerical simulation using the material point method according to the multiphase contact model established in step 4 to calculate the mechanical and thermodynamic properties of the composite material composed of PEEK (including graphene particle reinforced PEEK) and HA particles at the mesoscale; Step 6: Construct a macro-scale model of biomedical composite materials based on continuous media, input the mechanical and thermodynamic property parameters of the biocomposite materials containing explicit interfaces at the micro-scale obtained in step 5 to define boundary conditions and constraints, and use the finite element method to calculate the mechanical and thermodynamic responses at the macro-scale.

2. A multi-scale simulation calculation method for mechanical and thermodynamic properties of particle-reinforced biocomposite materials according to claim 1, characterized in that: The step 1 comprises constructing three small molecules of difluorobenzophenone, hydroquinone and graphene, and optimizing their structures by using density functional theory method to obtain a stable monomer molecular structure.

3. The multi-scale simulation calculation method for mechanical and thermodynamic properties of particle-reinforced biocomposite materials according to claim 1, characterized in that: The step 2 includes establishing a polymer PEEK model and a PEEK-based composite material unit cell model after adding graphene with different mass ratios. The unit cell model of the polymer PEEK and its composite material adopts a dynamic crosslinking algorithm, sets the chemical active sites R1 and R2 of the difluorobenzophenone molecule and the hydroquinone molecule, sets the maximum cutoff radius to determine whether crosslinking occurs, forms a PEEK-based molecular unit cell model, and then adds different amounts of graphene molecules to construct a particle-reinforced PEEK-based composite material amorphous unit cell model.

4. The multi-scale simulation calculation method for mechanical and thermodynamic properties of particle-reinforced biocomposite materials according to claim 1, characterized in that: The step 3 includes relaxing the crystal structure obtained in step 2, and using a molecular dynamics simulation method to calculate the thermodynamic properties of the PEEK-based material, including thermal conductivity, isobaric heat capacity, thermal expansion coefficient, and mechanical properties, including elastic modulus, Poisson's ratio, and friction coefficient.

5. A multi-scale simulation calculation method for mechanical and thermodynamic properties of particle-reinforced biocomposite materials according to claim 4, characterized in that: The thermal conductivity calculation formula is: Where m i is the atomic mass, v i is the speed, k b is the Boltzmann constant.

6. A multi-scale simulation calculation method for mechanical and thermodynamic properties of particle-reinforced biocomposite materials according to claim 4, characterized in that: The calculation formula for isobaric heat capacity is: Where m is the mass of the substance, ΔE represents the change in energy during the heating process, and ΔT represents the change in temperature.

7. A multi-scale simulation calculation method for mechanical and thermodynamic properties of particle-reinforced biocomposite materials according to claim 4, characterized in that: The formula for calculating the coefficient of thermal expansion is: Where L0 represents the initial length, ΔL represents the change in length during the temperature change, and ΔT is the change in temperature.

8. A multi-scale simulation calculation method for mechanical and thermodynamic properties of particle-reinforced biocomposite materials according to claim 4, characterized in that: The calculation formulas for shear modulus, bulk modulus, Young's modulus, and Poisson's ratio are: Among them, C 11 , C 12 etc. are the elastic matrix values ​​obtained by uniaxial compression calculation.

9. A multi-scale simulation calculation method for mechanical and thermodynamic properties of particle-reinforced biocomposite materials according to claim 4, characterized in that: The calculation formula of friction coefficient is: where F f represents friction and N represents positive pressure.

10. The multi-scale simulation calculation method for mechanical and thermodynamic properties of particle-reinforced biocomposite materials according to claim 1, characterized in that: The step 4 includes constructing a representative volume element model filled with hydroxyapatite (HA) particles in different proportions based on real biocomposites, specifically including randomly generated non-intersecting circular HA particles of different particle sizes, a PEEK-based polymer composite material filled outside the hydroxyapatite (HA), and setting a pressure head in the model for applying a load to form a final biocomposite model.

11. A multi-scale simulation calculation method for mechanical and thermodynamic properties of particle-reinforced biocomposite materials according to claim 1, characterized in that: The step 5 includes setting the contact criteria between multiphase materials according to the representative volume element model of the biocomposite material constructed in step 4, describing the interface relationship between different materials by Coulomb friction, bringing in the material parameters calculated at the microscopic scale in step 3, using the material point method, and performing numerical simulation by uniaxial compression, and obtaining the mechanical properties of different materials by simulating a variety of different situations, including equivalent stress, equivalent strain, and equivalent Young's modulus.

12. A multi-scale simulation calculation method for mechanical and thermodynamic properties of particle-reinforced biocomposite materials according to claim 1, characterized in that: The step 6 includes constructing a corresponding finite element three-dimensional geometric model based on the scenario of a real medical biocomposite material, introducing the parameters calculated by the material point method in step 5, constructing a parameter model and using it in the finite element model, defining loads and boundary conditions and constraints, using a solver to solve the operation, and observing changes in its mechanical behavior.

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