Computational efficiency characterization method of particle filling material and related equipment

Abstract

The invention relates to the field of materials, and particularly provides a computational efficiency characterization method and related equipment for a particle filling material, and the method comprises the steps: determining a minimum effective representative volume element size corresponding to the particle filling material based on a microstructure model of the particle filling material; aiming at the minimum effective representative volume element size, constructing a finite element model through different grid division parameters, and carrying out mechanical property simulation to obtain a simulation result; according to the simulation result, quantifying the relevance between the calculation efficiency and the calculation precision, and defining a comprehensive calculation effect index; and based on the comprehensive calculation effect index, screening an optimal combination of the representative volume element size and the grid size. According to the method, the representative volume unit size and the grid division are reasonably selected, and the accuracy of the calculation result and the calculation time are comprehensively measured, so that the balance of the calculation efficiency and the precision in the micro-mechanical simulation of the particle filling material is realized.

Description

Technical Field

[0001] The present application relates to the field of material technology, and in particular to a method for characterizing the computational efficiency of a particle-filled material and related equipment. Background Art

[0002] Particle-filled materials are widely used in numerous fields, and their mesoscopic models are crucial for understanding and predicting the macroscopic mechanical behavior of materials. Through mesoscopic mechanical simulations, it is possible to deeply analyze the details of the material's internal structure, such as grains, phase interfaces, and defects, thereby optimizing material design and improving material performance. Furthermore, mesoscopic models are crucial for analyzing the fracture characteristics of particle-filled polymer composites. They can help researchers observe the distribution characteristics of particles, construct gradation structural models that conform to the normal distribution law, and use finite element models to analyze the effects of particle volume fraction and particle size distribution on crack propagation.

[0003] During the construction of the microscopic model, the concept of a representative volume element (RVE) was introduced to identify the smallest volume unit capable of reflecting the macroscopic physical properties of the material. The selection of the RVE size must meet two core requirements: first, it must be able to accurately calculate and characterize the key mechanical properties of the particle-filled material, including but not limited to parameters such as relaxation modulus, ultimate strength, and maximum strain; second, the computational complexity of the finite element model must be considered to ensure that the microscopic mechanical behavior of the material can be effectively reflected within the limited computational power.

[0004] However, there are some problems with the selection of RVEs in current simulation calculations. When computing resources are limited, the size of the RVE is often simply reduced to meet modeling and computational requirements. However, this approach does not consider the representativeness of the model and the accuracy of the volume ratio of the material's microstructure. When computing resources are sufficient, on the other hand, the tendency is to build a sufficiently large RVE model, but the rationality of the RVE size and computational efficiency are ignored. Therefore, how to reasonably select the RVE size to improve computational efficiency while ensuring the diversity of the material's microstructure and computational accuracy has become a technical challenge that needs to be solved urgently.

[0005] The preceding description is intended to provide general background information and does not necessarily constitute prior art. Summary of the Invention

[0006] The embodiments of the present application provide a method and related equipment for characterizing the computational efficiency of granular filling materials. By rationally selecting the representative volume unit size and grid division, the accuracy of the calculation results and the calculation time are comprehensively weighed to achieve a balance between computational efficiency and accuracy in the micromechanical simulation of granular filling materials.

[0007] In a first aspect, an embodiment of the present application provides a method for characterizing the computational efficiency of a particle filling material, comprising:

[0008] Determining a minimum effective representative volume unit size corresponding to the granular filling material based on a mesoscopic structural model of the granular filling material;

[0009] For the minimum effective representative volume unit size, a finite element model is constructed by using different mesh partitioning parameters and mechanical property simulation is performed to obtain simulation results;

[0010] Based on the simulation results, quantify the correlation between computational efficiency and computational accuracy, and define a comprehensive computational effect index;

[0011] Based on the comprehensive calculation effect index, the optimal combination of the representative volume unit size and the grid size is screened.

[0012] Optionally, in some embodiments of the present application, determining the minimum effective representative volume unit size corresponding to the granular filling material based on the mesoscopic structural model of the granular filling material includes:

[0013] constructing a three-dimensional microstructure model of the particle filling material by CT scanning or three-dimensional reconstruction technology, wherein the three-dimensional microstructure model includes particle distribution characteristics, matrix characteristics, and pore characteristics;

[0014] Select representative volume unit models with different side lengths and calculate the oscillation curve of the target parameter as the representative volume unit size changes;

[0015] Based on the oscillation change curve, a critical size at which the target parameter tends to be stable is selected as the minimum effective representative volume unit size corresponding to the particle filling material.

[0016] Optionally, in some embodiments of the present application, the target parameter is at least one of porosity, particle volume fraction or interface volume ratio, and the critical size is determined by experimental fitting or numerical simulation, and the value is not less than 600 μm.

[0017] Optionally, in some embodiments of the present application, for the minimum effective representative volume unit size, constructing a finite element model by using different meshing parameters and performing mechanical property simulation to obtain simulation results includes:

[0018] For the minimum effective representative volume size, setting at least three different grid division schemes, wherein the grid size range of the grid division scheme is 5 μm-20 μm;

[0019] Insert cohesive elements into the finite element model to characterize the dewetting effect at the interface between the particles and the matrix, and set the interface stiffness, adhesion, and failure displacement parameters.

[0020] A mechanical property simulation is performed based on the finite element model to obtain simulation results.

[0021] Optionally, in some embodiments of the present application, the mechanical parameters of the cohesive unit are defined by a bilinear constitutive model, the loading condition is a relaxation process under constant strain, the strain level is 5% and the loading rate is 500 mm / min.

[0022] Optionally, in some embodiments of the present application, the correlation between computational efficiency and computational accuracy is quantified based on the simulation results to define a comprehensive computational effect index, including:

[0023] Based on the simulation results, the calculation accuracy index is determined by characterizing the relative deviation percentage between the simulation value and the experimental value;

[0024] Based on the simulation results, determining a computing efficiency index by calculating resource consumption time or quantifying the number of computing nodes;

[0025] The comprehensive calculation effect index is determined based on the calculation accuracy index and the calculation efficiency index, wherein the comprehensive calculation effect index is defined as the product of the relative deviation and the calculation time, and / or the comprehensive calculation effect index is defined as the evaluation result after weighted evaluation of multiple groups of model parameters through a normalized formula.

[0026] Optionally, in some embodiments of the present application, screening the optimal combination of the representative volume unit size and the grid size based on the comprehensive calculation effect index includes:

[0027] Taking the minimum comprehensive calculation effect index as the optimization goal, the optimal combination of the representative volume unit size and the grid size is selected based on the calculation accuracy index and the calculation efficiency index;

[0028] Performing a variable angle tensile shear numerical simulation to verify the optimal combination, and obtaining a simulation verification result;

[0029] The optimal combination is adjusted based on the simulation verification result.

[0030] In a second aspect, an embodiment of the present application provides a device for characterizing the computational efficiency of a granular filling material, comprising:

[0031] A size determination module, configured to determine a minimum effective representative volume unit size corresponding to the granular filling material based on a mesoscopic structural model of the granular filling material;

[0032] A performance simulation module is used to construct a finite element model and perform mechanical performance simulation based on the minimum effective representative volume unit size using different mesh partitioning parameters to obtain simulation results;

[0033] An effect evaluation module is used to quantify the correlation between calculation efficiency and calculation accuracy based on the simulation results and define a comprehensive calculation effect index;

[0034] The combination screening module is used to screen the optimal combination of the representative volume unit size and the grid size based on the comprehensive calculation effect index.

[0035] In a third aspect, an embodiment of the present application further provides an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the steps of the method for characterizing the computational efficiency of the particle filling material as described in the first aspect are performed.

[0036] In a fourth aspect, an embodiment of the present application further provides a readable storage medium, wherein the storage medium stores a computer program, which, when executed by a processor, implements the method for characterizing the computational efficiency of the particle filling material as described in the first aspect.

[0037] The present application provides a method for characterizing the computational efficiency of granular filling materials and related equipment, wherein the method includes: determining the minimum effective representative volume unit size corresponding to the granular filling material based on a microscopic structural model of the granular filling material; constructing a finite element model with different meshing parameters for the minimum effective representative volume unit size and performing mechanical property simulation to obtain simulation results; quantifying the correlation between computational efficiency and computational accuracy based on the simulation results, defining a comprehensive computational effect index; and screening the optimal combination of representative volume unit size and mesh size based on the comprehensive computational effect index. The present application provides a systematic and scientific representative volume unit (RVE) size and mesh parameter selection scheme for the computational simulation process of granular filling materials, which determines the minimum effective RVE size based on the microscopic structural model to ensure the representativeness and accuracy of subsequent simulations; then constructing a finite element model with different meshing parameters and simulating mechanical properties to comprehensively study the influence of mesh size on simulation results; then defining a comprehensive computational effect index by quantifying the correlation between computational efficiency and accuracy, and organically combining the two for evaluation; and finally screening the optimal combination of RVE size and mesh size based on the comprehensive computational effect index. This application can effectively solve the problems of unreasonable RVE size selection and difficulty in balancing calculation efficiency and accuracy in the existing technology, significantly improve the efficiency and feasibility of constructing the calculation model of particle filling materials, provide strong support for the optimal design and performance prediction of materials, and has important practical application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following is a brief introduction to the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For those skilled in the art, other drawings can be obtained based on these drawings without creative work.

[0039] Figure 1 This is an application environment diagram of the computational efficiency characterization method for granular filling materials provided in an embodiment of the present application;

[0040] Figure 2 1 is a flow chart of a method for characterizing the computational efficiency of a particle filling material provided in an embodiment of the present application;

[0041] Figure 3 is a schematic diagram of a CT-based three-dimensional mesoscopic model provided in an embodiment of the present application;

[0042] Figure 4 Schematic diagram of a model for selecting RVEs with different side lengths provided in an embodiment of the present application;

[0043] Figure 5 This is a schematic diagram showing the effect of different REV sizes on porosity provided in the examples of this application;

[0044] Figure 6 Schematic diagram of a mesoscopic RVE model of filling materials with particles of different sizes provided in an embodiment of the present application;

[0045] Figure 7 is a comparison chart of the simulated relaxation modulus values ​​provided in the examples of the present application;

[0046] Figure 8 is a comparison diagram of relative errors of different finite element models provided in the embodiments of the present application;

[0047] Figure 9 This is a comparison chart of the changes in the computing performance of different models provided in the embodiments of the present application;

[0048] Figure 10 2 is a schematic structural diagram of a device for characterizing the computational efficiency of a particle filling material provided in an embodiment of the present application;

[0049] Figure 11 It is a structural diagram of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0050] Exemplary embodiments will be described in detail herein, with examples illustrated in the accompanying drawings. In the following description, when referring to the drawings, identical numerals in different figures represent identical or similar elements, unless otherwise indicated. The embodiments described in the following exemplary embodiments are not intended to represent all embodiments consistent with the present application. Rather, they are merely examples of systems and methods consistent with aspects of the present application, as detailed in the appended claims.

[0051] It should be noted that, in this document, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive descriptions such as inclusion, so that a process, method, article or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, an element defined by the sentence "comprising a ..." does not exclude the presence of other identical elements in the process, method, article or device comprising the element. In addition, components, features, and elements with the same name in different embodiments of the present application may have the same meaning or different meanings, and their specific meanings need to be determined by their explanation in the specific embodiment or further combined with the context of the specific embodiment.

[0052] It should be understood that the specific embodiments described herein are only used to explain the present application and are not intended to limit the present application.

[0053] In the subsequent description, the use of suffixes such as "module", "component" or "unit" to represent elements is only for the purpose of facilitating the description of the present application and has no specific meaning. Therefore, "module", "component" or "unit" can be used interchangeably.

[0054] In order to solve the above-mentioned technical problems and overcome the defects of the existing technology, the embodiments of the present application provide a method for characterizing the computational efficiency of granular filling materials and related equipment. By reasonably selecting the representative volume unit size and grid division, the accuracy of the calculation results and the calculation time are comprehensively measured to achieve a balance between computational efficiency and accuracy in the micromechanical simulation of granular filling materials.

[0055] Figure 1 FIG. 1 is an application environment diagram of a method for characterizing the computational efficiency of a particle filling material in one embodiment. Figure 1, the computational efficiency characterization method of the particle filling material is applied to the computational efficiency characterization system of the particle filling material. The computational efficiency characterization system of the particle filling material includes a terminal 110 and a server 120. The terminal 110 and the server 120 are connected via a network. The terminal 110 can be a desktop terminal or a mobile terminal. The mobile terminal can be at least one of a mobile phone, a tablet computer, a laptop computer, etc. The server 120 can be implemented as an independent server or a server cluster composed of multiple servers. The terminal 110 is used to determine the minimum effective representative volume unit size corresponding to the particle filling material based on the microscopic structure model of the particle filling material; for the minimum effective representative volume unit size, a finite element model is constructed through different mesh division parameters and a mechanical property simulation is performed to obtain a simulation result; based on the simulation result, the correlation between computational efficiency and computational accuracy is quantified, and a comprehensive computational effect index is defined; based on the comprehensive computational effect index, the optimal combination of the representative volume unit size and the mesh size is screened.

[0056] See also Figure 2 , Figure 2 : This is a flow chart of a method for characterizing the computational efficiency of a granular filling material provided in one embodiment of the present application. This embodiment mainly uses the method for characterizing the computational efficiency of a granular filling material as an example for application to a computer device. The method for characterizing the computational efficiency of a granular filling material provided in one embodiment of the present application may specifically include the following steps:

[0057] S1. Determine the minimum effective representative volume unit size corresponding to the granular filling material based on the microstructure model of the granular filling material;

[0058] Specifically, for step S1, it is required to establish a microscopic structural model of the particle filling material to accurately capture the characteristics of the particle distribution, matrix, and pores inside the material. The three-dimensional structural information of the material is obtained through CT scanning or three-dimensional reconstruction technology to provide a basis for subsequent analysis. Next, representative volume element (RVE) models with different side lengths are selected to calculate the oscillation change curve of the target parameters (such as porosity, particle volume fraction, etc.) as the RVE size changes. Analyze the curve to determine the critical size at which the target parameters tend to be stable, that is, the minimum effective representative volume unit size corresponding to the particle filling material, to ensure that the selected RVE size can represent the macroscopic properties of the material without increasing unnecessary computational burden due to excessive size.

[0059] In specific embodiments, in addition to CT scanning and 3D reconstruction techniques, high-resolution imaging techniques such as synchrotron CT and focused ion beam scanning (FIB-SEM) can also be used to obtain more accurate microstructural models. When selecting RVE dimensions, the RVE dimensions can be further optimized based on the material's actual application scenarios and performance requirements. For example, for materials whose mechanical properties require special attention in a specific direction, RVEs of different shapes and orientations can be selected to analyze their impact on the performance in that direction.

[0060] This embodiment accurately determines the minimum effective RVE size to ensure the representativeness and accuracy of subsequent mechanical property simulations and computational efficiency characterization, avoiding problems such as large deviations in simulation results due to too small RVE size and waste of computational resources due to too large RVE size, thereby laying a solid foundation for the entire computational efficiency characterization method.

[0061] S2. Construct a finite element model using different meshing parameters for the minimum effective representative volume element size and perform mechanical property simulations to obtain simulation results;

[0062] Specifically, for step S2, after determining the minimum effective RVE size, at least three different mesh division schemes are set for this size, and the mesh size range is usually 5μm-20μm. Through reasonable mesh division, the microstructure of the continuous particle filling material is discretized into a finite number of units for numerical simulation calculations. When constructing the finite element model, cohesive units are inserted to characterize the interface dewetting effect between the particles and the matrix, and parameters such as interface stiffness, adhesion and failure displacement are set so that the model can more realistically reflect the mechanical behavior and damage evolution process inside the material. Based on the constructed finite element model, mechanical property simulation is performed, such as relaxation process simulation under constant strain, and simulation results are obtained, including key mechanical performance parameters such as relaxation modulus.

[0063] In a specific embodiment, in addition to relaxation modulus simulation, other mechanical properties simulations can be performed according to actual needs, such as mechanical response simulation under different loading conditions such as tension, compression, and shear, to comprehensively evaluate the performance of granular filler materials under different working conditions. In terms of meshing, different mesh types and meshing algorithms, such as tetrahedral meshes and hexahedral meshes, can be used to compare and analyze the impact of different meshing methods on simulation results and computational efficiency. In addition, adaptive meshing technology can be combined to automatically adjust the mesh density according to the distribution of stress and strain during the simulation process, further improving simulation accuracy and computational efficiency.

[0064] This embodiment constructs a finite element model and performs mechanical property simulation by using different mesh partitioning parameters. It can systematically study the influence of factors such as mesh size on the simulation results, provide rich data support for the subsequent quantitative correlation between calculation efficiency and calculation accuracy, and screen the optimal combination, which helps to deeply understand the mechanical properties of particle-filled materials and optimize the calculation model.

[0065] S3. Based on the simulation results, quantify the correlation between computational efficiency and computational accuracy, and define comprehensive computational performance indicators.

[0066] Specifically, for step S3, based on the results obtained from the above-mentioned mechanical properties simulation, on the one hand, the calculation accuracy index is determined by characterizing the relative deviation percentage between the simulation value and the experimental value, reflecting the accuracy of the simulation result; on the other hand, the calculation efficiency index is determined by quantifying the computing resource consumption time or the number of computing nodes, reflecting the time and resource cost required for the simulation calculation. Then, based on the calculation accuracy index and the calculation efficiency index, a comprehensive calculation effect index is defined. The comprehensive calculation effect index can be defined as the product of the relative deviation and the calculation time, or it can be defined as the evaluation result after weighted evaluation of multiple groups of model parameters through a normalized formula, thereby comprehensively evaluating the two mutually restrictive factors of calculation accuracy and calculation efficiency.

[0067] In a specific embodiment, in terms of computational accuracy indicators, in addition to the relative deviation percentage, other indicators that can more comprehensively and accurately reflect the degree of agreement between the simulation results and the experimental results can also be used, such as the root mean square error (RMSE), the mean absolute error (MAE), etc. In terms of computational efficiency indicators, in addition to the computation time and the number of computing nodes, indicators such as the utilization rate of resources during the computation process can also be considered to more comprehensively evaluate the computational efficiency. In addition, the definition of the comprehensive computational effect indicator can be further combined with specific application scenarios and actual needs, and different weights can be assigned to computational accuracy and computational efficiency to highlight the importance of different aspects.

[0068] This embodiment quantifies the correlation between computational efficiency and computational accuracy and defines a comprehensive computational effect index, thereby organically combining the two. This provides a scientific and reasonable evaluation basis for subsequent screening of the optimal combination of representative volume unit size and grid size, and helps to maximize computational efficiency while ensuring a certain level of computational accuracy, thereby meeting the demand for fast and accurate simulation calculations in practical engineering applications.

[0069] S4. Based on comprehensive computational performance indicators, select the optimal combination of representative volume unit size and grid size;

[0070] Specifically, in step S4, with the minimum comprehensive computational effect index as the optimization goal, different combinations of representative volume unit sizes and grid sizes are comprehensively evaluated and screened based on computational accuracy and efficiency. By analyzing the comprehensive computational effect index values ​​of different combinations, the optimal combination with the highest computational efficiency is determined while meeting the computational accuracy requirements. To further verify the reliability and applicability of the selected optimal combination, numerical simulations of variable-angle stretching and shearing are performed on it. The simulation verification results are then used to make necessary adjustments and optimizations to the optimal combination.

[0071] In a specific embodiment, in the process of screening the optimal combination, a variety of optimization algorithms, such as genetic algorithms and particle swarm optimization algorithms, can be used to improve the efficiency and accuracy of the screening. In addition, in addition to the numerical simulation verification of variable-angle tensile shear, other types of mechanical property simulation verifications, such as fatigue loading simulation and impact simulation, can also be performed based on the actual application characteristics of the material to ensure that the optimal combination has good performance under different working conditions. At the same time, the optimal combination screened out can be applied to the design and performance prediction of specific particle filling materials in combination with actual engineering cases to further verify its effectiveness and superiority in actual applications.

[0072] This embodiment screens out the optimal combination of representative volume unit size and grid size through comprehensive calculation effect indicators, and verifies and adjusts them. It can provide an efficient and accurate model parameter selection scheme for the computational simulation of particle-filled materials, significantly improve computational efficiency and feasibility, reduce computational costs and time consumption, and provide strong support for material optimization design and performance prediction, which has important practical application value.

[0073] Optionally, in some embodiments, step S1 of “determining the minimum effective representative volume unit size corresponding to the granular filling material based on the mesoscopic structure model of the granular filling material” may specifically include:

[0074] S11. Construct a three-dimensional mesostructure model of the particle-filled material using CT scanning or three-dimensional reconstruction technology. The three-dimensional mesostructure model includes particle distribution characteristics, matrix characteristics, and pore characteristics.

[0075] Specifically, for step S11, a three-dimensional microstructure model of the particle-filled material is obtained using CT scanning or three-dimensional reconstruction technology. CT scanning can provide high-resolution tomographic images of the interior of the material, and these images are converted into three-dimensional models through reconstruction algorithms, thereby showing in detail the distribution of particles, the morphology of the matrix, and the position and size of pores and other characteristics. The constructed three-dimensional microstructure model should be accurate enough to truly reflect the internal structure of the material and provide a basis for subsequent RVE size selection and mechanical property simulation. In addition to CT scanning and three-dimensional reconstruction technology, high-resolution imaging technologies such as synchrotron radiation CT and focused ion beam scanning (FIB-SEM) can also be used to obtain more accurate microstructure models. These technologies can provide higher resolution and clearer internal structure details, which help to more accurately capture the characteristics of particles, matrix and pores. In addition, the advantages of multiple imaging technologies can be combined to perform multi-scale imaging and data fusion to obtain more comprehensive material structure information.

[0076] This step uses high-precision imaging technology to construct a 3D microstructure model, accurately capturing the internal structural characteristics of the particle-filled material and providing reliable basic data for subsequent RVE size selection and mechanical property simulation. This helps improve the accuracy and reliability of the entire computational efficiency characterization method, ensuring the authenticity and validity of subsequent analysis results.

[0077] S12. Select representative volume unit models with different side lengths and calculate the oscillation change curve of the target parameter as the representative volume unit size changes;

[0078] Specifically, for step S12, representative volume element (RVE) models with different side lengths are selected in the constructed three-dimensional microstructure model. For each RVE model, the oscillation change curve of the target parameter (such as porosity, particle volume fraction or interface volume ratio, etc.) as the RVE size changes is calculated. Through this method, the fluctuation of the target parameter under different RVE sizes can be observed, so as to understand the influence of RVE size on the stability of the target parameter. When selecting the RVE model, a variety of selection methods can be adopted, such as random selection, uniform distribution selection, etc., to ensure that the selected RVE model can fully represent the overall properties of the material. In addition, the calculated oscillation change curve can be analyzed in combination with statistical methods to extract more statistical features, such as mean, standard deviation, coefficient of variation, etc., to more comprehensively evaluate the stability of the target parameter.

[0079] This step calculates the oscillation curve of the target parameter as it changes with RVE size, visually demonstrating the impact of RVE size on the stability of the target parameter and helping to determine the critical size at which the target parameter stabilizes. This provides important data support for the subsequent determination of the minimum effective RVE size, ensuring that the selected RVE size accurately represents the material's macroscopic properties and avoiding simulation result deviations caused by inappropriate RVE size.

[0080] S13. Based on the oscillation change curve, select the critical size at which the target parameter tends to be stable as the minimum effective representative volume unit size corresponding to the particle filling material;

[0081] Specifically, for step S13, the oscillation change curve obtained by calculation is analyzed to determine the critical size at which the target parameter tends to be stable. When the RVE size reaches or exceeds the critical size, the fluctuation amplitude of the target parameter is significantly reduced and tends to be stable. The critical size is used as the minimum effective representative volume unit size corresponding to the particle filling material to ensure that the selected RVE size can represent the macroscopic properties of the material without increasing unnecessary calculation burden due to excessive size. When determining the critical size, the oscillation change curve can be further analyzed and processed in combination with experimental fitting or numerical simulation methods. For example, curve fitting technology is used to fit the relationship curve between the target parameter and the RVE size, and the stable area of ​​the curve is determined by methods such as derivation or extreme value analysis. In addition, relevant theoretical models and empirical formulas can be referred to to predict and verify the critical size to improve the accuracy of the determination results.

[0082] This step ensures the representativeness and accuracy of subsequent mechanical property simulations and computational efficiency characterization by accurately determining the minimum effective RVE size. This avoids problems such as large deviations in simulation results due to too small an RVE size and waste of computational resources due to too large an RVE size, thus laying a solid foundation for the entire computational efficiency characterization method.

[0083] Optionally, in some embodiments, the target parameter is at least one of porosity, particle volume fraction, or interface volume fraction, and the critical size is determined by experimental fitting or numerical simulation, and the value is not less than 600 μm.

[0084] Specifically, in the computational efficiency characterization methods for particle-filled materials, the selection of target parameters is crucial for determining the minimum effective RVE size. Porosity, particle volume fraction, and interface volume fraction are three common parameters that reflect the internal structural characteristics of particle-filled materials. Porosity indicates the volume fraction of pores in the material, particle volume fraction indicates the proportion of the particle phase in the total material volume, and interface volume fraction reflects the volume fraction of the interface layer between the particles and the matrix. Selecting at least one of these parameters as the target parameter can effectively characterize the impact of RVE size on the representativeness of the material's internal structure. In addition to the three parameters mentioned above, other parameters that reflect key material properties can also be selected as target parameters based on the specific research objectives and material properties. For example, for certain functional particle-filled materials, parameters such as particle orientation and aspect ratio distribution can be considered to more comprehensively evaluate the impact of RVE size on material performance. Furthermore, comprehensive analysis can be conducted by combining multiple parameters, using statistical methods such as principal component analysis (PCA) to determine the correlation and importance between different parameters, thereby more accurately assessing the rationality of RVE size.

[0085] Determining the critical size is a key step in ensuring the rationality of RVE sizing. Through experimental fitting or numerical simulation, an oscillatory curve can be obtained showing the target parameter's oscillation with RVE size. Experimental fitting typically uses actual measured data points, using regression analysis and other methods to construct a curve that correlates the parameter with size. Numerical simulation, on the other hand, establishes computational models for RVEs of varying sizes and simulates the corresponding parameter values. Curve analysis indicates that when the RVE size reaches a certain value, the fluctuation amplitude of the target parameter significantly decreases and stabilizes. This size is considered the critical size. Furthermore, to ensure that the RVE size adequately represents the material's microstructural characteristics and avoid statistical errors and inaccurate simulation results caused by undersizing, a critical size of no less than 600 μm is specified. Scientifically determining a critical size of no less than 600 μm ensures that the selected RVE size accurately reflects the macroscopic properties of the particle-filled material while avoiding significant deviations in simulation results due to undersizing. This provides a reliable foundation for subsequent mechanical property simulations and computational efficiency characterization, enhancing the accuracy and reliability of the overall computational efficiency characterization method.

[0086] Optionally, in some embodiments, step S2 of "constructing a finite element model with different meshing parameters for the minimum effective representative volume unit size and performing mechanical property simulation to obtain simulation results" may specifically include:

[0087] S21. Set at least three different meshing schemes for the minimum effective representative volume size, wherein the mesh size range of the meshing scheme is 5 μm-20 μm;

[0088] Specifically, for step S21, after determining the minimum effective representative volume element (RVE) size, it is necessary to set at least three different mesh division schemes for this size. The mesh size range of the mesh division scheme is set to 5μm to 20μm. By setting division schemes with different mesh sizes, the influence of mesh size on finite element simulation results can be systematically studied, including two aspects: calculation accuracy and calculation efficiency. Smaller mesh sizes can capture the mechanical behavior inside the material more carefully, but will increase the amount of calculation and resource consumption; larger mesh sizes have higher calculation efficiency, but may sacrifice a certain degree of calculation accuracy. When dividing the mesh, a variety of mesh types can be used, such as tetrahedral meshes, hexahedral meshes, etc., and the effects of different mesh types on simulation results and calculation efficiency can be compared and analyzed. In addition, adaptive mesh division technology can be combined to automatically adjust the mesh density according to the distribution of stress and strain during the simulation process to further improve simulation accuracy and calculation efficiency.

[0089] By setting different grid division schemes, this step can comprehensively evaluate the impact of grid size on calculation accuracy and efficiency, provide rich data support for subsequent screening of the optimal combination, and help find the optimal balance between calculation accuracy and efficiency.

[0090] S22. Insert cohesive elements into the finite element model to characterize the dewetting effect at the interface between the particles and the matrix, and set the interface stiffness, adhesion, and failure displacement parameters.

[0091] Specifically, for step S22, in order to more realistically simulate the mechanical behavior inside the particle filling material, especially the dewetting effect at the interface between the particles and the matrix, it is necessary to insert a cohesive force unit into the finite element model. The cohesive force unit can characterize the mechanical properties of the interface, including parameters such as interface stiffness, adhesion and failure displacement. Interface stiffness reflects the ability of the interface to resist deformation, adhesion represents the maximum stress that the interface can withstand, and failure displacement is the displacement when the interface is damaged. By reasonably setting these parameters, the model can more accurately simulate the damage and destruction process of the interface. In addition to the bilinear cohesive force model, a more complex nonlinear cohesive force model can also be used to describe the mechanical behavior of the interface to more accurately simulate the response of the interface under different loading conditions. In addition, the determination of the interface parameters can be achieved by fitting experimental data or referring to research results in relevant literature to ensure the rationality and accuracy of the parameters.

[0092] By inserting cohesive units and properly setting interface parameters, this step can more realistically simulate the dewetting effect at the interface between particles and the matrix, improve the accuracy and reliability of the model, and contribute to a deeper understanding of the mechanical properties and damage mechanisms of the material.

[0093] S23. Perform mechanical property simulation based on the finite element model and obtain simulation results;

[0094] Specifically, for step S23, a mechanical property simulation is performed using the constructed finite element model. The loading condition of the simulation is a relaxation process under constant strain, the strain level is 5%, and the loading rate is 500 mm / min. During the simulation, the stress relaxation behavior of the material is recorded to obtain key mechanical property parameters such as relaxation modulus. By comparing the simulation results under different meshing schemes, the influence of mesh size on calculation accuracy and efficiency can be analyzed. In addition to relaxation modulus simulation, other mechanical property simulations can be performed according to actual needs, such as mechanical response simulation under different loading conditions such as tension, compression, and shear, to comprehensively evaluate the performance of particle-filled materials under different working conditions. In addition, multi-field coupling simulation techniques, such as thermal-mechanical coupling, force-electric coupling, etc., can be combined to study the mechanical behavior of particle-filled materials under multi-field action.

[0095] Through mechanical property simulation, this step can obtain detailed mechanical property data under different mesh division schemes, providing a basis for the subsequent quantitative correlation between calculation efficiency and accuracy, and helping to deeply understand the mechanical properties of particle-filled materials and optimize the calculation model.

[0096] Optionally, in some embodiments, the mechanical parameters of the cohesive unit are defined by a bilinear constitutive model, and the loading condition is a relaxation process under constant strain, with a strain level of 5% and a loading rate of 500 mm / min.

[0097] Specifically, the mechanical parameters of the cohesive force unit are defined using a bilinear constitutive model. The bilinear constitutive model is a common model used to describe the mechanical behavior of material interfaces. It can better simulate the elastic response and plastic damage evolution of the interface during loading. The model describes the stress-strain relationship of the interface through two linear stages: the first stage is the elastic stage, the interface stiffness is high, and the stress and strain are in a linear relationship; the second stage is the damage stage. When a certain adhesion force is reached, the interface is damaged, the stiffness decreases, and finally it is destroyed. Through the bilinear constitutive model, the mechanical parameters of the cohesive force unit can be accurately defined, including interface stiffness, adhesion force, and failure displacement, so as to more realistically simulate the interfacial dewetting effect between particles and the matrix. Using a bilinear constitutive model to define the mechanical parameters of the cohesive force unit can more accurately simulate the interfacial dewetting effect between particles and the matrix, improve the accuracy and reliability of the finite element model, and help to deeply understand the interfacial mechanical properties and damage mechanism of the material.

[0098] When simulating mechanical properties, the relaxation process under constant strain is used as the loading condition. Specifically, the strain of the model is increased to 5%, and then the strain level is kept constant to observe the stress relaxation behavior of the material under constant strain. The loading rate is 500mm / min, which can ensure that the simulation process is completed within a reasonable time frame while better capturing the relaxation characteristics of the material. Through this loading condition, it is possible to simulate long-term loading conditions under constant strain that the material may encounter in actual applications, such as the long-term stress relaxation behavior of structural components under fixed deformation. Using the relaxation process under constant strain as the loading condition can effectively simulate the stress relaxation behavior of particle-filled materials in actual applications, provide important data support for studying the long-term mechanical properties and damage evolution of materials, and help improve the practicality and credibility of the simulation results.

[0099] Optionally, in some embodiments, step S3 of "quantifying the correlation between computational efficiency and computational accuracy based on the simulation results and defining a comprehensive computational effect index" may specifically include:

[0100] S31. Based on the simulation results, the calculation accuracy index is determined by characterizing the relative deviation percentage between the simulation value and the experimental value;

[0101] Specifically, for step S31, after performing the mechanical property simulation, the mechanical property parameters (such as relaxation modulus, etc.) obtained by simulation are compared with the corresponding parameters obtained by actual experimental measurement, and the relative deviation percentage between them is calculated. The calculation formula of the relative deviation percentage is usually: (simulation value-experimental value) / experimental value×100%. In this way, the accuracy of the simulation results can be quantitatively evaluated. The smaller the relative deviation percentage, the more consistent the simulation results are with the experimental results, and the higher the calculation accuracy. In addition to the relative deviation percentage, other statistical indicators can also be used to characterize the calculation accuracy, such as root mean square error (RMSE), mean absolute error (MAE), etc. These indicators can reflect the difference between the simulation value and the experimental value from different angles, providing a more comprehensive perspective for the evaluation of calculation accuracy. In addition, the error propagation theory can be combined to analyze the impact of each link in the simulation process on the final accuracy, thereby providing targeted improvement directions for improving calculation accuracy.

[0102] This step determines the calculation accuracy index through indicators such as relative deviation percentage, which can intuitively and quantitatively reflect the accuracy of the simulation results, provide key data support for the definition of subsequent comprehensive calculation effect indicators, and help to clarify the accuracy performance during the model parameter screening process, ensuring that the final selected model parameter combination can generate reliable simulation results.

[0103] S32. Based on the simulation results, determine the computing efficiency index by calculating the resource consumption time or the number of computing nodes;

[0104] Specifically, for step S32, the computational efficiency index is determined based on the computational resources consumed during the simulation process, primarily quantified by the computational resource consumption duration or the number of computing nodes. Computational resource consumption duration refers to the length of time required to complete a simulation, typically measured in seconds, minutes, or hours; the number of computing nodes refers to the number of computing nodes (such as CPU cores, computing servers, etc.) involved in the simulation in a parallel computing environment. By statistically analyzing these indicators, the computational efficiency under different model parameter combinations can be evaluated. The shorter the computational resource consumption duration or the fewer the number of computing nodes, the higher the computational efficiency. In addition to computational resource consumption duration and the number of computing nodes, other factors related to computational efficiency can also be considered, such as resource utilization during the computation process (such as CPU utilization, memory utilization, etc.), to more comprehensively evaluate computational efficiency. Furthermore, computational complexity theory can be combined to analyze the impact of model parameters (such as RVE size, grid size, etc.) on computational complexity, establish a quantitative relationship model between model parameters and computational efficiency, and provide a theoretical basis for optimizing the selection of model parameters.

[0105] This step determines the computational efficiency index by quantifying the computational resource consumption time or the number of computing nodes. This intuitively reflects the time and resource costs of the simulation calculations, providing a quantitative basis for the definition of comprehensive computational performance indicators. This helps to balance the relationship between computational accuracy and efficiency when screening model parameters, avoiding excessive pursuit of high accuracy that leads to low computational efficiency, or sacrificing too much accuracy due to a one-sided pursuit of efficiency.

[0106] S33. Determine a comprehensive calculation effect index based on the calculation accuracy index and the calculation efficiency index, wherein the comprehensive calculation effect index is defined as the product of the relative deviation and the calculation time, and / or, the comprehensive calculation effect index is defined as the evaluation result after weighted evaluation of multiple groups of model parameters by a normalization formula;

[0107] Specifically, for step S33, the comprehensive calculation effect index combines the calculation accuracy index and the calculation efficiency index to comprehensively evaluate the overall calculation effect of different model parameter combinations. One definition method is to directly multiply the relative deviation (computational accuracy index) by the calculation time (computational efficiency index) to obtain the comprehensive calculation effect index. This definition method is simple and intuitive and can directly reflect the combined impact of accuracy and efficiency: the smaller the relative deviation and the shorter the calculation time, the smaller the comprehensive calculation effect index value, indicating a better model parameter combination. Another definition method is to normalize the calculation accuracy index and calculation efficiency index of multiple groups of model parameters using a normalization formula, and then perform a weighted sum according to a certain weight to obtain the evaluation result of the comprehensive calculation effect index. Normalization can convert indicators of different dimensions and orders of magnitude into numerical values ​​on the same scale, facilitating comprehensive evaluation; the setting of weights can be adjusted according to the relative emphasis on accuracy and efficiency in actual applications. When defining the comprehensive calculation effect index, in addition to the two methods mentioned above, other multi-index comprehensive evaluation methods can also be used, such as principal component analysis (PCA) and analytic hierarchy process (AHP). These methods can more comprehensively consider the correlation and relative importance between various indicators, providing a more scientific and reasonable solution for evaluating comprehensive computing effects. Furthermore, they can be combined with machine learning algorithms, such as support vector machines (SVMs) and neural networks, to train on a large number of sample data sets of known model parameter combinations and their computing effects, establishing a mapping relationship between model parameters and comprehensive computing effects. This allows for rapid and accurate prediction of the comprehensive computing effects of unknown model parameter combinations.

[0108] This step achieves an organic combination of computational accuracy and efficiency through the definition of a comprehensive computational performance index, providing a comprehensive, quantitative evaluation standard for the screening of model parameter combinations. This index enables objective and fair comparison and selection among different model parameter combinations, identifying the model parameter combination that strikes the optimal balance between accuracy and efficiency. This improves the overall effectiveness and feasibility of computational simulations of granular filling materials, providing strong support for practical engineering applications.

[0109] Optionally, in some embodiments, step S4 of “screening the optimal combination of the representative volume unit size and the grid size based on the comprehensive calculation effect index” may specifically include:

[0110] S41. Taking the minimum comprehensive calculation effect index as the optimization goal, select the optimal combination of representative volume unit size and grid size based on the calculation accuracy index and calculation efficiency index;

[0111] Specifically, for step S41, after determining the comprehensive calculation effect index, the combination of different representative volume unit sizes and grid sizes is comprehensively evaluated and screened with the minimum of this index as the optimization goal. By comparing the comprehensive calculation effect index values ​​of each combination, the optimal combination with the highest calculation efficiency while meeting the calculation accuracy requirements is found. This process requires comprehensive consideration of both calculation accuracy and calculation efficiency, and weighing the relationship between the two to find the best balance point. When screening the optimal combination, a variety of optimization algorithms can be used, such as genetic algorithms, particle swarm optimization algorithms, simulated annealing algorithms, etc. These algorithms can efficiently search for optimal solutions in complex parameter spaces, thereby improving the efficiency and accuracy of screening. In addition, it is also possible to combine proxy model technologies, such as response surface method, Kriging model, etc., to establish an approximate relationship between model parameters and comprehensive calculation effect indicators, reduce the number of actual simulation calculations, and further improve the efficiency of the optimization process.

[0112] This step screens the optimal combination with the minimum comprehensive calculation effect index as the optimization goal, ensuring that the selected model parameter combination achieves the best balance between calculation accuracy and efficiency. It not only guarantees the accuracy of the simulation results, but also maximizes the calculation efficiency, reduces the calculation cost and time consumption, and provides the optimal parameter configuration scheme for the computational simulation of particle filling materials.

[0113] S42. Performing numerical simulation on the optimal combination of variable angle tensile shear to obtain simulation verification results;

[0114] Specifically, for step S42, in order to verify the reliability and applicability of the selected optimal combination, a variable angle tensile shear numerical simulation verification is performed on it. Variable angle tensile shear simulation refers to the simulation of the mechanical properties of the material under different angles and load conditions. In this way, the performance of the optimal combination under different working conditions can be comprehensively evaluated to check whether it can maintain high calculation accuracy and efficiency under various conditions. In addition to the variable angle tensile shear numerical simulation verification, other types of mechanical property simulation verifications can also be performed according to the actual application characteristics of the material, such as fatigue loading simulation, impact simulation, creep simulation, etc., to ensure that the optimal combination has good performance under different working conditions. In addition, the simulation verification results can be further compared and calibrated in combination with experimental data to improve the accuracy and credibility of the verification process.

[0115] This step validates the optimal combination through variable-angle tensile shear numerical simulations, comprehensively evaluating its performance under different operating conditions and ensuring its reliability and stability. This step helps identify potential problems and deficiencies, providing a basis for subsequent adjustments and optimizations, and further improving the applicability and effectiveness of the model parameter combination.

[0116] S43. Adjust the optimal combination based on the simulation verification results;

[0117] Specifically, for step S43, necessary adjustments and optimizations are made to the optimal combination based on the results obtained from the variable-angle tensile shear numerical simulation verification. If the verification results show that the optimal combination has problems with insufficient calculation accuracy or reduced efficiency under certain working conditions, the representative volume unit size or grid size can be adjusted in a targeted manner, or other parameters of the finite element model can be optimized to improve its performance. When adjusting the optimal combination, sensitivity analysis techniques can be combined to determine the degree of influence of each model parameter on calculation accuracy and efficiency, and parameters with greater impact on performance can be adjusted first. In addition, a multi-objective optimization method can be used to simultaneously consider multiple performance indicators during the adjustment process, and to seek an adjustment solution that achieves the best balance between different indicators.

[0118] This step, by adjusting the optimal combination based on simulation verification results, further optimizes the model parameter configuration, improving its performance under different operating conditions and ensuring its reliability and effectiveness in practical applications. This step helps continuously refine the model parameter combination to better meet actual engineering needs and improve the overall quality and effectiveness of granular fill material simulations.

[0119] To facilitate understanding of the calculation efficiency characterization method for the particle filling material provided in this application, this embodiment also provides a specific implementation of the calculation efficiency characterization method for the particle filling material, including the following steps:

[0120] (1) Selection of microscopic calculation model:

[0121] like Figure 3 As shown in the figure, a true three-dimensional microscopic model of a granular filling material is obtained based on experimental equipment such as CT. The granular filling material is composed of filling particles of different sizes and types and a matrix. In addition, it also contains initial pores. The model is required to be large enough to meet all the requirements of the representative element volume (REV). Figure 4 Select RVEs with different side lengths at the same location in the model and calculate their porosity (the volume proportion of the more important components in the granular filling material can be used as an evaluation parameter, and a mixture of multiple components can also be used as a reference. Here, only porosity is used as an example). Figure 5 The following is a schematic diagram showing the effect of different REV sizes on porosity. The results show that when the REV side length reaches and exceeds 600 μm, the porosity tends to stabilize. Therefore, in this example, a REV with a side length of at least 600 μm was used for subsequent quantitative characterization and analysis, and all subsequent analysis will be based on 600 μm.

[0122] like Figure 6As shown in the figure, four RVE models with different sizes (L = 1200 μm, 1000 μm, 800 μm, and 600 μm) were selected based on a 600 μm grid. Each RVE size was then divided into three finite element models based on the mesh size (M = 5 μm, 10 μm, and 20 μm) to analyze the effect of mesh size on the calculation results and accuracy.

[0123] (2) Analyze the influence of RVE size and grid size:

[0124] Here, we continue to investigate the effects of RVE size and mesh size using a common particulate filler material as an example. As a viscoelastic material, composite solid propellants exhibit typical relaxation mechanical properties, and the relaxation modulus is a key parameter reflecting these relaxation characteristics. Currently, studies of the relaxation modulus of composite solid propellants are typically based on relaxation mechanical experiments or two-dimensional microscopic numerical simulations. However, numerical simulations of the relaxation process of composite solid propellants have not yet analyzed the impact of the size and mesh size of representative volume element finite element models on computational accuracy and efficiency. Furthermore, few studies have used three-dimensional microscopic finite element models based on the realistic mesostructure of composite solid propellants. To investigate the effects of RVE size and mesh size on the calculated relaxation modulus of composite solid propellants and to determine appropriate three-dimensional finite element model and mesh sizes, 12 different finite element models with four RVE sizes and three mesh sizes developed in the previous section were used for calculations. In composite solid propellants, the load between the binder matrix and filler particles is transferred through the interface layer, which has relatively low strength. When the stress on the propellant is less than the strength of the matrix and filler particles, damage to the interface layer may occur. The "dewetting" effect between the solid particles and the matrix inside the composite solid propellant is considered, and cohesive elements are inserted into the three-dimensional solid propellant microscopic model.

[0125] The loading conditions are: the strain of the model is increased to 5% at a loading rate of 500 mm / min, and then the strain level is maintained at 5% to calculate the equivalent relaxation modulus of the model. In terms of material properties, the modulus of the matrix is ​​obtained by performing a relaxation test on the matrix film. The relaxation modulus of the matrix is ​​also expressed in the form of a Prony series, as shown in formula (1). At room temperature (298.15 K), the Prony series parameters of the matrix are shown in Table 1, in MPa. The elastic modulus of AP particles and Al particles is much higher than that of the matrix. AP particles and Al particles can be regarded as elastic materials, and their mechanical properties adopt a linear elastic model. The mechanical properties of AP particles and Al particles are less affected by the loading rate and can be ignored. The material parameters of AP particles and Al particles at room temperature are shown in Table 2. The bilinear cohesion model is used to simulate the mechanical properties of the interface unit, and the quadratic nominal stress and quadratic energy release rate criteria are used as the damage initiation and damage evolution criteria of the interface bonding unit. The bilinear cohesion model includes three mechanical parameters, namely, interface stiffness k, bonding force σ max and interface failure displacement σ f The parameter values ​​of the bilinear cohesive force model of the AP particle / matrix interface in the reference are adopted. The AP particle / matrix interface parameters of HTPB propellant are: interface stiffness k = 10 MPa / mm, cohesive force σ max =0.8MPa, failure displacement σ f =0.035mm.

[0126] The relaxation modulus of the HTPB composite solid propellant was obtained through relaxation testing. The test and analysis methods were based on existing standards. The relaxation modulus was expressed as a Prony series, as shown in Equation (1), in MPa, with a Poisson's ratio of υ = 0.495.

[0127]

[0128] Table 1. Parameters of the linear viscoelastic constitutive model of the propellant matrix

[0129]

[0130] Table 2. Mechanical properties of the linear elastic model of AP particles and Al particles

[0131]

[0132] In terms of meshing, the dimensions of the 3D microscopic finite element model, the model element size settings, and the number and type of elements in each component are shown in Table 3. In finite element calculations, the degree of damage to the interface elements is primarily measured using the stiffness reduction factor (SDEG). When SDEG is 0, the interface element is intact; when SDEG is 1, it indicates that the interface element has been completely damaged and removed. To prevent mutual intrusion between the matrix and the particles during loading and deformation, a penalty function contact constraint is defined at the AP particle / matrix interface.

[0133] Figure 7 The following are the simulation results of the relaxation modulus of 12 different solid propellant micro-models within 1000 seconds. Under the action of the relaxation load, due to the small strain, dewetting has not occurred. The relative error between the numerical simulation and experimental values ​​of different finite element models within 1000 seconds is shown as follows: Figure 8 Table 3 shows the maximum relative deviation and calculation time of the calculation results of each model within 1000 seconds. In this study, all 12 finite element models were calculated based on the high-performance cloud computing platform of China Union Computer, using 1000 CPU cores. Figure 7 It can be seen from Table 3 that the relaxation modulus obtained from the real microscopic model has a certain consistency.

[0134] Table 3. Information about the microscopic model and calculation results

[0135]

[0136] For a computational model, the shorter the calculation time, the more beneficial it is for engineering applications. Furthermore, the smaller the relative deviation between the calculated and experimental results, the more realistic it is and the more effective it is. However, computational efficiency and accuracy cannot be improved simultaneously; a balance must be found through comprehensive consideration. Therefore, to provide a reasonable evaluation metric to comprehensively measure computational efficiency and accuracy, this paper proposes computational performance as an indicator: computational performance = relative deviation * computational time. The smaller the value of computational performance, the more appropriate the established model.

[0137] Figure 9 The figure shows the performance changes of different models. It can be seen that, across the 12 models, when the RVE size remains constant, the performance initially decreases rapidly before stabilizing as the mesh size increases. When the mesh size remains constant, the performance increases with increasing RVE size, and this phenomenon becomes more pronounced with larger mesh sizes. The best performance is achieved when the RVE size is 800 μm and the mesh size is 10 μm. Therefore, an RVE size of 800 μm and a mesh size of 10 μm are selected for subsequent numerical simulations of variable-angle tensile shear.

[0138] We can also use the 20μm grid with the best calculation effect in 600μm as the basis and normalize other calculation models to obtain:

[0139]

[0140] When the model's calculated result is greater than the standard value, the result is set to 0. The greater the calculation efficiency, the more appropriate the established model. The results are shown in the last column of Table 3. When the RVE size is 800 μm and the grid size is 10 μm, the calculation efficiency is the best and the image is clearer.

[0141] In summary, the computational efficiency characterization method for granular filling materials provided in this embodiment first determines the minimum effective representative volume unit size corresponding to the granular filling material based on the microscopic structural model of the granular filling material; then, for the minimum effective representative volume unit size, a finite element model is constructed using different mesh division parameters and mechanical performance simulation is performed to obtain simulation results; then, based on the simulation results, the correlation between computational efficiency and computational accuracy is quantified, and a comprehensive computational effect index is defined; finally, based on the comprehensive computational effect index, the optimal combination of representative volume unit size and mesh size is screened.

[0142] Compared with existing technologies, the computational efficiency characterization scheme for granular-filled materials provided in this embodiment ensures model representativeness and accuracy by determining the minimum effective RVE size, avoiding the problem of unreasonable RVE size selection in existing technologies. Finite element models are constructed and simulated using different meshing parameters to comprehensively evaluate the impact of meshing parameters. The trade-off between computational efficiency and accuracy is quantified by quantifying the correlation and defining comprehensive computational performance indicators. Ultimately, the optimal model parameter combination is selected, improving computational efficiency and feasibility while reducing computational cost and time consumption. This scheme has important practical application value. It is not only applicable to granular-filled materials but can also be extended to other materials with complex microstructures, demonstrating its broad applicability and scalability.

[0143] It should be understood that although Figure 2 The steps in the flowchart are shown in sequence as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. In addition, Figure 2 At least part of the steps may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least part of the sub-steps or stages of other steps.

[0144] To facilitate better implementation of the computational efficiency characterization method for a granular filling material according to an embodiment of the present application, an embodiment of the present invention further provides a computational efficiency characterization device for a granular filling material based on the computational efficiency characterization method for a granular filling material. The meanings of the terms herein are the same as those in the computational efficiency characterization method for a granular filling material, and specific implementation details can be found in the description of the method embodiment.

[0145] See also Figure 10 , Figure 10 This is a schematic diagram of the structure of a computational efficiency characterization device for a granular filling material provided in an embodiment of the present application. The computational efficiency characterization device for a granular filling material may include a size determination module 201, a performance simulation module 202, an effect evaluation module 20, and a combination screening module 204. Specifically, it may be as follows:

[0146] A size determination module 201 is used to determine the minimum effective representative volume unit size corresponding to the granular filling material based on the microstructure model of the granular filling material;

[0147] The performance simulation module 202 is used to construct a finite element model and perform mechanical performance simulation based on the minimum effective representative volume unit size using different mesh partitioning parameters to obtain simulation results;

[0148] The effect evaluation module 203 is used to quantify the correlation between calculation efficiency and calculation accuracy based on the simulation results and define a comprehensive calculation effect index;

[0149] The combination screening module 204 is used to screen the optimal combination of the representative volume unit size and the grid size based on the comprehensive calculation effect index.

[0150] The specific definition of the device for characterizing the computational efficiency of granular filling materials can be found in the definition of the method for characterizing the computational efficiency of granular filling materials described above and will not be repeated here. The various modules in the above-mentioned device for characterizing the computational efficiency of granular filling materials can be implemented in whole or in part by software, hardware, or a combination thereof. The above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory of the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above modules.

[0151] The computational efficiency characterization device for granular filling materials provided in this embodiment determines the minimum effective RVE size based on a microscopic structural model to ensure the representativeness and accuracy of subsequent simulations; then, a finite element model is constructed through different mesh divisions and mechanical properties are simulated to comprehensively study the influence of mesh size on the simulation results; then, a comprehensive computational effect index is defined by quantifying the correlation between computational efficiency and accuracy, and the two are organically combined for evaluation; finally, the optimal combination of RVE size and mesh size is screened out based on the comprehensive computational effect index, which can effectively solve the problems of unreasonable RVE size selection and difficulty in balancing computational efficiency and accuracy in the prior art, and significantly improve the efficiency and feasibility of constructing computational models for granular filling materials.

[0152] In addition, the present invention also provides an electronic device, such as Figure 11 , which shows a schematic diagram of the structure of the electronic device involved in the embodiment of the present application, specifically:

[0153] The electronic device may include one or more processors 301 of processing cores, one or more computer-readable storage media memories 302, a power supply 303, an input unit 304 and other components. Those skilled in the art will appreciate that Figure 11 The electronic device structure shown in the figure does not constitute a limitation of the electronic device, and may include more or fewer components than shown in the figure, or combine certain components, or arrange components differently.

[0154] The processor 301 is the control center of the electronic device. It connects all parts of the electronic device using various interfaces and lines. By running or executing software programs and / or modules stored in the memory 302 and accessing data stored in the memory 302, it performs various functions of the electronic device and processes data, thereby monitoring the electronic device as a whole. Optionally, the processor 301 may include one or more processing cores; preferably, the processor 301 may integrate an application processor and a modem processor, wherein the application processor primarily processes the operating system, user interface, and application programs, while the modem processor primarily handles wireless communications. It is understood that the modem processor may not be integrated into the processor 301.

[0155] The memory 302 can be used to store software programs and modules. The processor 301 executes various functional applications and the computational efficiency characterization method of the particle filling material by running the software programs and modules stored in the memory 302. The memory 302 may mainly include a program storage area and a data storage area, wherein the program storage area may store an operating system, an application required for at least one function (such as a sound playback function, an image playback function, etc.), etc.; the data storage area may store data created according to the use of the electronic device, etc. In addition, the memory 302 may include a high-speed random access memory, and may also include a non-volatile memory, such as at least one disk storage device, a flash memory device, or other volatile solid-state storage device. Accordingly, the memory 302 may also include a memory controller to provide the processor 301 with access to the memory 302.

[0156] The electronic device also includes a power supply 303 for supplying power to various components. Preferably, the power supply 303 can be logically connected to the processor 301 via a power management system, thereby enabling the power management system to manage charging, discharging, and power consumption. The power supply 303 can also include one or more DC or AC power supplies, a recharging system, a power failure detection circuit, a power converter or inverter, a power status indicator, and other arbitrary components.

[0157] The electronic device may further include an input unit 304, which may be configured to receive input digital or character information and generate keyboard, mouse, joystick, optical or trackball signal inputs related to user settings and function control.

[0158] Although not shown, the electronic device may further include a display unit, etc., which will not be described in detail here. Specifically, in this embodiment, the processor 301 in the electronic device will load the executable files corresponding to the processes of one or more application programs into the memory 302 according to the following instructions, and the processor 301 will run the application programs stored in the memory 302 to implement various functions as follows:

[0159] Based on the microstructure model of the granular filling material, the minimum effective representative volume unit size corresponding to the granular filling material is determined; for the minimum effective representative volume unit size, a finite element model is constructed using different mesh division parameters and mechanical performance simulation is performed to obtain simulation results; based on the simulation results, the correlation between computational efficiency and computational accuracy is quantified, and a comprehensive computational effect index is defined; based on the comprehensive computational effect index, the optimal combination of representative volume unit size and mesh size is screened.

[0160] The specific implementation of the above operations can be found in the previous embodiments and will not be repeated here.

[0161] The embodiment of the present application determines the minimum effective RVE size based on the microstructure model to ensure the representativeness and accuracy of subsequent simulations; then constructs a finite element model through different mesh divisions and simulates the mechanical properties, and comprehensively studies the influence of mesh size on the simulation results; then defines a comprehensive computing effect index by quantifying the correlation between computing efficiency and accuracy, and organically combines the two for evaluation; finally, based on the comprehensive computing effect index, the optimal combination of RVE size and mesh size is screened out, which can effectively solve the problems of unreasonable RVE size selection and difficulty in balancing computing efficiency and accuracy in the prior art, significantly improves the efficiency and feasibility of constructing the computational model of particle-filled materials, provides strong support for the optimized design and performance prediction of materials, and has important practical application value.

[0162] Those skilled in the art will appreciate that all or part of the steps in the various methods of the above embodiments may be accomplished by instructions, or by controlling related hardware through instructions. The instructions may be stored in a computer-readable storage medium and loaded and executed by a processor.

[0163] To this end, an embodiment of the present application provides a storage medium storing a plurality of instructions that can be loaded by a processor to execute the steps in the computational efficiency characterization of any particle filling material provided in the embodiment of the present application. For example, the instructions can execute the following steps:

[0164] Based on the microstructure model of the granular filling material, the minimum effective representative volume unit size corresponding to the granular filling material is determined; for the minimum effective representative volume unit size, a finite element model is constructed using different mesh division parameters and mechanical performance simulation is performed to obtain simulation results; based on the simulation results, the correlation between computational efficiency and computational accuracy is quantified, and a comprehensive computational effect index is defined; based on the comprehensive computational effect index, the optimal combination of representative volume unit size and mesh size is screened.

[0165] The specific implementation of the above operations can be found in the previous embodiments and will not be repeated here.

[0166] The storage medium may include a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk, etc.

[0167] Since the instructions stored in the storage medium can execute the steps in the calculation efficiency characterization method of any particle filling material provided in the embodiments of the present application, the beneficial effects that can be achieved by the calculation efficiency characterization method of any particle filling material provided in the embodiments of the present application can be achieved. Please refer to the previous embodiments for details and will not be repeated here.

[0168] The above is a detailed introduction to the computational efficiency characterization method and related equipment for a particle filling material provided in the embodiments of the present application. Specific examples are used herein to illustrate the principles and implementation methods of the present application. The description of the above embodiments is only used to help understand the method and core idea of ​​the present application. At the same time, for those skilled in the art, based on the ideas of the present application, there may be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on the present application.

Claims

1. A method for characterizing the computational efficiency of a granular filling material, characterized in that: The steps include: Determining a minimum effective representative volume unit size corresponding to the granular filling material based on a mesoscopic structural model of the granular filling material; For the minimum effective representative volume unit size, a finite element model is constructed by using different mesh partitioning parameters and mechanical property simulation is performed to obtain simulation results; Based on the simulation results, quantify the correlation between computational efficiency and computational accuracy, and define a comprehensive computational effect index; Based on the comprehensive calculation effect index, the optimal combination of the representative volume unit size and the grid size is screened.

2. The method for characterizing the computational efficiency of a granular filling material according to claim 1, wherein: The determining of the minimum effective representative volume unit size corresponding to the granular filling material based on the microstructure model of the granular filling material comprises: constructing a three-dimensional microstructure model of the particle filling material by CT scanning or three-dimensional reconstruction technology, wherein the three-dimensional microstructure model includes particle distribution characteristics, matrix characteristics, and pore characteristics; Select representative volume unit models with different side lengths and calculate the oscillation curve of the target parameter as the representative volume unit size changes; Based on the oscillation change curve, a critical size at which the target parameter tends to be stable is selected as the minimum effective representative volume unit size corresponding to the particle filling material.

3. The method for characterizing the computational efficiency of a granular filling material according to claim 2, wherein: The target parameter is at least one of porosity, particle volume fraction or interface volume ratio, and the critical size is determined by experimental fitting or numerical simulation and has a value of not less than 600 μm.

4. The method for characterizing the computational efficiency of a particle filling material according to claim 1, wherein: The method of constructing a finite element model and performing mechanical property simulation based on the minimum effective representative volume unit size by using different mesh partitioning parameters to obtain simulation results includes: For the minimum effective representative volume size, setting at least three different grid division schemes, wherein the grid size range of the grid division scheme is 5 μm-20 μm; Insert cohesive elements into the finite element model to characterize the dewetting effect at the interface between the particles and the matrix, and set the interface stiffness, adhesion, and failure displacement parameters. A mechanical property simulation is performed based on the finite element model to obtain simulation results.

5. The method for characterizing the computational efficiency of a granular filling material according to claim 4, wherein: The mechanical parameters of the cohesive unit are defined by a bilinear constitutive model, and the loading condition is a relaxation process under constant strain, with a strain level of 5% and a loading rate of 500 mm / min.

6. The method for characterizing the computational efficiency of a particle filling material according to claim 1, wherein: According to the simulation results, the correlation between the computational efficiency and the computational accuracy is quantified, and a comprehensive computational effect index is defined, including: Based on the simulation results, the calculation accuracy index is determined by characterizing the relative deviation percentage between the simulation value and the experimental value; Based on the simulation results, determining a computing efficiency index by calculating resource consumption time or quantifying the number of computing nodes; The comprehensive calculation effect index is determined based on the calculation accuracy index and the calculation efficiency index, wherein the comprehensive calculation effect index is defined as the product of the relative deviation and the calculation time, and / or the comprehensive calculation effect index is defined as the evaluation result after weighted evaluation of multiple groups of model parameters through a normalized formula.

7. The method for characterizing the computational efficiency of a particle filling material according to claim 6, wherein: The screening of the optimal combination of the representative volume unit size and the grid size based on the comprehensive calculation effect index includes: Taking the minimum comprehensive calculation effect index as the optimization goal, the optimal combination of the representative volume unit size and the grid size is selected based on the calculation accuracy index and the calculation efficiency index; Performing a variable angle tensile shear numerical simulation to verify the optimal combination, and obtaining a simulation verification result; The optimal combination is adjusted based on the simulation verification result.

8. A device for characterizing the computational efficiency of a granular filling material, characterized in that: include: A size determination module, configured to determine a minimum effective representative volume unit size corresponding to the granular filling material based on a mesoscopic structural model of the granular filling material; A performance simulation module is used to construct a finite element model and perform mechanical performance simulation based on the minimum effective representative volume unit size using different mesh partitioning parameters to obtain simulation results; An effect evaluation module is used to quantify the correlation between calculation efficiency and calculation accuracy based on the simulation results and define a comprehensive calculation effect index; The combination screening module is used to screen the optimal combination of the representative volume unit size and the grid size based on the comprehensive calculation effect index.

9. An electronic device, characterized in that: include: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the steps of the method for characterizing the computational efficiency of a particulate filling material according to any one of claims 1 to 7 are implemented.

10. A storage medium, characterized in that: The computer program is stored and can be loaded by a processor to execute the method for characterizing the computational efficiency of a granular filling material according to any one of claims 1 to 7.

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