Nonlinear heterogeneous material layered multiscale modeling method based on finite volume method

Abstract

The application discloses a nonlinear heterogeneous material layered multi-scale modeling method based on a finite volume method, belongs to the field of nonlinear solid material multi-scale mechanical behavior simulation, and comprises the following steps: S1, constructing a discrete macroscopic balance equation of an incremental Lagrange format; S2, establishing a macro-micro scale mapping mechanism to transfer the deformation gradient of a macroscopic control volume center point to a microcosmic representative volume element boundary; S3, developing a generalized boundary condition engine to replace a periodic constraint with a Hill-Mandel energy equivalent force condition; S4, solving a microcosmic stress field by using a finite volume method flux integral, homogenizing the volume average stress of the microcosmic representative volume element by the Hill-Mandel energy equivalent force condition and feeding back to a macroscopic constitutive relation; and S5, introducing a numerical diffusion term in the discrete macroscopic balance equation, and triggering adaptive promotion of a diffusion coefficient when an equivalent plastic strain exceeds a preset threshold value. Through the collaborative innovation of the layered FVM architecture and the generalized boundary engine, the application realizes efficiency leap, boundary liberation and precision breakthrough.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of numerical simulation of multi-scale mechanical behavior of nonlinear solid materials, and in particular to a hierarchical multi-scale modeling method for nonlinear heterogeneous materials based on finite volume method. BACKGROUND

[0002] In the field of computational solid mechanics, it is always a great challenge to accurately predict the mechanical response of nonlinear heterogeneous materials (such as composites containing random pores, fibers or phase interfaces). Traditional single-scale methods have fundamental limitations: macro-homogenization models (such as phenomenological constitutive equations) cannot capture local failure (such as pore collapse or shear band formation) caused by microstructure evolution; while global micro-discretization can describe details, the computational cost increases exponentially with the scale, making it completely impractical for engineering-level models (such as aircraft engine blades).

[0003] To balance accuracy and efficiency, multi-scale modeling methods have developed rapidly in the past two decades, forming two major technical routes, but both have significant defects:

[0004] 1. The representative technologies of concurrent method include quasi-continuum (QC) and extended finite element method (XFEM), QC couples molecular dynamics with continuum region through atom-node displacement matching, and XFEM embeds micro-model in local region such as crack tip; however, these methods have the problem of "scale sticking", and the energy transfer at the strong coupling interface needs to be accurately matched (such as the displacement coordination of atoms and nodes in QC), which easily causes stress oscillation (error exceeding 15%) in actual operation; at the same time, its strong dependence on geometry requires that the microstructure must be known globally (such as through micro-CT scanning), which cannot be applied to random pores of additive manufacturing parts.

[0005] 2. The dominant solution of information passing method FE² model realizes macro-micro coupling through nested solution: macro deformation gradient F drives micro RVE finite element solution, and homogenized stress P is fed back to the macro constitutive response; although it is widely adopted, it has three major defects: computational efficiency collapse - each macro integration point needs to solve the RVE boundary value problem independently, for example, a 3D hole plate model containing 900 RVEs, the single step time is 200 times longer than the single scale model; periodic boundary "cage" - RVE needs to satisfy the periodic boundary condition (Periodic BC), but actual materials (such as cast alloys) contain non-periodic defects, resulting in a stress distortion error of up to 5% at the free boundary; grid dependence - micro RVE needs to fit complex geometry (such as pores), and grid distortion causes stress accuracy collapse.

[0006] Although the finite volume method (FVM) is mature in fluid mechanics, its exploration in solid multi-scale modeling has always been unable to break through three major bottlenecks: microscopic scale isolated-cell model only predicts linear elastic response, plastic deformation error exceeds 20%; concurrent coupling fails - micro-cracks are embedded in macro-FVM grids, but crack paths are dominated by grid orientation; numerical instability is a stubborn problem - homogenous grids cause stress oscillation in large deformation of solids, and if an artificial diffusion term is not introduced, the stress amplitude in the plastic zone reaches 15%. Existing commercial tools are difficult to support complex multi-scale workflows: ABAQUS user subroutines require manual coding of more than 40,000 lines of code to implement scale coupling, and the parallel acceleration ratio is less than 2; COMSOL multi-physics module only supports weak coupling (such as thermal-mechanical), and there is no strong mechanical interface; the open source field is also empty, and the mainstream FE framework lacks mature multi-scale modules, forcing the industry to rely on self-developed tools.

[0007] The technical contradiction matrix reveals the "impossible triangle" in the multi-scale field: FE² model has extremely low computational efficiency (time complexity is O(N²)), and has weak adaptability to non-periodic structures (depends on Periodic BC); concurrent FVM has moderate computational efficiency, moderate adaptability to non-periodic structures, but low numerical stability; and industrial demand requires efficiency O(N log N), strong adaptability to non-periodic structures (random defects), and high numerical stability (large deformation). Typical cases such as additive manufacturing titanium alloy support, random porosity 7% causes FE² periodic boundary failure, fatigue life prediction deviation 40%, and global microscopic discrete calculation time-consuming 168 hours (far exceeding the industrial 4-hour threshold).

[0008] The existing technology is trapped in a three-fold dilemma in the multi-scale field: finite element calculation efficiency collapses, periodic boundary assumption deviates from engineering reality, and FVM solid application is marginalized. Existing industrial scenarios urgently need new multi-scale modeling methods, such as fiber fracture and matrix debonding in aerospace composites, nanometer-micrometer multi-phase interfaces in new energy battery electrodes (such as carbon gel phase nanopores), and multi-scale fracture networks in geological reservoirs (large-scale faults control small-scale fractures). Non-ideal structures require a cross-scale solution that breaks away from the periodic cage, is compatible with the high-efficiency conservation characteristics of FVM, and is resistant to large deformation instability. SUMMARY

[0009] The purpose of the present application is to overcome the problems existing in the prior art, and to provide a nonlinear heterogeneous material layered multi-scale modeling method based on the finite volume method. For the first time, an FVM-driven layered multi-scale closed loop is constructed, and the incremental Lagrangian format is used to unify the control equation and the generalized boundary condition engine to break through the shackles, and finally to realize efficiency leap, boundary liberation and precision breakthrough, so that multi-scale modeling is transformed from "academic toy" to "industrial engine".

[0010] The purpose of the present application is achieved by the following technical solutions:

[0011] A nonlinear heterogeneous material hierarchical multiscale modeling method based on finite volume method is provided, such as Figure 1 , comprising the following steps:

[0012] S1. Constructing a discrete macroscopic balance equation in incremental Lagrangian form;

[0013] S2. Establishing a macro-micro scale mapping mechanism to transfer the deformation gradient of the macroscopic control volume center point to the micro-representative volume element boundary;

[0014] S3. Developing a generalized boundary condition engine to replace the periodic constraint with Hill-Mandel energy equivalent force condition;

[0015] S4. Solving the micro stress field using finite volume method flux integration, homogenizing the volume average stress of the micro-representative volume element by Hill-Mandel energy equivalent force condition and feeding back to the macroscopic constitutive relationship;

[0016] S5. Introducing a stress gradient-based numerical diffusion term in the discrete macroscopic balance equation, triggering the adaptive promotion of the diffusion coefficient when the equivalent plastic strain exceeds the preset threshold.

[0017] In some embodiments, the discrete macroscopic balance equation is as follows:

[0018] wherein, represents the physical quantity of the face center position, is the determinant of the deformation gradient, is the total deformation gradient, is a closed surface with an outward pointing unit normal vector ; and represents the face center term, which is obtained by linear interpolation of the corresponding element center value. The element center displacement gradient used for deformation gradient and Cauchy stress calculation is solved by least squares method to ensure the accuracy and stability of the gradient calculation.

[0019] In some embodiments, the step S1 further comprises:

[0020] Optimizing the calculation of the isoparametric grid displacement gradient by least squares method.

[0021] In some embodiments, the step S3 specifically comprises:

[0022] Dynamically selecting displacement control type, stress control type or hybrid type boundary condition to adapt to non-periodic microstructure;

[0023] Automatically switching to hybrid type boundary condition at the macroscopic free boundary.

[0024] In some embodiments, the volume average stress of the microcosmic representative volume element homogenized by Hill-Mandel energy equivalent force condition is fed back to the macroscopic constitutive relation, comprising:

[0025] The calculation is performed by the following formula:

[0026] , wherein, is the volume of the representative volume element under the reference configuration, is the microcosmic first Piola-Kirchhoff stress vector, represents the macroscopic Piola-Kirchhoff stress tensor, represents the infinitesimal difference in the limit process, represents the microcosmic deformation gradient, represents the macroscopic deformation gradient.

[0027] In some embodiments, the numerical diffusion term is an implicit-explicit Laplace term, and after introducing the numerical diffusion term, the discrete macroscopic balance equation becomes:

[0028] , wherein, and are the Lame parameters, is the displacement fluctuation increment between two loading steps, represents the normal direction, represents the outward pointing unit normal closed surface. The balance equation takes as the solving variable, the linear part is discretized implicitly, and the nonlinear part is calculated explicitly using the solution of the previous iteration.

[0029] In some embodiments, the discrete macroscopic balance equation is solved by using an explicit-implicit separation solver.

[0030] In some embodiments, when solving the microcosmic stress field in the step S4, the RVE solving task is dynamically distributed by using the OpenFOAM parallel architecture.

[0031] It should be further pointed out that the technical features corresponding to the above-mentioned embodiments can be combined or replaced with each other to form new technical solutions without conflict.

[0032] Compared with the prior art, the present application has the following advantages:

[0033] The application firstly designs the FVM control equation of the incremental Lagrange format, adopts FVM to discretize the balance equation in the macro domain, maps the deformation gradient to the RVE boundary through localization in the micro domain, and then solves the micro stress field by FVM flux integration, so that the macro and micro control equations are unified in the Lagrange framework; secondly, a generalized boundary condition engine is developed to replace the periodic constraint with the Hill-Mandel energy equivalent force condition, support Dirichlet type (displacement control), Neumann type (stress control) and mixed type boundary conditions, so that random pores, broken phases and other non-periodic microstructures can be directly embedded in the macro field; finally, a numerical diffusion term is introduced to suppress the same grid oscillation, which is constructed based on the second derivative of the stress gradient, and the diffusion effect is automatically triggered in the plastic zone, so that the stress oscillation amplitude is reduced to less than 5%, while the numerical accuracy in the elastic zone is maintained. The invention shows three breakthrough beneficial effects compared with the prior art: a leap in computing efficiency, a substantial breakthrough in adaptability to non-ideal structures, and simultaneous achievement of industrial-level simulation accuracy. Through the collaborative innovation of the layered FVM architecture and the generalized boundary engine, the precision-efficiency-applicability synergy is achieved in the aerospace composite material damage prediction, additive manufacturing defect evolution analysis and other scenes, which is embodied as follows:

[0034] I. Computing efficiency: qualitative change from "unfeasible" to "real-time"

[0035] 1. Cross-scale coupling overhead compression

[0036] Nested solution paradigm innovation: the traditional FE² model needs to independently solve the RVE finite element model for each macroscopic integration point (such as 900 RVE 3D hole plates), and the single-step time consumption increases to 200 times that of the single-scale model; the application converts the micro RVE solution into a conservation law integral problem by using the FVM flux transmission mechanism, and combines the explicit-implicit separation solver (fixed point iteration instead of Newton method) to compress the nested calculation overhead to less than 2 times that of the single-scale model.

[0037] 2. Deep adaptation of parallel architecture

[0038] OpenFOAM multi-core task allocation: the dynamic scheduling algorithm allocates RVE solving tasks to multiple CPU cores, achieving a weakly scalable speedup ratio of >12 in a 900-RVE 3D model (compared to the FE² user subroutine speedup ratio of <2).

[0039] II. Precision breakthrough: scientific reproduction of non-periodic structures and error eradication

[0040] 1. Generalized boundary engine liberates "periodic prison"

[0041] Free boundary error suppression: traditional FE² suffers from 5% stress prediction drift at the free edge of the orifice due to the enforced periodic boundary condition (BC); the Dirichlet-Neumann mixed BC mode in the present invention dynamically compensates at the free boundary, reducing the error to <3.8% while successfully capturing the local strain concentration induced by random pores (porosity 8%).

[0042] 2. Numerical stabilization algorithm to eliminate stress oscillation

[0043] Adaptive triggering of artificial diffusion term: the native FVM discretization scheme induces stress checkerboard oscillation (amplitude 15%) in the plastic zone; the present invention suppresses the oscillation amplitude to <2% by correlating the diffusion term with the plastic strain, while maintaining the accuracy in the elastic zone.

[0044] III. Applicability expansion: from “ideal model” to “industrial black box”

[0045] 1. Direct compatibility with non-structural micro-topology

[0046] Seamless embedding of CT scanned pores: the generalized boundary engine supports STL format micro-geometry import, breaking the limitation that periodic structures must be regularly arranged;

[0047] Multi-phase material interface coupling: by independently solving the multi-material domains within the micro RVE, the present invention has the ability to predict the interfacial debonding of carbon fiber / epoxy laminates.

[0048] 2. Industrial software ecosystem integration

[0049] OpenFOAM plugin interface: user-defined constitutive models (e.g., hyperelastic-plastic equations) can be loaded through dynamic link libraries, avoiding the need for 40,000+ lines of code for secondary development in ABAQUS;

[0050] Multi-physics extension capability: the incremental Lagrangian format can couple thermal, mechanical, and chemical fields, with reserved interfaces in the architecture. BRIEF DESCRIPTION OF DRAWINGS

[0051] Figure 1 Flowchart of the nonlinear heterogeneous material layered multiscale modeling method based on finite volume method shown in the embodiments of the present invention;

[0052] Figure 2 Schematic diagram of finite volume discretization shown in the embodiments of the present invention;

[0053] Figure 3 Macro-micro correlation schematic diagram shown in the embodiments of the present invention;

[0054] Figure 4 Homogenization calculation flowchart shown in the embodiments of the present invention;

[0055] Figure 5 This is a diagram illustrating the microstructure configuration of an embodiment of the present invention;

[0056] Figure 6 This is a schematic diagram of single-scale model mesh generation shown in an embodiment of the present invention;

[0057] Figure 7 This is a schematic diagram of multi-scale model mesh generation shown in an embodiment of the present invention;

[0058] Figure 8 The stress-displacement curve at the free boundary of the orifice plate is shown in an embodiment of the present invention. Detailed Implementation

[0059] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0060] It should be noted that the defects in the solutions in the prior art are all the results of the inventors' practice and careful research. Therefore, the discovery process of the above problems and the solutions proposed by the embodiments of this application in the following text should be the inventors' contributions to this application in the process of invention and creation, and should not be understood as technical content known to those skilled in the art.

[0061] In an exemplary embodiment, the hierarchical multi-scale modeling method for nonlinear heterogeneous materials based on the finite volume method mainly includes the following:

[0062] I. Layered Multi-Scale Architecture Design: FVM-Driven Information Transfer Closed Loop

[0063] 1. Macroscale FVM Discretization

[0064] The macroscopic equilibrium equations are discretized using the incremental full Lagrange scheme. The discrete macroscopic equilibrium equations are as follows:

[0065] ,in, A physical quantity representing the position of the face center. Let be the determinant of the deformation gradient. For the total deformation gradient, For the unit normal vector with an outer index Closed surface; The face center value is obtained by linear interpolation. The displacement gradient at the element center is solved by least square method to ensure the accuracy and stability of the gradient calculation.

[0066] Collocated grid optimization: the displacement gradient is calculated by least square method to avoid the reconstruction error of traditional FVM. As shown in Figure 2 The finite volume discretization is given to show the geometric parameter definition of the unstructured polyhedral control volume (CV): P / N is the adjacent element center point, f is the shared face, is the face unit normal vector, is the vector from P to N, is the face area, represents the volume calculation domain, represents the position vector. This figure demonstrates the collocated grid optimization algorithm-the displacement gradient is calculated by least square method to avoid the reconstruction error of traditional FVM, which provides a discrete basis for the subsequent stress diffusion term.

[0067] 2. Microscale RVE mapping mechanism

[0068] Each macroscopic control volume (CV) center point is associated with a microscale representative volume element (RVE), and the macroscopic deformation gradient F drives the RVE boundary condition through the scale transfer relationship, as shown in Figure 3 , which shows the geometric relationship between the macroscopic continuum ( Figure 3 (a) and the locally embedded microscale representative volume element (RVE). The macroscopic control volume (CV) center point is associated with an independent RVE ( Figure 3 (b)), where the gray area is the matrix material, and the white circle represents a microvoid defect. This figure verifies the non-nested data transfer architecture pioneered by the present application-the macroscopic deformation gradient directly drives the RVE boundary condition, breaking through the grid coupling limitation of traditional FE² model. The characteristic length of the RVE is much smaller than the characteristic length of the macroscopic continuum , as shown in Figure 3 (b). The area of the RVE is composed of two parts: the solid part and the void part .

[0069] 3. Stress feedback closed loop

[0070] The RVE volume average stress P is fed back to the macroscopic point through the Hill-Mandel condition to form a "macroscopic deformation gradient → microscale solution → homogenized stress → macroscopic constitutive" closed loop. It is calculated by the following formula:

[0071] , wherein, Vrefis the volume of a representative volume element (RVE) in the reference configuration, is the micro Piola-Kirchhoff stress vector of the first kind, is the macro Piola-Kirchhoff stress tensor, is the infinitesimal difference in the limit process, is the micro deformation gradient, is the macro deformation gradient.

[0072] Exemplarily, Figure 4 is the homogenization process chart, which reveals the macro-micro bidirectional data closed loop: ① the macro deformation gradient F is transmitted to the RVE boundary; ② the micro displacement wave field is solved in the RVE based on the finite volume method; ③ the micro stress P is homogenized through the Hill-Mandel condition; ④ feedback to the macroscopic constitutive relationship. The arrow color identifies the key physical quantities (blue: kinematic quantity; yellow: mechanical quantity), which embodies the core role of the unified control equation (incremental Lagrange format) in the cross-scale coupling.

[0073] II. Key technical breakthrough

[0074] 1. Generalized boundary condition engine (breakthrough periodic constraint)

[0075] Three-mode boundary self-adaptation: dynamically select Dirichlet type (displacement control), Neumann type (stress control) or mixed type boundary conditions to adapt to non-periodic microstructures. For example, in the free boundary or high gradient area, forced displacement boundary; in the uniform deformation area or isolated hole, stress boundary is applied; in the dense pore group or plastic area, partitioned displacement boundary and stress boundary are applied.

[0076] Free boundary compensation algorithm: automatically switch to a mixed boundary mode at the macro free boundary (such as the hole edge), balance the mechanical contradiction between displacement control and stress relaxation, and eliminate the 5% stress drift caused by traditional periodic boundaries by removing the improper constraint of periodic boundaries on micro deformation.

[0077] 2. Numerical stabilization core algorithm (overcome the same position grid oscillation)

[0078] Artificial diffusion term implantation: an implicit-explicit Laplace term is introduced into the discrete equation to suppress stress chessboard oscillation:

[0079] where, and are the Lame parameters, is the displacement wave increment between two loading steps, represents the normal direction, represents a closed surface with a unit normal pointing outward. The equilibrium equation is As the solving variable, its linear part is implicitly discretized, while the nonlinear part is explicitly calculated using the solution of the previous iteration.

[0080] 3. Calculation efficiency optimization engine

[0081] Explicit-implicit separation solver: Fixed-point Gauss-Seidel is used instead of Newton method to avoid repeated assembly of Jacobian matrix, and the number of iterations is reduced by 40% (compared with FE2 Newton method).

[0082] OpenFOAM parallel architecture adaptation: RVE solving tasks are dynamically allocated to multiple CPU cores to achieve a weakly scalable speedup ratio of >12 (900 RVE models). The dynamic allocation process of RVE solving tasks in the OpenFOAM parallel architecture includes a three-level cooperative mechanism of region decomposition strategy, master-worker node communication protocol, and load balancing algorithm. The core process is as follows: First, the macroscopic calculation domain is divided into subdomains equal to the number of CPU cores, and each subdomain is assigned an MPI process as a master node (Master). When the macroscopic solver enters the RVE calling stage, the master node encapsulates the deformation gradient of the current step as a task package and pushes it to the global task pool. The worker node (Worker) competes for the task package through a dynamic stealing algorithm, and each Worker constructs an RVE subgrid in local memory and independently executes micro-solution. The calculation results are returned to the master node asynchronously, and the master node aggregates the data to update the macroscopic stress field.

[0083] III. System-level verification and industrial adaptation

[0084] 1. Multi-scale consistency verification

[0085] Single-scale benchmark comparison: 2D / 3D hole-containing plate stretching shows that the stress-displacement curve coincidence degree is >95%, and the maximum error of the free boundary is 3.8%.

[0086] For example, the effects of a single-scale model and a multi-scale model of the application are compared, Figure 5 the geometric parameters of a uniform porous plate ( Figure 5 (a) and a heterogeneous porous plate containing a central large hole ( Figure 5 (b) are given. The uniform porous plate contains 180 periodic holes, and the heterogeneous porous plate contains 161 holes + a central 5mm hole. The length of the uniform porous plate is 18mm, and the width is 10mm. The maximum length of the heterogeneous porous plate is 18mm, and the maximum width is 10mm. Figure 6 the single-scale model grid division is given in the following table, wherein, Figure 6 (a) is the single-scale model grid division of the uniform porous plate, Figure 6 (b) is the single-scale model grid division of the heterogeneous porous plate containing a central large hole.Figure 7 The multi-scale model grid partitioning of the present application is shown in the figure, Figure 7 (a) is a multi-scale model grid partitioning of a uniform porous plate, Figure 7 (b) is a multi-scale model grid partitioning of a heterogeneous porous plate with a central large hole, Figure 7 (c) is a multi-scale model grid partitioning of a central large hole. The single-scale model needs 20,880 micro-units to finely disperse the hole; the multi-scale model of the present application only uses 154 macro-units + 116 RVE units. The grid density ratio is 1:180, which intuitively proves the leap in computing efficiency (time consumption is reduced to 1% of single-scale).

[0087] Further, the stress-displacement curve comparison at the free boundary of the hole plate is shown in the figure Figure 8 As shown by the purple solid line (single-scale benchmark) and the green solid line (the present application), the coincidence degree is >95%, verifying that the boundary compensation algorithm suppresses the maximum error to 3.8%.

[0088] 2. Industrial scene interface design

[0089] Material model plug-in: support user-defined constitutive, dynamically loaded through OpenFOAM runtime.

[0090] Non-structured grid compatibility: macroscopic layer supports polyhedral grid, micro-RVE can import STL geometry (such as CT scanning pore model).

[0091] Exemplarily, through multi-scale analysis of an additive manufacturing aluminum rib component containing random pores, the layered FVM framework is used to realize efficiency leap (calculation time is 3.2 hours), precision locking (free boundary stress error <4%) and engineering practicability (supporting industrial CT scanning geometry) simultaneously, the specific implementation process is as follows: build a macro-micro double-scale model in the OpenFOAM 4.1 environment, the macroscopic domain is divided into rib contours using unstructured polyhedral grid, each macroscopic unit center point is associated with a representative volume element (RVE), the RVE is embedded with actual CT scanning random pore structure, and the mixed boundary mode is dynamically selected through the generalized boundary condition engine: Dirichlet-Neumann mixed boundary (displacement-stress composite control) is enabled at the free boundary of the rib bolt hole (high stress gradient area), and periodic boundary is used in the internal area; the macroscopic deformation gradient F drives the RVE boundary through scale transmission, and the micro-solver calculates the displacement wave field based on the incremental Lagrangian FVM format, and the adaptive diffusion term is triggered in the plastic zone to suppress stress oscillation; stress homogenization is fed back to the macroscopic point through Hill-Mandel condition, the overall process is controlled by the explicit-implicit separation solver, the displacement increment linear system is calculated in parallel by the PCG solver, and finally the global stress distribution and local pore collapse risk area of the rib under tensile load are output.

[0092] The above detailed description is a detailed description of the application, and cannot be considered as limiting the specific embodiments of the application to these descriptions. For those skilled in the art, without departing from the concept of the application, some simple deductions and substitutions can be made, which should be considered as falling within the protection scope of the application.

Claims

1. A hierarchical multi-scale modeling method for nonlinear heterogeneous materials based on the finite volume method, characterized in that, Includes the following steps: S1. Construct the discrete macroscopic equilibrium equations in the incremental Lagrange scheme; S2. Establish a macro-micro scale mapping mechanism to transfer the deformation gradient of the macro-control volume center point to the boundary of the micro-representative volume unit; S3. Develop a generalized boundary condition engine to replace periodic constraints with Hill-Mandel energy equivalent conditions; specifically including: Dynamically select displacement-controlled, stress-controlled, or hybrid boundary conditions to adapt to aperiodic microstructures. Specifically, in free boundaries or high gradient regions, forced displacement boundaries are applied; in uniform deformation regions or isolated pores, stress boundaries are applied; and in dense pore groups or plastic regions, displacement boundaries and stress boundaries are applied in separate zones. At the macroscopic free boundary, it automatically switches to a hybrid boundary condition to release the improper constraints of the periodic boundary on the microscopic deformation, while balancing the mechanical contradiction between displacement control and stress relaxation. S4. Solve the micro-stress field using flux integration with the finite volume method, homogenize the volume-average stress of the micro-representative volume element through the Hill-Mandel energy equivalence condition, and feed it back to the macro-constitutive relation; S5. A numerical diffusion term based on stress gradient is introduced into the discrete macroscopic equilibrium equation. When the equivalent plastic strain exceeds a preset threshold, the diffusion coefficient is adaptively increased. The numerical diffusion term is an implicit-explicit Laplace term. After introducing the numerical diffusion term, the discrete macroscopic equilibrium equation becomes: ,in, and For Lamé parameters, This represents the displacement fluctuation increment between two loading steps. Indicates the normal direction. This represents a closed surface pointing outwards with the unit of normal.

2. The hierarchical multi-scale modeling method for nonlinear heterogeneous materials based on the finite volume method according to claim 1, characterized in that, The discrete macroscopic equilibrium equations are as follows: ,in, A physical quantity representing the position of the face center. Let be the determinant of the deformation gradient. For the total deformation gradient, For the unit normal vector with outward index Closed surface; This represents the face-centered term, which is obtained by linear interpolation of the corresponding element center value.

3. The hierarchical multi-scale modeling method for nonlinear heterogeneous materials based on the finite volume method according to claim 1, characterized in that, Step S1 also includes: The displacement gradient calculation of the same grid is optimized by using the least squares method.

4. The hierarchical multi-scale modeling method for nonlinear heterogeneous materials based on the finite volume method according to claim 1, characterized in that, The process of homogenizing the volume-average stress of the microscopic representative volume element through the Hill-Mandel energy equivalence condition and feeding it back to the macroscopic constitutive relation includes: The calculation is performed using the following formula: ,in, For the volume of a representative volume element in the reference configuration, For the first type of microscopic Piola–Kirchhoff stress vector, Represents the macroscopic Piola-Kirchhoff stress tensor. This represents the small differences in the limiting process. Represents the microscopic deformation gradient. This represents the macroscopic deformation gradient.

5. The hierarchical multi-scale modeling method for nonlinear heterogeneous materials based on the finite volume method according to claim 1, characterized in that, The discrete macroscopic equilibrium equations are solved using an explicit-implicit separation solver.

6. The hierarchical multi-scale modeling method for nonlinear heterogeneous materials based on the finite volume method according to claim 1, characterized in that, In step S4, when solving for the micro-stress field, the RVE solution task is dynamically allocated through the OpenFOAM parallel architecture.

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