Self-adaptive grid generation method in material simulation

Abstract

The invention belongs to the technical field of computational material science and scientific calculation, and relates to a self-adaptive grid generation method in material simulation, which comprises the following steps: S1, generating an atomic region grid and a continuous region grid of a three-dimensional material, and splicing the grids to obtain a coupled grid; s2, optimizing the grid by using a local adaptive grid refinement strategy to obtain a grid; s3, detecting whether the calculation precision of the material under the grid accords with a preset value or not, and if not, executing the step S4; s4, expanding the atomic region grid of the grid to obtain the grid; s5, units intersecting with the grids are removed from the continuous area grids of the grids, and the grids are obtained; s6, constructing a cavity transition grid, and splicing the grid with the cavity transition grid to obtain a grid; s7, judging whether a convergence condition is met or not, and if yes, obtaining a final coupling grid; otherwise, optimizing the grid, and returning to the step S4; according to the invention, the atomic region and the continuous region are automatically identified and connected with high quality in three-dimensional geometry.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of computational materials science and scientific computing, and relates to a self-adaptive mesh generation method in material simulation. BACKGROUND

[0002] In multiscale material simulation, the atom-continuum coupling method is an important technique, and the key lies in constructing the coupling mesh covering the atom region and the continuum region. The existing mesh generation methods mainly rely on general triangular or body mesh division tools (such as Delaunay, Gmsh, TetGen, etc.), which have good applicability in general continuum medium simulation.

[0003] However, in the three-dimensional atom-continuum multiscale modeling scenario, these methods have the following problems and technical defects:

[0004] 1. In three-dimensional atom-continuum coupling simulation, the generation of mesh is much more complex than in two-dimensional cases. In two-dimensional cases, defects often appear in the form of points or lines, boundary fitting is relatively simple, and there is no significant change in the topology of real materials. However, in three-dimensional systems, the atom region is composed of complex spatial point sets, often containing various real defects such as dislocations, cracks, vacancies and grain boundaries. These defects form highly irregular curved surface structures at the boundary, resulting in serious geometric mismatch and scale incompatibility problems at the interface between the atom region and the continuum region.

[0005] 2. In three-dimensional atom-continuum coupling mesh, the migration and evolution of defects often lead to local stress concentration and rapid change of stress gradient. If not adjusted by targeted mesh refinement, it is easy to cause local error to be too large, simulation results to be distorted, etc. In contrast, in two-dimensional materials, there is no real topological change problem, and the interface transition only involves the adjustment of boundary lines, so there is usually no need to consider the complex structure of the transition zone. Therefore, compared with two-dimensional scenarios, three-dimensional not only needs to deal with more complex defect morphology (such as cavity, non-convex surface), but also must ensure the mesh quality and geometric consistency of the interpolation interface region.

[0006] 3. In 3D atomic / continuous coupling simulations, mesh generation typically involves constructing a complete coupled mesh in one go, given the boundary conditions between atomic and continuous regions, using methods such as constrained Delaunay meshing and quality optimization. The goal is to ensure overall geometric consistency and element quality. However, during defect evolution or atomic region expansion, the original coupling boundary undergoes topological changes, and the initial mesh structure can no longer meet the new geometric constraints. In this case, adaptive mesh reconstruction is necessary. In the 2D case, the interface between atomic and continuous regions consists only of points and lines, without involving complex surfaces or topological reconstruction, making the operation relatively simple and eliminating the risk of voids or distorted elements. However, the processing of 3D dynamic adaptive meshes is not only significantly more difficult but also requires meticulous design to accommodate topological changes.

[0007] In summary, existing mesh generation methods struggle to connect atomic regions and continuous regions with high quality and efficiency in complex 3D geometry, and cannot dynamically optimize mesh distribution during simulation, resulting in insufficient simulation accuracy and computational efficiency. Summary of the Invention

[0008] To address the aforementioned problems in the prior art, this invention employs an adaptive mesh generation method in material simulation, comprising:

[0009] S1. Divide the three-dimensional material into atomic regions and continuous regions, and generate atomic region meshes and continuous region meshes for the three-dimensional material based on the atomic regions and continuous regions; stitch the atomic region meshes and continuous region meshes of the three-dimensional material together to obtain the coupled mesh of the three-dimensional material.

[0010] S2. Optimize the coupled mesh using a local adaptive mesh refinement strategy to obtain the optimized coupled mesh;

[0011] S3. Check whether the calculation accuracy of the 3D material under the optimized coupled mesh meets the preset. If yes, use the optimized coupled mesh obtained in step S2 as the final coupled mesh; otherwise, proceed to step S4.

[0012] S4. Mark the set of atoms to be expanded into atomic regions in the continuous region grid of the optimized coupled grid. Expand the atomic region grid in the optimized coupled grid according to the set of atoms to be expanded into atomic regions to obtain the expanded atomic region grid.

[0013] S5. Remove the mesh cells that intersect with the extended atomic region mesh from the continuous region mesh of the optimized coupled mesh to obtain the divided continuous region mesh.

[0014] S6. Construct a cavity transition mesh by splicing the extended atomic region mesh, the divided continuous region mesh, and the cavity transition mesh to obtain a new coupled mesh.

[0015] S7. Determine whether the preset convergence condition has been met. If so, the final coupled mesh is obtained. Otherwise, the coupled mesh obtained in step S6 is optimized using a local adaptive mesh refinement strategy to obtain an optimized coupled mesh. Then, return to step S4 to process the optimized coupled mesh obtained in step S7.

[0016] Beneficial effects:

[0017] 1. To address the challenges posed by curved boundaries and topological changes in real 3D materials, this invention introduces a 3D Delaunay meshing algorithm combined with a maximum inscribed sphere radius constraint to generate atomic region meshes, thus avoiding the generation of large-scale inferior elements at atomic region boundaries. The mesh nodes of the continuous region mesh are initialized based on the boundaries of the continuous region, and mesh information of the coupling boundary between the atomic and continuous regions is extracted. A constrained 3D Delaunay meshing algorithm is introduced to generate an initial mesh based on the mesh nodes of the continuous region mesh boundaries and the extracted mesh information of the coupling boundary. Boundary restoration and invalid element removal algorithms are used to remove mesh elements falling into the atomic region mesh from the initial mesh, thereby ensuring the geometric integrity and topological consistency of the coupling interface. 2. This invention introduces a gradient-based posterior error estimator to analyze the correspondence between the atomic and continuous region meshes, identify error-concentrated mesh elements in the coupling mesh, and locally refine these error-concentrated mesh elements to avoid global over-refinement and improve computational efficiency. Simultaneously, combined with boundary restoration and invalid element removal mechanisms, the mesh structure at the atomic-continuous interface is ensured to maintain geometric and topological consistency after refinement. To improve the consistency of the mesh and enhance simulation stability, this invention avoids voids or non-physical units caused by refinement. Finally, by using a quality optimization strategy, edge swapping is performed on the refined mesh units to improve the shape quality of the refined units and ensure a smooth transition of the mesh in the coupling region. Therefore, this invention can dynamically maintain high accuracy in defective regions while avoiding global over-refinement, thus balancing computational efficiency and simulation stability. 3. When the computational accuracy of the 3D material under the optimized coupling mesh does not meet the preset requirements, this invention expands the atomic region mesh and removes mesh units that intersect with the expanded atomic region mesh in the continuous region mesh, forming a topologically clear cavity. Then, a cavity transition mesh is generated in the cavity region using restricted 3D Delaunay meshing, and the expanded atomic region mesh, the divided continuous region mesh, and the cavity transition mesh are smoothly spliced ​​together, thereby supporting the dynamic expansion of the atomic region. This avoids the generation of deformed units and voids while ensuring simulation accuracy and computational efficiency. Attached Figure Description

[0018] Figure 1 A flowchart illustrating an adaptive mesh generation method in materials simulation provided by an embodiment of the present invention;

[0019] Figure 2 A detailed flowchart of an adaptive mesh generation method in material simulation provided by an embodiment of the present invention;

[0020] Figure 3 This is a schematic diagram of an adaptive mesh provided in an embodiment of the present invention;

[0021] Figure 4 A schematic diagram illustrating the quality of mesh generation in each iteration, provided in an embodiment of the present invention;

[0022] Figure 5 A schematic diagram illustrating the accuracy of the mesh generation method provided in this embodiment of the invention;

[0023] Figure 6 This is a schematic diagram illustrating the iteration time overhead under different degrees of freedom when adaptively generating BCC tungsten meshes according to an embodiment of the present invention. Detailed Implementation

[0024] The technical solutions of the embodiments 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, and not all embodiments. 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.

[0025] like Figure 1 , Figure 2 As shown, this embodiment of the invention employs an adaptive mesh generation method in material simulation, comprising:

[0026] S1. Divide the three-dimensional material into atomic regions and continuous regions, and generate an atomic region mesh for the three-dimensional material based on the atomic regions and continuous regions. and continuous region grid ; Mesh the atomic regions of three-dimensional materials and continuous region grid By splicing the meshes, a coupled mesh of the three-dimensional material is obtained. ;

[0027] The criteria for dividing three-dimensional material regions are usually based on the length of material characteristics or the scale of physical processes. For example: atomic regions: regions that contain defects (such as crack tips and dislocations) and interfaces (such as grain boundaries) that require precise description of microscopic behavior; continuous regions: regions far from microscopic disturbances, ignoring atomic-level details.

[0028] Obtaining atomic coordinates of an atomic region includes: measuring atomic position coordinates using techniques such as X-ray diffraction and cryo-electron microscopy, or performing molecular dynamics (MD) relaxation on the atomic region to obtain atomic coordinates in equilibrium.

[0029] Generating atomic region meshes and continuous region meshes of a 3D material based on its atomic regions and continuous regions includes: obtaining the atomic coordinates of the atomic regions of the material and generating the atomic region mesh of the material based on the atomic coordinates of the atomic regions; and generating the continuous region mesh of the material based on the boundaries of the continuous regions of the material and the atomic region meshes.

[0030] Generating atomic region meshes based on atomic coordinates includes:

[0031] The 3D Delaunay meshing algorithm provided in the Tetgen software package is used to perform 3D meshing of the atomic coordinates of the atomic regions of the 3D material, generating the original preprocessed mesh Ta-pre. An element culling algorithm based on the maximum inscribed sphere radius constraint is then used to remove low-quality mesh cells at the boundaries of the original preprocessed mesh, resulting in the atomic region mesh of the 3D material. .

[0032] To improve spatial search efficiency, this invention introduces a biased randomized insertion order (BRIO) technique to optimize the sorting of atoms during the construction of the 3D Delaunay triangulation, and uses the Bowyer-Watson algorithm to iteratively construct high-quality mesh cells by inserting points. The Bowyer-Watson algorithm is a classic incremental Delaunay triangulation algorithm.

[0033] Considering the presence of non-convex topologies such as defects and interfaces in atomic regions, the original preprocessed mesh may contain a large number of low-quality elements, especially concentrated near boundaries or convex hulls. Therefore, this step introduces an element culling algorithm based on the maximum inscribed sphere radius constraint to remove low-quality mesh elements at the boundaries of the original preprocessed mesh.

[0034] Specifically, removing low-quality mesh cells at the boundaries of the original preprocessed mesh includes: setting the maximum inscribed sphere radius r_max for the mesh cells; calculating the inscribed sphere radius of the mesh cells at the boundaries of the original preprocessed mesh; removing mesh cells with inscribed sphere radii greater than the maximum inscribed sphere radius r_max to obtain the removed original preprocessed mesh; and performing topology repair on the removed original preprocessed mesh to obtain a mesh that meets the coupling requirements. Among them, the maximum inscribed sphere radius r_max can flexibly control the mesh density and quality, and is suitable for processing complex defect structures containing dislocations, vacancies and other defects.

[0035] Directly removing mesh cells can result in holes or dangling vertices in the mesh. Topology repair is necessary to ensure mesh integrity. The specific process includes: filling the hole areas (boundary gaps formed after cell removal) with a local re-subdivision algorithm: using the boundary vertices of the hole as a basis, generating new high-quality cells using the 3D Delaunay subdivision algorithm; for dangling vertices / edges generated after removing mesh cells, if the dangling vertex is too close to other boundary vertices, directly delete the vertex and merge the associated edges; if the distance is far, eliminate the dangling structure by edge shrinking (merging the two vertices of the dangling edge).

[0036] The above-mentioned generation process of atomic region meshes provides high-quality geometric support at the atomic scale for the entire coupled mesh system, laying the foundation for subsequent steps such as interface splicing and adaptive encryption.

[0037] The continuous region mesh of the material is generated based on the boundaries of the continuous region of the 3D material and the atomic region mesh. The aim is to maintain mesh topological consistency and smooth transition in the coupling region between the atomic region mesh and the continuous region mesh, so as to ensure the stability and accuracy of the entire multi-scale simulation.

[0038] Generating continuous region meshes for 3D materials includes:

[0039] S11. Initialize the boundary mesh nodes of the continuous region mesh based on the boundary of the continuous region of the 3D material. Extracting mesh information of the coupling boundary between atomic regions and continuous regions from atomic region meshes. ;

[0040] The boundaries of continuous regions, such as the loading and fixing ends of macroscopic components, are typically on the micrometer scale with low node density. Coupled boundaries are the edges connecting atomic regions to continuous regions in three-dimensional materials.

[0041] Mesh information of coupled boundaries This includes: mesh nodes and boundary width of the coupling boundary in the atomic region mesh.

[0042] S12. Generate an initial mesh based on the mesh nodes of the boundary of the continuous region mesh and the mesh information of the extracted coupled boundary;

[0043] The mesh generation process utilizes the Constrained Delaunay Triangulation (CDT) algorithm. The core objective is to use the CDT algorithm to separate the mesh nodes at the boundaries of continuous region meshes. and the extracted mesh information of the coupling boundary As a boundary constraint for the continuous regional grid, an initial grid covering the coupling transition zone is generated to ensure that the node distribution takes into account both macro-scale and micro-scale constraints.

[0044] During this partitioning process, atomic regions may be temporarily entered, containing some invalid units.

[0045] S13. Remove mesh elements that fall into the atomic region mesh from the initial mesh using the boundary restoration and invalid element removal mechanism;

[0046] Boundary restoration and invalid cell removal mechanisms typically need to work together to form a progressive solution of "first repairing the integrity of the interface structure, then optimizing the cell quality," ultimately ensuring the geometric correctness, topological consistency, and computational applicability of the mesh. Specifically, removing mesh cells that fall into the atomic region mesh from the initial mesh includes: identifying and removing mesh cells that fall into the atomic region mesh from the initial mesh; after removing the mesh cells, repairing the boundaries of the remaining mesh (such as filling holes and reconstructing boundary cells); and then removing invalid mesh cells (such as low-quality mesh cells) to ensure the geometric and topological consistency between the continuous region mesh and the atomic region mesh (such as boundary closure and correct cell connection relationships).

[0047] S14. Refine the mesh obtained in step S13 to obtain a continuous region mesh of the three-dimensional material. .

[0048] This step employs the Quality Mesh Refinement (QMR) method to refine the mesh, improve the shape quality of the mesh cells, ensure a smooth transition in mesh size near the coupling region, and enhance the simulation performance of the entire coupled mesh.

[0049] The continuous region mesh and atomic region mesh constructed through the above steps are seamlessly spliced ​​at the boundary, and have good element quality and local density adjustability, which can meet the coupled simulation requirements of various material systems and lay the foundation for subsequent mesh splicing and global adaptive adjustment.

[0050] S2. Using a local adaptive mesh refinement strategy to refine the coupled mesh of 3D materials. Optimization is performed to obtain the optimized coupled mesh. ;

[0051] Coupled mesh for 3D materials Optimization includes:

[0052] S21, Coupled mesh of three-dimensional material Atom-continuous multi-scale calculations are performed on the surface to obtain the coupled mesh. Basic data;

[0053] The basic data includes physical quantities such as displacement field, energy distribution, and stress response, which provide basic data support for subsequent adaptive mesh adjustment.

[0054] S22. Using a posterior error estimator based on the coupled mesh Basic data identification coupled mesh Error-concentrated grid cells;

[0055] The migration and evolution of defects often lead to local stress concentration and drastic changes in solution gradients. Without targeted mesh refinement adjustments, problems such as excessive local errors and distorted simulation results can easily occur. Compared to two-dimensional scenarios, three-dimensional scenarios not only need to handle more complex defect morphologies (such as cavities and non-convex surfaces), but also must ensure the mesh quality and geometric consistency of the interpolation interface region. Therefore, adaptive refinement driven by posterior error is particularly crucial.

[0056] The posterior error estimator is a posterior error estimator based on the geometric gradient field. It calculates the difference in displacement gradient between the solution in the continuous region and the reference solution in the atomic region to evaluate the local error level of the mesh in the solution space; specifically, it identifies coupled meshes. The error-concentrated grid cell includes: setting an error threshold, finding the atomic region grid cell corresponding to each continuous region grid cell at the coupling boundary in the coupled grid, calculating the gradient error between the continuous region grid cell and its corresponding atomic region grid cell according to the L2 norm, and taking the continuous region grid cell with gradient error greater than the error threshold as the error-concentrated grid cell, providing a criterion for local refinement of the continuous region; wherein, the gradient error can be displacement gradient error, energy gradient error, or geometric gradient error.

[0057] The atomic region grid cell corresponding to the continuous region grid cell space refers to the atomic region grid cell whose spatial location falls completely or partially within the continuous region grid cell space. The gradient error calculation includes: taking the statistical average (or weighted average, with the weight determined by the spatial overlap area) of the gradients of all atomic region grid cells corresponding to the continuous region grid cell space to obtain the equivalent gradient of the atomic region grid cell within the continuous region grid cell space; and calculating the L2 norm error between the gradient of the continuous region grid cell and its corresponding equivalent gradient.

[0058] S23. Optimize all error-concentrated mesh elements of the coupled mesh to obtain the optimized coupled mesh. The optimized coupled mesh includes atomic region meshes and continuous region meshes.

[0059] Two types of adaptive techniques are used to optimize all error-saturated mesh elements in the coupled mesh, including:

[0060] Each error-concentrated grid cell in the coupled mesh is refined by interpolation along the centroid to improve local resolution, resulting in a new grid cell after interpolation refinement of each error-concentrated grid cell; the new grid cell consists of four tetrahedral elements.

[0061] By utilizing boundary restoration and invalid cell removal mechanisms, the new mesh cells after interpolation and refinement of each error set mesh cell are subjected to consistency processing to avoid voids or non-physical cells caused by local refinement, thus obtaining the new mesh cells after consistency processing of each error set mesh cell.

[0062] By employing a quality optimization strategy, edge swapping operations are performed on the new mesh cells after consistency processing of each mesh cell in the error set to ensure a smooth transition of the mesh in the coupling region, resulting in an optimized coupled mesh.

[0063] Specifically, edge swapping operations using quality optimization strategies include:

[0064] For each edge in the new mesh cell after the consistency processing of the error set mesh cells, calculate the quality index of all related tetrahedral cells before and after the swap, and determine whether the quality index of all related tetrahedral cells after the swap meets the quality improvement condition. If it does, then perform the edge swap operation.

[0065] In this embodiment, the quality index of the tetrahedral unit is the ratio of the tetrahedral volume to the side length, and the quality improvement condition is 1.01Q(A) < Q(B), where Q(B) is the quality index after the exchange, and Q(A) is the quality index before the exchange.

[0066] In one embodiment, before performing the edge swap operation, a series of topological validity checks are performed on all relevant tetrahedral elements after the swap to ensure that geometric defects such as face flipping, edge crossing, or inconsistent face orientation are not introduced. The system will only update the mesh topology if both quality and topological validity checks are passed and the conditions for validity and quality are met.

[0067] Through the above steps, the present invention can achieve a smooth transition of mesh density changes at the boundary of the coupling region and significantly improve the ability to distinguish local stress concentration or defect evolution in the simulation.

[0068] S3. Check whether the calculation accuracy of the 3D material under the optimized coupled mesh meets the preset. If yes, use the optimized coupled mesh obtained in step S2 as the final coupled mesh; otherwise, proceed to step S4.

[0069] The defective parts of the three-dimensional material (i.e., the coupled mesh) Regions with large gradient errors may change under certain conditions (such as when subjected to an external force that forces material deformation). Therefore, to further improve simulation accuracy, it is necessary to check whether the computational accuracy of the 3D material under the optimized coupled mesh meets the preset requirements. If not, the coupled mesh needs to be adjusted. Mesh cells with large gradient errors are expanded into atomic regions to adapt to the changed material.

[0070] The process of checking whether the computational accuracy of the 3D material under the optimized coupled mesh meets the preset requirements includes: performing atomic-continuous multi-scale calculations on the optimized coupled mesh to obtain the basic data of the coupled mesh (such as element size, temperature field, displacement field, stress field, etc.); calculating various indicators of the mesh based on the basic data of the coupled mesh, such as the relative errors of key physical quantities (such as stress and displacement), and judging whether the various indicators of the coupled mesh meet the preset conditions.

[0071] S4. In the optimized coupled mesh Mark the set of atoms to be expanded into atomic regions in the continuous region grid. Based on the set of atoms to be expanded into atomic regions For the optimized coupled mesh The atomic region mesh in the original text is expanded to obtain the expanded atomic region mesh. ;in, The iteration number is T, where T is the preset maximum iteration number, and the coupled mesh obtained in step S3 is... This refers to the coupled mesh of the first iteration;

[0072] The set of atoms to be marked as to be expanded into atomic regions includes: computation of the coupled mesh. The gradient error of each grid cell in the continuous region grid is used to arrange the grid cells in the continuous region grid from largest to smallest according to the gradient error. The top 30% of the grid cells in the continuous region grid are selected and marked to obtain the set of atoms to be expanded into atomic regions.

[0073] Computational Coupled Mesh The process of calculating the gradient error of each grid cell in the continuous region grid is similar to step S22, and the specific steps include: calculating the coupled grid. The displacement gradient error of each grid cell in a continuous region grid and its spatially corresponding grid cell.

[0074] For the optimized coupled mesh Atomic region expansion of the atomic region mesh includes:

[0075] The set of atoms to be expanded into atomic regions and the coupled mesh The atomic sets of the atomic region mesh are merged to obtain an expanded atomic set, and an extended atomic region mesh is generated based on the expanded atomic set using an existing partitioning algorithm (such as the 3D Delaunay partitioning algorithm).

[0076] S5. In the optimized coupled mesh Removing and expanding atomic region meshes in continuous region meshes Intersecting grid cells result in a continuous region grid. ;

[0077] Since the extended atomic region mesh may partially overlap with the continuous region of the material, to avoid redefinition, all mesh elements intersecting with the extended atomic region mesh are removed from the continuous region mesh of the 3D material, forming a clear cavity boundary to prepare for subsequent mesh splicing. This process ensures that the atomic region and the continuous region do not interfere with each other spatially and reserves geometric degrees of freedom for the interface transition.

[0078] S6. Construct a cavity transition mesh, extending the atomic region mesh. Continuous region grid after division By splicing the cavity transition mesh, a new coupled mesh is obtained. ;

[0079] Constructing the cavity transition mesh includes: dividing the resulting continuous region mesh. Boundary and extended atomic region mesh Using the boundary as geometric constraint information, a cavity transition mesh is constructed based on the geometric constraint information using the constrained 3D Delaunay meshing algorithm. The mesh quality refinement (QMR) method is then used to optimize the mesh to obtain the final cavity transition mesh, which is used to fill the cavity between the atomic region and the continuum region.

[0080] Expand atomic region grid Continuous region grid after division The splicing with the cavity transition mesh includes: to ensure the smoothness of the mesh and the stability of the simulation in the splicing area, performing a Laplace smoothing operation on the nodes of the continuous region mesh at the interface, optimizing the node layout and improving the mesh quality.

[0081] Through this process, the atom-continuum interface can be dynamically updated during the simulation, which avoids the generation of malformed cells and voids, and ensures the overall computational accuracy and stability.

[0082] The final new coupled mesh can be used for subsequent multi-scale simulation tasks, and has the advantages of reasonable region partitioning, smooth structural transition, and excellent element quality.

[0083] S7. Determine whether the preset convergence condition has been met. If so, obtain the final coupled mesh; otherwise, refine the coupled mesh obtained in step S6 using a local adaptive mesh refinement strategy. Optimization is performed to obtain the optimized coupled mesh. And return to step S4 to optimize the coupled mesh obtained in step S7. Process it.

[0084] The optimization process for this step is the same as that for step S2.

[0085] The convergence condition is: the number of nodes in the coupled mesh obtained in step S6 reaches the preset maximum number of nodes or the number of iterations reaches the preset maximum number of iterations.

[0086] It is generally recommended to set the maximum number of nodes to 3,000-10,000 and the maximum number of iterations to 10-20.

[0087] like Figure 3 As shown, the final coupled mesh can be called by the multi-scale solver or used for subsequent analysis and processing, such as material defect evolution simulation, stress field calculation or interface structure response study, etc. The adaptive mesh generation process ends here.

[0088] Example: Simulation of edge dislocations in BCC tungsten.

[0089] This embodiment selects linear edge dislocations in BCC tungsten crystals as the test object to verify the applicability and accuracy of the adaptive mesh generation method proposed in this invention in the simulation of complex crystal defects. This type of dislocation is one of the common line defect forms in crystalline materials, and it has a significant impact on the mechanical properties of materials. To construct this type of defect structure, this embodiment uses a modeling method to apply specific boundary conditions to the tungsten crystal model: a clamping boundary is applied in the xy plane, and a periodic boundary condition is applied in the z direction. To ensure the stability in the structural optimization calculation, three layers of virtual atoms (ghost atoms) are introduced into the boundary layer, where the ghost atoms in the xy plane are relaxed to improve the geometric optimization performance.

[0090] Figure 6 This embodiment demonstrates the iteration time overhead of adaptive mesh generation for BCC tungsten under different degrees of freedom. The total computation time for mesh generation and adaptive meshing accounts for less than 5%, indicating that the present invention has significant efficiency advantages in actual simulation.

[0091] Furthermore, during the adaptive mesh iteration of BCC tungsten, the posterior error estimator constructed in this invention can effectively guide the mesh refinement location and control the overall error convergence behavior. For example... Figure 5As shown, this invention exhibits approximately half-order convergence behavior in calculating geometric errors, verifying its stability and adaptability in complex defect evolution processes. Figure 4 As shown, the mesh quality was evaluated using a mesh quality index for the four iterations. The proportions of high-quality cells (i.e., quality score of 1) were 66.47%, 63.56%, 66.70%, and 69.36%, respectively. This indicates that the present invention can maintain stable mesh quality during the iteration process without significant degradation, making it suitable for accurate analysis of subsequent coupled models. In summary, the adaptive mesh generation method proposed in this invention demonstrates accuracy, robustness, and computational efficiency in simulating complex multi-scale problems such as crystal defects, and has broad engineering application prospects.

[0092] The above-described embodiments further illustrate the purpose, technical solution, and advantages of the present invention. It should be understood that the above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made to the present invention within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An adaptive mesh generation method for materials simulation, characterized in that, include: S1. Divide the three-dimensional material into atomic regions and continuous regions, and generate atomic region meshes and continuous region meshes for the three-dimensional material based on the atomic regions and continuous regions of the three-dimensional material. By splicing the atomic region mesh and the continuous region mesh of the three-dimensional material, a coupled mesh of the three-dimensional material is obtained; S2. Optimize the coupled mesh using a local adaptive mesh refinement strategy to obtain the optimized coupled mesh; S3. Check whether the calculation accuracy of the three-dimensional material under the optimized coupled mesh meets the preset. If so, the optimized coupled mesh obtained in step S2 is used as the final coupled mesh. Otherwise, proceed to step S4; S4. Mark the set of atoms to be expanded into atomic regions in the continuous region grid of the optimized coupled grid. Expand the atomic region grid in the optimized coupled grid according to the set of atoms to be expanded into atomic regions to obtain the expanded atomic region grid. S5. Remove the mesh cells that intersect with the extended atomic region mesh from the continuous region mesh of the optimized coupled mesh to obtain the divided continuous region mesh. S6. Construct a cavity transition mesh by splicing the extended atomic region mesh, the divided continuous region mesh, and the cavity transition mesh to obtain a new coupled mesh. S7. Determine whether the preset convergence condition has been met. If so, the final coupled mesh is obtained. Otherwise, the coupled mesh obtained in step S6 is optimized using a local adaptive mesh refinement strategy to obtain an optimized coupled mesh. Then, return to step S4 to process the optimized coupled mesh obtained in step S7.

2. The adaptive mesh generation method in material simulation according to claim 1, characterized in that, Generating atomic region meshes and continuous region meshes of a three-dimensional material based on its atomic regions and continuous regions includes: obtaining the atomic coordinates of the atomic regions of the three-dimensional material and generating the atomic region mesh of the three-dimensional material based on the atomic coordinates of the atomic regions; and generating the continuous region mesh of the three-dimensional material based on the boundaries of the continuous regions of the three-dimensional material and the atomic region mesh.

3. The adaptive mesh generation method in material simulation according to claim 2, characterized in that, The atomic region mesh for generating three-dimensional materials includes: The atomic coordinates of the atomic region are three-dimensionally partitioned using the 3D Delaunay subdivision algorithm to generate the original preprocessed mesh. The maximum inscribed sphere radius of the mesh cell is set, the inscribed sphere radius of the mesh cell at the boundary of the original preprocessed mesh is calculated, mesh cells with inscribed sphere radii greater than the maximum inscribed sphere radius are removed, and the original preprocessed mesh after removal is topologically repaired to obtain the atomic region mesh of the 3D material.

4. The adaptive mesh generation method in material simulation according to claim 2, characterized in that, Generating continuous region meshes for 3D materials includes: S11. Initialize the boundary mesh nodes of the continuous region mesh according to the boundary of the continuous region of the three-dimensional material, and extract the mesh information of the coupling boundary between the atomic region and the continuous region from the atomic region mesh. S12. Generate an initial mesh based on the mesh nodes of the boundary of the continuous region mesh and the mesh information of the extracted coupled boundary using the restricted 3D Delaunay meshing algorithm; S13. Use boundary restoration and invalid element removal algorithms to remove mesh cells that fall into the atomic region mesh from the initial mesh; S14. Refine the mesh obtained in step S13 to obtain a continuous region mesh of the three-dimensional material.

5. The adaptive mesh generation method in material simulation according to claim 1, characterized in that, Optimization of coupled meshes for 3D materials includes: S21. Perform atomic-continuous multi-scale calculations on the coupled mesh of the three-dimensional material to obtain the basic data of the coupled mesh; S22. Use the posterior error estimator to identify the error saturation grid cells of the coupled grid based on the basic data of the coupled grid; S23. Optimize all error-concentrated mesh elements of the coupled mesh to obtain the optimized coupled mesh.

6. The adaptive mesh generation method in material simulation according to claim 5, characterized in that, Identifying error-concentrated grid cells in coupled meshes includes: setting an error threshold, finding the atomic region grid cells corresponding to each continuous region grid cell at the coupling boundary in the coupled mesh, calculating the gradient error between the continuous region grid cell and its corresponding atomic region grid cell based on the L2 norm, and identifying continuous region grid cells with gradient errors greater than the error threshold as error-concentrated grid cells.

7. The adaptive mesh generation method in material simulation according to claim 5, characterized in that, The optimization of all error-concentrated mesh elements in the coupled mesh includes: performing quarter-interpolation refinement on each error-concentrated mesh element in the coupled mesh to obtain a new mesh element after interpolation refinement; using boundary restoration and invalid element removal mechanisms to perform consistency processing on the new mesh elements after interpolation refinement on each error-concentrated mesh element to obtain a new mesh element after consistency processing on each error-concentrated mesh element; and using a quality optimization strategy to perform edge swapping operations on the new mesh elements after consistency processing on each error-concentrated mesh element to obtain the optimized coupled mesh.

8. The adaptive mesh generation method in material simulation according to claim 1, characterized in that, The process of marking the atomic set to be expanded into an atomic region involves: calculating the gradient error of each grid cell in the continuous region grid of the optimized coupled grid; arranging the grid cells of the continuous region grid from largest to smallest according to the gradient error; selecting the top 30% of the grid cells in the continuous region grid; marking the selected grid cells; and obtaining the atomic set to be expanded into an atomic region.

9. The adaptive mesh generation method in material simulation according to claim 1, characterized in that, The process of expanding the atomic regions in the optimized coupled mesh includes: merging the set of atoms to be expanded into atomic regions with the set of atoms in the optimized coupled mesh to obtain the expanded set of atoms; and using the 3D Delaunay subdivision algorithm to generate the expanded atomic region mesh based on the expanded set of atoms.

10. The adaptive mesh generation method in material simulation according to claim 1, characterized in that, The construction of the cavity transition mesh includes: using the boundaries of the continuous region mesh and the boundaries of the extended atomic region mesh as geometric constraint information, and constructing the cavity transition mesh based on the geometric constraint information using the constrained 3D Delaunay meshing algorithm and mesh quality optimization method.

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