An adaptive mesh generation method in material simulation

Abstract

The present application belongs to the field of computational materials science and scientific computing technology, and relates to a self-adaptive grid generation method in material simulation, comprising: 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 self-adaptive grid refinement strategy to obtain a grid; S3, detecting whether the calculation accuracy of the material under the grid meets a preset, and if not, executing step S4; S4, expanding the atomic region grid of the grid to obtain a grid; S5, eliminating elements intersecting with the grid in the continuous region grid of the grid to obtain a grid; S6, constructing a cavity transition grid, splicing the grid with the cavity transition grid to obtain a grid; S7, judging whether a convergence condition is reached, and if yes, obtaining a final coupled grid; otherwise, optimizing the grid and returning to step S4; the present application automatically identifies and connects the atomic region and the continuous region 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 the three-dimensional atom / continuous coupling simulation, the generation of the grid is usually to construct the complete coupling grid by means of limited Delaunay subdivision and quality optimization under the boundary conditions of the given atomic region and the continuous region, and the target is to ensure the overall geometric consistency and element quality. In the defect evolution or atomic region expansion process, the original coupling boundary will change in topology, and the initial grid structure cannot meet the new geometric constraints, so adaptive grid reconstruction must be carried out. In the two-dimensional case, the interface between the atomic region and the continuous region is only composed of points and lines, and there is no complex surface and topology reconstruction, so the operation is relatively simple, and there is no risk of empty or abnormal cells, but the processing of the three-dimensional dynamic adaptive grid not only increases the difficulty by several times, but also needs to be designed in detail for the topology change.

[0007] In summary, the existing grid generation method is difficult to connect the atomic region and the continuous region in three-dimensional complex geometry with high quality and high efficiency, and cannot dynamically optimize the grid distribution in the simulation process, so as to cause the simulation accuracy and calculation efficiency to be not good enough. SUMMARY

[0008] To solve the above technical problems of the prior art, the application adopts an adaptive grid generation method in material simulation, comprising:

[0009] S1, dividing the atomic region and the continuous region of the three-dimensional material, generating the atomic region grid and the continuous region grid of the three-dimensional material according to the atomic region and the continuous region of the three-dimensional material, and splicing the atomic region grid and the continuous region grid of the three-dimensional material to obtain the coupling grid of the three-dimensional material;

[0010] S2, optimizing the coupling grid by using a local adaptive grid refinement strategy to obtain the optimized coupling grid;

[0011] S3, detecting whether the calculation accuracy of the three-dimensional material under the optimized coupling grid meets the preset, if yes, taking the optimized coupling grid obtained in step S2 as the final coupling grid; otherwise, executing step S4;

[0012] S4, marking out the atomic set to be expanded as the atomic region in the continuous region grid of the optimized coupling grid, expanding the atomic region grid in the optimized coupling grid according to the atomic set to be expanded as the atomic region, and obtaining the expanded atomic region grid;

[0013] S5, eliminating the grid elements intersecting with the expanded atomic region grid in the continuous region grid of the optimized coupling grid to obtain the divided continuous region grid;

[0014] S6, constructing a cavity transition grid, splicing the expanded atomic region grid, the divided continuous region grid and the cavity transition grid to obtain a new coupling grid;

[0015] S7, judge whether the preset convergence condition is reached, if yes, obtain the final coupling grid, otherwise, optimize the coupling grid obtained in step S6 by using a local adaptive mesh refinement strategy, obtain the optimized coupling grid, and return to step S4 to process the optimized coupling grid obtained in step S7.

[0016] Advantages:

[0017] 1. In view of the challenge brought by the curved boundary and topological change in the real three-dimensional material, the three-dimensional Delaunay subdivision algorithm is introduced and combined with the maximum inscribed radius constraint to generate the atomic region grid, so as to avoid the generation of large-scale poor quality elements at the boundary of the atomic region; the mesh nodes of the boundary of the continuous region grid are initialized according to the boundary of the continuous region, the mesh information of the coupling boundary of the atomic region and the continuous region is extracted; the limited three-dimensional Delaunay subdivision algorithm is introduced to generate the initial grid based on the mesh nodes of the boundary of the continuous region grid and the extracted mesh information of the coupling boundary, and the mesh elements falling into the atomic region grid are removed from the initial grid by using the boundary recovery and invalid element elimination algorithm, so as to ensure the geometric integrity and topological consistency of the coupling interface; 2. The present application introduces a gradient-based posterior error estimator to analyze the corresponding relationship between the atomic region grid and the continuous region grid, identify the error concentrated mesh elements in the coupling grid, and locally refine the error concentrated mesh elements, so as to avoid global over-refinement, improve the calculation efficiency, and at the same time, combined with the boundary recovery and invalid element elimination mechanism, ensure that the mesh structure at the atomic-continuous interface remains consistent in geometry and topology after refinement, improve the simulation stability, avoid the generation of holes or non-physical elements caused by refinement, and finally, through the quality optimization strategy, further perform the edge exchange operation on the refined mesh elements, improve the shape quality of the refined elements, and ensure the smooth transition of the mesh in the coupling region, so that the present application can dynamically maintain high precision in the defect area while avoiding global over-refinement, and balance the calculation efficiency and simulation stability; 3. When the calculation accuracy of the three-dimensional material under the optimized coupling grid does not meet the preset, the present application expands the atomic region grid, removes the mesh elements intersecting with the expanded atomic region grid in the continuous region grid, forms a topologically clear cavity, and then generates a cavity transition grid in the cavity region by using the limited three-dimensional Delaunay subdivision, and smoothes and splices the expanded atomic region grid, the divided continuous region grid and the cavity transition grid, so as to support the dynamic expansion of the atomic region, avoid the generation of abnormal elements and holes, and ensure the simulation accuracy and calculation efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0018] Figure 1 A flowchart of a material simulation adaptive mesh generation method provided by the embodiment of the present application;

[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 for 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 the three-dimensional material and continuous region grid By splicing, 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] The generating the atomic region grid and the continuous region grid of the material according to the atomic region and the continuous region of the three-dimensional material comprises: obtaining atomic coordinates of the atomic region of the material, and generating the atomic region grid of the material according to the atomic coordinates of the atomic region; and generating the continuous region grid of the material according to the boundary of the continuous region of the material and the atomic region grid.

[0030] The generating the atomic region grid according to the atomic coordinates comprises:

[0031] The atomic coordinates of the atomic region of the three-dimensional material are subjected to three-dimensional partitioning by using a three-dimensional Delaunay partitioning algorithm provided in a Tetgen software package to generate a raw preprocessing grid Ta-pre of the material; and a maximum inscribed sphere radius constraint-based element removal algorithm is used to remove low-quality grid cells at the boundary of the raw preprocessing grid to obtain the atomic region grid of the three-dimensional material .

[0032] To improve the spatial search efficiency, the application introduces a biased randomized insertion order (BRIO, Biased Randomized Insertion Order) optimization sorting technique for atoms in the construction of a three-dimensional Delaunay partitioning process, and uses a Bowyer-Watson algorithm to iteratively insert points to construct high-quality grid cells. The Bowyer-Watson algorithm is a classic incremental Delaunay triangulation algorithm.

[0033] Considering that there are defects, interfaces and other non-convex topological structures in the atomic region, the raw preprocessing grid may contain a large number of low-quality cells, especially concentrated near the boundary or convex hull. Therefore, a maximum inscribed sphere radius constraint-based element removal algorithm is introduced to remove low-quality grid cells at the boundary of the raw preprocessing grid.

[0034] Specifically, the removing the low-quality grid cells at the boundary of the raw preprocessing grid comprises: setting a maximum inscribed sphere radius r_max of the grid cells, calculating the inscribed sphere radius of the grid cells at the boundary of the raw preprocessing grid, removing the grid cells with an inscribed sphere radius greater than the maximum inscribed sphere radius r_max, obtaining a removed raw preprocessing grid, and performing topological repair on the removed raw preprocessing grid to obtain a grid that meets the coupling requirements ; wherein the maximum inscribed sphere radius r_max can flexibly control the grid density and quality, and is suitable for processing complex defect structures containing dislocations, vacancies and the like.

[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] The splitting process may temporarily penetrate into the atomic region, containing part of the invalid cells.

[0045] S13, removing the grid cells falling into the atomic region grid from the initial grid by using the boundary recovery and invalid cell elimination mechanism;

[0046] The boundary recovery and invalid cell elimination mechanism usually work together to form a progressive solution of "repairing the interface structure integrity first, then optimizing the cell quality", which finally guarantees the geometric correctness, topological consistency and computational applicability of the grid. Specifically, removing the grid cells falling into the atomic region grid from the initial grid includes: identifying and removing the grid cells falling into the atomic region grid from the initial grid, after removing the grid cells, repairing the boundary of the remaining grid (such as filling the hole, reconstructing the boundary cell), and then eliminating the invalid grid cells (such as low-quality grid cells), to ensure the consistency of the continuous region grid and the atomic region grid in geometry and topology (such as boundary closure, correct cell connection relationship).

[0047] S14, performing grid refinement on the grid obtained in step S13 to obtain the continuous region grid of the three-dimensional material .

[0048] This step uses the Quality Mesh Refinement (QMR) method for grid refinement to improve the shape quality of the grid cells and ensure smooth transition of the grid size near the coupling region, improving the simulation performance of the entire coupling grid.

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

[0050] S2, optimizing the coupling grid of the three-dimensional material by using a local adaptive grid refinement strategy to obtain an optimized coupling grid .

[0051] Optimizing the coupling grid of the three-dimensional material includes:

[0052] S21, performing atomic-continuous multi-scale calculation on the coupling grid of the three-dimensional material to obtain basic data of the coupling grid .

[0053] The basic data includes displacement field, energy distribution, stress response and other physical quantities, which provides basic data support for subsequent grid adaptive adjustment.

[0054] S22, identifying error concentrated grid cells of the coupled grid based on the basis data by using the posterior error estimator;

[0055] The migration and evolution of defects often lead to local stress concentration and sharp change of solution gradient. If targeted grid refinement adjustment is not performed, local error may be too large, and simulation results may be distorted. Compared with two-dimensional scenes, in three-dimensional scenes, not only more complex defect morphologies (such as cavities and non-convex surfaces) need to be dealt with, but also the grid quality and geometric consistency of the interpolation interface area must be ensured. Therefore, posterior error driven adaptive refinement is particularly important.

[0056] The posterior error estimator is a posterior error estimator based on a geometric gradient field, which calculates the difference between the displacement gradient of the continuous region solution and the atomic region reference solution, and is used to evaluate the local error level of the grid in the solution space. Specifically, identifying error concentrated grid cells of the coupled grid includes setting an error threshold, finding, in the coupled grid, an atomic region grid cell corresponding to each continuous region grid cell space at the coupled boundary, calculating the gradient error of the continuous region grid cell and the atomic region grid cell corresponding to the space thereof according to the L2 norm, and taking the continuous region grid cell with a gradient error greater than the error threshold as an error concentrated grid cell to provide 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 all atomic region grid cells whose spatial positions are completely or partially within the range of the continuous region grid cell. Then, calculating the gradient error includes: taking a statistical average (or a weighted average, the weight being 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 spatial range of the continuous region grid cell; and calculating the L2 norm error of the gradient of the continuous region grid cell and the equivalent gradient corresponding thereto.

[0058] S23, optimizing all error concentrated grid cells of the coupled grid to obtain an optimized coupled grid ; the optimized coupled grid includes atomic region grids and continuous region grids.

[0059] Optimizing all error concentrated grid cells of the coupled grid by using two types of adaptive technology includes:

[0060] ​The barycenter of each error concentration grid unit of the coupled grid is respectively subdivided by four-point interpolation to improve local resolution, and new grid units after interpolation of each error concentration grid unit are obtained; the new grid units are four tetrahedron units;

[0061] The new grid units after interpolation of each error concentration grid unit are respectively processed by a boundary recovery and invalid unit elimination mechanism to avoid cavities or non-physical units caused by local subdivision, and new grid units after consistency processing of each error concentration grid unit are obtained;

[0062] The new grid units after consistency processing of each error concentration grid unit are respectively subjected to edge exchange operation by a quality optimization strategy to ensure smooth transition of the grid in the coupling region, and the optimized coupled grid is obtained.

[0063] Specifically, the edge exchange operation by the quality optimization strategy includes:

[0064] For each edge in the new grid units after consistency processing of the error concentration grid unit, the quality indicators of all related tetrahedron units before and after exchange are calculated, and it is judged whether the quality indicators of all related tetrahedron units after exchange meet the quality improvement condition, and if so, the edge exchange operation is performed.

[0065] In this embodiment, the quality indicator of the tetrahedron unit is the ratio of the tetrahedron volume to the edge length, and the quality improvement condition is 1.01Q(A) < Q(B), wherein Q(B) is the quality indicator after exchange, and Q(A) is the quality indicator before exchange.

[0066] In one embodiment, before performing the edge exchange operation, a series of topological legality tests are also performed on all related tetrahedron units after exchange to ensure that no geometric defects such as face flipping, edge crossing or inconsistent face orientation are introduced. Through quality and topological legality tests, the system will only update the grid topology when the legality and quality meet the conditions.

[0067] Through the above steps, the present application can realize smooth transition of grid density changes at the boundary of the coupling region, and significantly improve the resolution capability of local stress concentration or defect evolution in simulation.

[0068] S3, detecting whether the calculation precision of the three-dimensional material under the optimized coupled grid meets the preset, if yes, the optimized coupled grid obtained in step S2 is taken as the final coupled grid; otherwise, step S4 is performed;

[0069] The defect part of the three-dimensional material (i.e. the coupling grid 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 atom set in the atom region grid in the material continuous region grid to obtain an extended atom set, and using an existing partition algorithm (such as a three-dimensional Delaunay partition algorithm) to generate an extended atom region grid according to the extended atom set.

[0076] S5, removing, in the optimized coupling grid , grid cells intersecting the extended atom region grid from the continuous region grid to obtain a divided continuous region grid ;

[0077] Since the extended atom region grid can overlap with the material continuous region, to avoid repeated definition, all grid cells intersecting the extended atom region grid are removed from the three-dimensional material continuous region grid to form a clear cavity boundary, which prepares for subsequent grid splicing. The above processing ensures that the atom region and the continuous region do not interfere with each other in space, and reserves geometric freedom for interface transition.

[0078] S6, constructing a cavity transition grid, splicing the extended atom region grid , the divided continuous region grid , and the cavity transition grid to obtain a new coupling grid ;

[0079] Constructing the cavity transition grid includes: taking the boundary of the divided continuous region grid and the boundary of the extended atom region grid as geometric constraint information, using a restricted three-dimensional Delaunay partition algorithm to construct the cavity transition grid according to the geometric constraint information, and using a mesh quality optimization (Quality Mesh Refinement, QMR) method to optimize to obtain the final cavity transition grid for filling the cavity between the atom region and the continuous region.

[0080] Splicing the extended atom region grid , the divided continuous region grid , and the cavity transition grid includes: to ensure the smoothness of the grid in the splicing area and the stability of the simulation, performing Laplace smoothing operation on the nodes of the continuous region grid at the interface to optimize the node layout and improve the grid quality.

[0081] Through this process, the atom-continuous interface can be dynamically updated during the simulation, which not only avoids the generation of abnormal cells and cavities, but also ensures the overall calculation accuracy and stability.

[0082] The final new coupling grid can be used for subsequent multi-scale simulation tasks, and has the advantages of reasonable region division, smooth structure transition, excellent cell quality, etc.

[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, the present application exhibits approximate semi-order convergence behavior in calculating geometric error, verifying the stability and adaptability of the present application in the evolution process of complex defects. Figure 4 As shown, the quality of the four iterations of the grid is evaluated by using the grid quality index, and the proportion of high-quality units (i.e., the quality score is 1) is 66.47%, 63.56%, 66.70%, and 69.36%, respectively, indicating that the present application can maintain the stability of the grid quality during the iteration process without significant degradation, and is suitable for accurate analysis of the subsequent coupled model. In summary, the self-adaptive grid generation method proposed by the present application has wide engineering application prospects in terms of accuracy, robustness, and computational efficiency in simulating complex multi-scale problems such as crystal defects.

[0092] The above examples further illustrate the purpose, technical solutions and advantages of the present application. It should be understood that the above examples are only preferred embodiments of the present application and do not limit the present application. Any modifications, equivalent replacements, improvements, etc. made to the present application within the spirit and principles of the present application should be included in the protection scope of the present application.

Claims

1. A method for adaptive mesh generation in material simulation, characterized in that, The method comprises the following steps: S1, dividing the atomic region and the continuous region of the three-dimensional material, and generating the atomic region grid and the continuous region grid of the three-dimensional material according to the atomic region and the continuous region of the three-dimensional material; The atomic region grid and the continuous region grid of the three-dimensional material are spliced to obtain a coupled grid of the three-dimensional material; S2, the coupled grid is optimized by using a local adaptive grid refinement strategy to obtain an optimized coupled grid; S3, whether the calculation accuracy of the three-dimensional material under the optimized coupled grid meets a preset is detected, if yes, the optimized coupled grid obtained in step S2 is taken as a final coupled grid; Otherwise, step S4 is executed; S4, an atomic set to be expanded into an atomic region is marked in the continuous region grid of the optimized coupled grid, and the atomic region grid in the optimized coupled grid is expanded according to the atomic set to be expanded into the atomic region to obtain an expanded atomic region grid; S5, the grid cells intersecting with the expanded atomic region grid are removed in the continuous region grid of the optimized coupled grid to obtain a divided continuous region grid; S6, a cavity transition grid is constructed, and the expanded atomic region grid, the divided continuous region grid and the cavity transition grid are spliced to obtain a new coupled grid; S7, whether a preset convergence condition is reached is judged, if yes, a final coupled grid is obtained; otherwise, the coupled grid obtained in step S6 is optimized by using the local adaptive grid refinement strategy to obtain an optimized coupled grid, and the optimized coupled grid obtained in step S7 is processed again.

2. The method of claim 1, wherein, The atomic region grid and the continuous region grid of the three-dimensional material are generated according to the atomic region and the continuous region of the three-dimensional material, which comprises the following steps:

3. The method of claim 2, wherein, The atomic region grid of the three-dimensional material is generated according to the atomic coordinates of the atomic region, and the continuous region grid of the three-dimensional material is generated according to the boundary of the continuous region and the atomic region grid. The atomic region grid of the three-dimensional material is generated by the following steps:

4. The method of claim 2, wherein, A three-dimensional Delaunay subdivision algorithm is used to perform three-dimensional subdivision on the atomic coordinates of the atomic region to generate an original preprocessing grid, the maximum inscribed sphere radius of the grid cells is set, the inscribed sphere radius of the grid cells at the boundary of the original preprocessing grid is calculated, the grid cells with the inscribed sphere radius greater than the maximum inscribed sphere radius are removed, and the atomic region grid of the three-dimensional material is obtained by performing topology repair on the original preprocessing grid after the removal. The continuous region grid of the three-dimensional material is generated by the following steps: S11, the grid nodes of the boundary of the continuous region grid are initialized according to the boundary of the continuous region of the three-dimensional material, and the grid information of the coupled boundary between the atomic region and the continuous region is extracted from the atomic region grid; S12, an initial grid is generated based on the grid nodes of the boundary of the continuous region grid and the extracted grid information of the coupled boundary by using a restricted three-dimensional Delaunay subdivision algorithm; S13, the grid cells falling into the atomic region grid are removed from the initial grid by using a boundary recovery and invalid element removal algorithm; S14, the grid obtained in step S13 is refined to obtain the continuous region grid of the three-dimensional material.

5. The method of claim 1, wherein, The optimization of the coupled grid of the three-dimensional material comprises: S21, performing atomic-continuum multi-scale calculation on the coupled grid of the three-dimensional material to obtain basic data of the coupled grid; S22, identifying error concentrated grid cells of the coupled grid according to the basic data of the coupled grid by using a posteriori error estimator; S23, optimizing all the error concentrated grid cells of the coupled grid to obtain an optimized coupled grid.

6. The method of claim 5, wherein, The identification of the error concentrated grid cells of the coupled grid comprises: setting an error threshold, finding, in the coupled grid, each continuous region grid cell space corresponding to an atomic region grid cell at a coupled boundary, calculating gradient error of the continuous region grid cell and the atomic region grid cell corresponding to the space of the continuous region grid cell according to L2 norm, and regarding the continuous region grid cell with the gradient error greater than the error threshold as an error concentrated grid cell.

7. The method of claim 5, wherein, The optimization of all the error concentrated grid cells of the coupled grid comprises: performing quad-tree insertion point refinement on each error concentrated grid cell of the coupled grid respectively to obtain new grid cells of each error concentrated grid cell after insertion point refinement; performing consistency processing on the new grid cells of each error concentrated grid cell after insertion point refinement respectively by using a boundary recovery and invalid cell elimination mechanism to obtain new grid cells of each error concentrated grid cell after consistency processing; and performing edge exchange operation on the new grid cells of each error concentrated grid cell after consistency processing respectively by using a quality optimization strategy to obtain the optimized coupled grid.

8. The method of claim 1, wherein, The marking of the atomic set to be expanded into an atomic region comprises: calculating gradient error of each grid cell of a continuous region grid in the optimized coupled grid, arranging the grid cells of the continuous region grid from large to small according to the gradient error, selecting the first 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 method of claim 1, wherein The atomic region expansion of the atomic region grid in the optimized coupled grid comprises: merging the atomic set to be expanded into an atomic region and an atomic set of the atomic region grid in the optimized coupled grid to obtain an expanded atomic set, and generating an expanded atomic region grid according to the expanded atomic set by using a three-dimensional Delaunay subdivision algorithm.

10. The method of claim 1, wherein The construction of the cavity transition grid comprises: taking boundaries of the divided continuous region grid and boundaries of the expanded atomic region grid as geometric constraint information, and constructing the cavity transition grid according to the geometric constraint information by using a restricted three-dimensional Delaunay subdivision algorithm and a grid quality optimization method.

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