An automated finite element simulation method and system for micro-nano structure surface effect

Abstract

The embodiment of the application discloses a kind of micro-nano structure surface effect automation finite element simulation method and system, belong to the field of computational solid mechanics.The automation finite element simulation method is built by Abaqus user-defined unit (UEL) subroutine respectively Matrix of Unit Stiffness and surface additional stiffness matrix and superimposed, realize the high-fidelity numerical simulation of zero-thickness surface elastic film;Surface unit automatic identification, INP file intelligent correction and result automatic extraction are realized by the whole process automation of Python script chain.The automation finite element simulation system includes pre-processing module, solver module and post-processing module, supports simple rule shape, complex single-connected and multi-connected structure surface automatic identification, compatible with ion diffusion, heat conduction, stress balance and other multi-physical field coupling analysis.

Description

Technical Field

[0001] This invention relates to the field of numerical simulation technology for micro- and nano-scale surface effects in computational solid mechanics, and relates to, but is not limited to, automated finite element simulation methods and systems for surface effects of micro- and nano-structures. Background Technology

[0002] When material sizes enter the micro-nano scale (<100 nm), the specific surface area increases significantly, and the proportion of surface atoms (coordination deficiencies, high-energy states) increases significantly, leading to mechanical properties completely different from those at the macroscopic scale: due to atomic coordination unsaturation, the material possesses high surface energy, thus exhibiting mechanical behavior different from the bulk, described by an independent surface elastic modulus, often accompanied by residual stress, which severely affects the deformation and failure behavior of materials at the micro-nano scale. The Gurtin-Murdoch (GM) theory models the surface as an "ideal elastic membrane with zero thickness but independent constitutive relations," where stress is composed of residual stress terms (derived from surface energy) and strain-related terms (derived from surface elasticity). This theory provides a continuum mechanics framework for describing micro-nano scale mechanical behavior, perfectly explaining phenomena such as the anomalous change in stiffness of nanobeams with thickness.

[0003] However, in existing technologies, the numerical implementation of this theory mainly relies on approximate simplification methods (such as thin-layer equivalence and property gradient) built into commercial software. The former lacks engineering practicality, while the latter fundamentally contradicts the zero-thickness assumption of the Gurtin-Murdoch theory, resulting in insufficient calculation accuracy (stress concentration factor error reaches 8-15%). In addition, existing simulation processes rely on manual operation, taking several hours from geometric modeling, surface element identification, parameter setting to post-processing analysis, and are prone to errors. This is almost infeasible for complex porous structures with hundreds of internal surfaces, and it lacks the ability to automatically analyze the coupling of surface effects with physical fields such as diffusion and fracture, which seriously restricts the engineering design and optimization of micro and nanomaterials in fields such as lithium battery electrodes and nanodevices.

[0004] Existing solutions are mostly "isolated" and customized, lacking an open framework that can easily integrate multiple surface recognition algorithms, be compatible with multiple surface constitutive models, and be extended to multi-physics coupled problems such as thermo-electric-chemical-mechanical problems. How to achieve high-precision, high-efficiency, and automated engineering applications of Gurtin-Murdoch theory without modifying the kernel of commercial finite element software, especially for multi-physics coupled fracture analysis of complex micro / nano structures (such as lithium battery electrodes), is a pressing problem that needs to be solved. Summary of the Invention

[0005] In view of this, the present invention addresses the core challenge of simulating the mechanical behavior of micro- and nano-scale materials by providing an automated finite element simulation method and system for surface effects of micro- and nano-structures.

[0006] The technical solution of this invention is implemented as follows: In a first aspect, embodiments of the present invention provide an automated finite element simulation method for surface effects of micro / nano structures, comprising: A geometric model of the micro / nano structure to be analyzed is constructed in geometric modeling software, and parametric modeling and mesh generation are performed to generate an initial finite element input file containing matrix elements and node information. Based on the mesh topology of the matrix elements, surface elements are automatically identified and labeled; where surface elements are the boundary edges or boundary surfaces of the matrix elements. Based on the Gurtin-Murdoch surface elasticity theory, the surface elements are modeled as zero-thickness elastic films. The initial finite element input file is modified to generate a UEL-compatible enhanced input file. The enhanced input file is read through the UEL subroutine of the finite element software, and the matrix element stiffness matrix and the surface additional stiffness matrix are calculated respectively. The matrix element stiffness matrix is ​​calculated based on the type of matrix element and the constitutive relation of the matrix material, and the surface additional stiffness matrix is ​​constructed based on the type of surface element and the constitutive relation based on the Gurtin-Murdoch theory. The surface additional stiffness matrix is ​​superimposed on the matrix element stiffness matrix to obtain the total stiffness matrix. Based on the total stiffness matrix, the overall stiffness matrix is ​​assembled and finite element calculation is performed to obtain the displacement field and stress field.

[0007] In some embodiments, the automatic identification and labeling of surface elements in the matrix element-based mesh topology includes: for simple regular shapes, automatically identifying surface elements through geometric features; the geometric features include the outward normal direction and / or radius of curvature; for complex simply connected models, identifying boundary nodes belonging to only one volume element based on a node-shared element counting algorithm to determine surface elements; for complex multi-connected structures or assemblies, directly resolving surface elements through predefined set names based on a named set-assisted method.

[0008] In some embodiments, the step of modifying the initial finite element input file to generate a UEL-compatible enhanced input file includes: parsing the initial finite element input file using regular expressions to identify standard element type definitions; replacing the standard element type with a UEL element type identifier; inserting user-defined parameters into the element attribute definition section to generate a UEL-compatible enhanced input file; the user-defined parameters include surface elastic constants, surface residual stress, and initial surface energy.

[0009] In some embodiments, the surface additional stiffness matrix is ​​calculated through the following process: If the current element is identified as a surface element, then for each marked boundary edge or boundary surface of the current element, the following calculations are performed: extracting the dimension-reduced subset nodes corresponding to the boundary edge or boundary surface; establishing a dimension-reduced local coordinate system and constructing a surface strain-displacement matrix that only relates the displacement and surface strain of the dimension-reduced subset nodes; constructing the surface elasticity matrix based on the Gurtin-Murdoch surface constitutive relation; and performing the following numerical integration calculations on the dimension-reduced geometric domain defined by the boundary edge or boundary surface to obtain the surface additional stiffness matrix: In the formula, To add a stiffness matrix to the surface of a specific boundary edge or boundary surface; This is the surface strain-displacement matrix; The surface elasticity matrix is ​​composed of the surface elastic constants and surface residual stresses. Decide; It is the geometric domain of the boundary edge or boundary surface.

[0010] In some embodiments, the material matrices of the matrix element stiffness matrix and the surface additional stiffness matrix are field variable functions. The UEL subroutine receives field variables through the state variable interface, wherein the field variables include temperature, lithium ion concentration, and electric potential, in order to realize thermo-mechanical, lithium ion diffusion-stress, or electro-mechanical coupling analysis.

[0011] Secondly, embodiments of the present invention provide an automated finite element simulation system for surface effects of micro / nano structures, comprising: The preprocessing module is configured to receive mesh data from geometric modeling software, generate a preliminary input file containing volume elements and node information, automatically identify and label surface elements, and generate a UEL-compatible enhanced input file. The solver module is configured to call the finite element software kernel to run the UEL subroutine, which implements the stiffness matrix calculation, superposition and solution process described in the first aspect above, and writes the calculation results into the result database. The post-processing module is configured to extract nodal displacement and stress field data from the results database and calculate fracture mechanics parameters according to user requirements.

[0012] In some embodiments, the post-processing module includes: J-integral calculation unit is configured to automatically calculate fracture driving force based on crack tip loop integral method; The VTK format conversion unit is configured to convert ODB format result files into VTK format that can be read by open-source visualization software.

[0013] In some embodiments, the preprocessing module is further configured to process multi-connected complex geometries, define the inner surface of the porous structure as a surface set through a single region selection, and automatically identify all surface units of the inner surface.

[0014] In some embodiments, the finite element software is Abaqus, and the UEL subroutine is written in Fortran and called through the Abaqus / Standard or Abaqus / Explicit solver.

[0015] Thirdly, embodiments of the present invention provide a method for predicting the fracture behavior of lithium-ion battery nanoelectrode particles, comprising: A geometric model of electrode particles containing pre-existing cracks is established, with particle sizes at the nanometer scale; wherein the pre-existing cracks are located on the particle surface or inside; the diffusion-induced stress field considering the surface effect is calculated using the aforementioned automated finite element simulation method or system for the surface effect of micro / nano structures, wherein the surface effect is introduced by superimposing the surface-added stiffness matrix implemented through the UEL subroutine; the J integral value at the crack tip is calculated based on the stress field, and the degree of suppression of fracture by the surface effect is evaluated; the J integral values ​​under the two conditions of considering the surface effect and not considering the surface effect are compared, and when the J integral value considering the surface effect decreases by more than a preset threshold, it is determined that the surface effect significantly suppresses crack propagation, and the crack resistance performance of the particles in charge-discharge cycles is predicted.

[0016] Fourthly, embodiments of the present invention provide a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps in the above-described automated finite element simulation method for surface effects of micro / nano structures.

[0017] The beneficial effects of the technical solutions provided in the embodiments of the present invention include at least the following: 1) The zero-thickness film model of Gurtin-Murdoch theory is strictly implemented in the UEL subroutine: the surface is regarded as a reduced-dimensional geometric entity, the matrix stiffness matrix and the surface additional stiffness matrix are calculated separately and accurately superimposed, avoiding the artificial thickness parameters and model distortion introduced by the traditional thin-layer approximation method.

[0018] 2) The fully automated script chain reduces the traditional manual operation that takes several hours to less than ten minutes, significantly improving simulation efficiency. The automatic surface unit identification algorithm can handle complex porous structures with hundreds of random pores, breaking through the operational limit of manually selecting hundreds of internal surfaces, making parametric research and optimization design of complex micro-nano structures possible.

[0019] 3) Without modifying the Abaqus kernel, the Gurtin-Murdoch theory is embedded into an industrial-grade solver through the UEL interface. This maintains theoretical fidelity (strict zero thickness) while gaining the parallel computing capabilities, rich material libraries, and mature contact algorithm support of commercial software, thus solving the long-standing industry problem of the disconnect between academic code and engineering applications. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort, wherein: Figure 1 A flowchart illustrating an automated finite element simulation method for surface effects of micro / nano structures provided in an embodiment of the present invention; Figure 2 A flowchart illustrating a method for predicting the fracture behavior of lithium-ion battery nanoelectrode particles, provided in an embodiment of the present invention. Figure 3 Thermographic diagram of concentration / stress evolution during simulated lithium-ion intercalation provided in embodiments of the present invention; Figure 4 Charging rate-J integral value curves with / without surface effect provided for embodiments of the present invention; Figure 5 A schematic diagram of the composition structure of an automated finite element simulation system for surface effects of micro-nano structures provided in an embodiment of the present invention; Figure 6 This is a flowchart illustrating the preprocessing module in the automated finite element simulation system provided in this embodiment of the invention. Figure 7 The logical flowchart of the UEL subroutine provided in the embodiment of the present invention. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, not all embodiments. The following embodiments are used to illustrate the present invention, but are not intended to limit the scope of the present invention. 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.

[0022] In the following description, references are made to “some embodiments,” which describe a subset of all possible embodiments. However, it is understood that “some embodiments” may be the same subset or different subsets of all possible embodiments and may be combined with each other without conflict.

[0023] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which these embodiments pertain. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art and should not be interpreted in an idealized or overly formal sense unless specifically defined as herein.

[0024] Surface effects, at the micro- and nano-scale, result in a significant increase in the proportion of surface atoms, leading to size-dependent phenomena in the overall mechanical properties of materials.

[0025] The Gurtin-Murdoch theory, a continuum mechanics framework, models solid surfaces as elastic membranes with zero thickness but independent mechanical properties (elasticity, residual stress), and is a classic theory describing surface effects. The stress in this elastic membrane is composed of residual stress terms (derived from surface energy) and strain-related terms (derived from surface elasticity).

[0026] User-defined elements (UELs) are high-level programming interfaces provided by the Abaqus software that allow users to write their own element types in Fortran, fully customizing the calculation methods for their element stiffness matrix and load vectors.

[0027] INP files, Abaqus' standard text input files, contain all the information about the model (nodes, elements, materials, loads, boundary conditions, etc.).

[0028] The stiffness matrix, in the finite element method, describes the linear relationship between nodal forces and nodal displacements of an element, and is the core of finite element analysis.

[0029] J-integral, an important parameter in elastoplastic fracture mechanics, is used to describe the intensity of the stress-strain field at the crack tip and is independent of the integration path.

[0030] This invention provides an automated finite element simulation method for surface effects of micro-nano structures, which is applied to an automated finite element simulation system. This system uses Abaqus as its core computing platform and deeply integrates custom functions through its open UEL interface and script (Python) interface.

[0031] Figure 1A flowchart illustrating an automated finite element simulation method for surface effects of micro / nano structures provided in this embodiment of the invention is shown below. Figure 1 As shown, the method includes at least the following steps: S110: Construct the geometric model of the micro / nano structure to be analyzed in the geometric modeling software, perform parametric modeling and mesh generation, and generate an initial finite element input file containing matrix elements and node information.

[0032] Here, the geometric modeling software includes open-source software such as Abaqus CAE / Gmsh / Hypermesh. The micro / nano structures to be analyzed are, for example, lithium-ion battery nanoelectrode particles, with characteristic sizes in the nanometer range (1-200 nm).

[0033] In implementation, users can choose to model directly in Abaqus CAE or use tools such as Gmsh to parametrically model the geometric model, defining key geometric parameters (such as particle radius, pore size, and crack length). An automatic mesh generation algorithm is used to generate a volume element mesh. The mesh generation process then generates the element and node topology relationships.

[0034] The initial finite element input file includes node numbers, node coordinates, element numbers and information, and element-node connection relationships. This initial finite element input file can be understood as a standard mesh file generated by any preprocessing tool. This system provides a script that can automatically convert Gmsh .msh format mesh files into an initial finite element input file, i.e., a preliminary .inp file, that Abaqus can recognize.

[0035] S120, based on a matrix element mesh topology, automatically identifies and marks surface elements.

[0036] Here, surface elements are the boundary edges or facets of the matrix elements. By analyzing the mesh structure generated from the geometric model, we identify and mark which element edges / faces require the application of the Gurtin-Murdoch surface effect. In implementation, multiple built-in surface recognition strategies can handle materials of varying complexity, from simple beams to porous foams, enabling automatic identification of surface elements and their corresponding boundary edges or facets.

[0037] S130, based on the Gurtin-Murdoch surface elasticity theory, the surface unit is modeled as a zero-thickness elastic film.

[0038] Here, based on the Gurtin-Murdoch surface elasticity theory, the surface constitutive relation is established: ,in For surface stress tensor, It represents the surface residual stress (constant tensor). It is the surface elasticity tensor (fourth-order tensor). Let be the surface strain tensor.

[0039] The surface element is reduced in dimension from the volume element boundary: the boundary surface of a three-dimensional volume element is reduced to a two-dimensional surface film, and the boundary edge of a two-dimensional volume element is reduced to a one-dimensional surface line. Mathematically, it is defined as having zero thickness, that is, the surface film has no volume and only has area (or length) properties.

[0040] S140 modifies the initial finite element input file to generate a UEL-compatible enhanced input file.

[0041] Here, a Python script reads the initial finite element input file, uses regular expressions to locate elements, performs format correction, and inserts UEL user-defined parameters to generate a UEL-compatible enhanced input file. This enhanced input file contains corrected element type definitions, a surface element label mapping table, and a UEL subroutine call interface.

[0042] S150 uses the UEL subroutine of the finite element software to read the enhanced input file and calculate the stiffness matrix of the base element and the additional surface stiffness matrix, respectively.

[0043] Here, the matrix element stiffness matrix is ​​calculated based on the element type of the matrix element and the constitutive relation of the matrix material, while the surface-added stiffness matrix is ​​constructed based on the type of the surface element and the constitutive relation based on Gurtin-Murdoch theory. The surface-added stiffness matrix is ​​obtained by integrating the surface constitutive relation on a zero-thickness geometric interface, rather than by modeling by assigning thickness to the solid.

[0044] UEL is the lowest-level user interface provided by Abaqus, allowing users to fully customize the element type, degrees of freedom, constitutive relations, and matrix assembly method. Unlike UMAT, which only defines material behavior at the integration point level, UEL requires the complete implementation of all computational logic from element geometry to stiffness matrix and right-hand side terms. This technology utilizes this interface to deeply integrate the Gurtin-Murdoch surface elasticity theory into the Abaqus / Standard solver kernel in the form of user-defined elements.

[0045] The UEL subroutine's main tasks include: 1) receiving surface information from the INP file and processing each matrix element cyclically; 2) calculating the element stiffness matrix of the matrix elements based on the element types defined in the model; 3) calculating the element stiffness matrix of the surface elements based on the matrix element types; 4) for surface elements, superimposing the surface stiffness matrix onto the matrix stiffness matrix; 5) determining if there are additional physical fields; if so, calculating the corresponding stiffness matrix based on the number of physical fields in the analysis problem (e.g., temperature, concentration); and 6) assembling the overall stiffness matrix and calculating the right-hand side terms based on the coupling type (e.g., unidirectional or bidirectional coupling). See the appendix for the detailed process. Figure 7 .

[0046] The UEL subroutine reads the node coordinates and matrix material parameters of the current element, and calculates the strain-displacement matrix of the element at the numerical integration point (Gaussian point) according to classical finite element theory. and material constitutive matrix Then, the stiffness matrix of the matrix element is assembled by integration. In the formula, the strain-displacement matrix Relationship between element nodal displacement and element strain for The transpose of the matrix, The elastic matrix, or material constitutive matrix, is used to describe the constitutive relation of the matrix material. It is derived from the material's elastic modulus. Compared to Poisson Decide, Let be the volume domain of the element.

[0047] It is worth noting that this invention strictly adheres to the Gurtin-Murdoch theory, avoiding the "thin-layer approximation" and instead mathematically precisely implementing a "zero-thickness elastic membrane" model. The surface is treated as a low-dimensional element on the boundary of a bulk element (one-dimensional edges correspond to two-dimensional bulk elements, and two-dimensional surfaces correspond to three-dimensional bulk elements), and its stiffness contribution is calculated independently and then superimposed. In other words, it employs the stiffness matrix superposition method instead of the traditional phase-field method or custom material subroutine (UMAT). This invention integrates the Gurtin-Murdoch theory into the Abaqus kernel through the UEL subroutine, enabling engineering applications in conjunction with automated scripts.

[0048] S160, the surface additional stiffness matrix is ​​superimposed on the matrix element stiffness matrix to obtain the total stiffness matrix.

[0049] Here, in the UEL subroutine, the stiffness matrix of the matrix element is... Add stiffness matrix to all surfaces By superimposing the results, the final overall stiffness matrix of the element is obtained. This allows for high-precision simulation of zero-thickness surface effects through stiffness superposition.

[0050] S170, based on the total stiffness matrix, assemble the overall stiffness matrix and perform finite element calculation to obtain the displacement field and stress field.

[0051] Here, the UEL subroutine will use the total stiffness matrix. The right-hand side (load vector) calculated based on the load is returned to the Abaqus master solver, which assembles it into a global system of equations and solves it.

[0052] In this embodiment of the invention, the zero-thickness film model of the Gurtin-Murdoch theory is strictly implemented in the UEL subroutine: the surface is regarded as a reduced-dimensional geometric entity, the matrix stiffness matrix and the surface additional stiffness matrix are calculated separately and accurately superimposed, thus avoiding the artificial thickness parameters and model distortion introduced by the traditional thin-layer approximation method.

[0053] In some embodiments, the above step S120 "automatically identify and label surface elements based on the mesh topology of the matrix elements" is further implemented through the following process: for simple regular shapes, surface elements are automatically identified through geometric features; the geometric features include the outward normal direction and / or radius of curvature; for complex simply connected models, boundary nodes belonging to only one volume element are identified based on the node shared element counting algorithm to determine the surface elements; for complex multi-connected structures or assemblies, surface elements are directly resolved through predefined set names based on the naming set-assisted method.

[0054] Here, for simple regular shapes such as spherical or cylindrical particles, the outward normal direction vector of the volume unit can be extracted, and the angle between the normals of adjacent units can be calculated; the surface region can be identified by judging the curvature radius threshold (e.g., curvature radius > 100nm is judged as a plane); and the boundary edges or boundary surfaces that meet the geometric features are marked as surface units.

[0055] For complex, simply connected models such as a single nanopore, a node-shared cell counting algorithm is used to identify boundaries by counting the number of cells to which a node belongs. In implementation, all nodes are traversed sequentially, and boundary nodes belonging to only one volume cell are identified (shared cell count = 1). Boundary edges or boundary surfaces are determined by these boundary nodes and marked as surface cells.

[0056] For complex, multi-connected structures or assemblies such as porous foam materials, predefined name sets (such as Set-InnerSurf, Set-OuterSurf) are used during the modeling phase; all boundary elements within the set are directly resolved by the set name; and a unique identifier tag is assigned to each surface element for subsequent UEL parameter passing.

[0057] Surface recognition is the core pre-process automation step in this technical solution. Its goal is to accurately determine which elements in the finite element mesh model are located on geometric surfaces, and further pinpoint which specific edge (for two-dimensional problems) or face (for three-dimensional problems) within these elements requires the application of a surface effect stiffness matrix. To address the recognition needs of models with varying complexity, this technology designs a three-level progressive recognition algorithm system, the specific implementation details of which are as follows: Algorithm 1: Geometric center distance method automatically identifies surface units through geometric features, suitable for rapid identification of regular shape models. Applicable scenarios: Models with a clear geometric center and regular boundaries, such as circles, spheres, rectangles, and cuboids. Implementation steps are as follows: 1) Determine the geometric center coordinates: Read the coordinates of all nodes in the model and calculate their arithmetic mean as the geometric center point. .

[0058] 2) Preset surface judgment threshold: Based on the theoretical outer contour dimensions of the model, a distance threshold is set. Typically, the theoretical radius or half-side length is multiplied by a coefficient slightly less than 1 (such as 0.98, determined by the model's scale) to eliminate the influence of numerical errors.

[0059] 3) Calculate the centroid coordinates of each cell in the model: .

[0060] 4) Distance Comparison and Judgment: Calculate the distance from the unit to the geometric center point. .like If so, then the element is determined to be a surface element.

[0061] 5) Surface boundary edge / face positioning: For the determined surface element, further calculate the midpoint coordinates of each edge (two-dimensional) or each face (three-dimensional) of the element, and select the edge / face farthest from the geometric center as the actual surface boundary in contact with the outside world.

[0062] Technical features: extremely high computational efficiency, with a time complexity of O(N) (N is the total number of units), but it depends on the geometric regularity of the model and fails for irregular shapes.

[0063] Algorithm 2: Node-shared unit counting method, suitable for topology identification of complex simply connected models. Applicable scenarios: Simply connected regions of arbitrary shape (i.e., without internal holes), such as irregularly shaped particles, irregularly shaped structural components, etc. Implementation steps are as follows: 1) Construct a node-cell association table: Traverse all cells and create each node. List of units to which it belongs And record the total number of times the node appears. .

[0064] 2) Statistical analysis: In continuous meshes, internal nodes are typically shared by multiple elements. For two-dimensional quadrilateral meshes, the number of shared elements for internal nodes is generally 4 or more; for three-dimensional hexahedral meshes, the number is generally 8 or more. However, the number of shared elements for surface nodes is below this threshold.

[0065] 3) Set node type threshold: Set a critical value based on the mesh type. (For two-dimensional, a value of 3 is generally used; for three-dimensional, a value of 5 is generally used). If Then mark the node. For surface nodes.

[0066] 4) Reverse surface element analysis: Traverse all elements and examine the set of nodes that make up the element. If at least one node of an element is marked as a surface node, then it is listed as a candidate surface element.

[0067] 5) Precisely locate the boundary edges / faces of the surface: For each candidate element, examine each edge (2D) or each face (3D) sequentially. If all nodes constituting the edge / face are surface nodes, then the edge / face is determined to be the actual surface boundary exposed to the outside. This step can eliminate false positives where only the corner points are located on the surface but the edge / face itself is located inside.

[0068] Technical features: It does not rely on geometric information, but only utilizes the mesh topology relationship, and is robust to arbitrarily complex shapes. Its time complexity is O(M) (M is the number of nodes), which is the core general algorithm of this technical solution.

[0069] Algorithm 3: Named Set Assisted Method, suitable for semi-automatic identification of complex multi-connected / assembly models. Applicable scenarios: Multi-connected regions containing holes and cavities, or complex structures assembled from multiple components, such as porous materials and microelectromechanical systems (MEMS). Implementation steps are as follows: 1) Predefined Modeling Stage: When performing geometric modeling in preprocessing software such as Abaqus CAE or GMSH, users manually select the physical surfaces to which surface effects need to be applied (such as the inner walls of holes or contact interfaces of components) through the graphical interface, and assign them meaningful names, such as "INNER_SURFACE" or "CRACK_FACE". This operation only needs to be done once, and for repetitive structures (such as each pore in a porous material), batch selection can be performed through software functions.

[0070] 2) Parsing the INP file to extract information: Run the pre-processing Python script of this technology to read the original INP file exported by the modeling software. Use regular expressions to parse the "*Elset" and "*Surface" keyword sections to extract all user-defined named sets and their contained cell and face numbers.

[0071] 3) Establish a mapping table: Organize the extracted information into a data structure and clearly record: set name -> list of included cell numbers -> index of the selected local face on each cell (such as face 1, face 2, etc.).

[0072] 4) Marking and Transmission: Use the "*UEL PROPERTY" keyword to add a specific identifier to the selected element so that it can be recognized by the UEL subroutine during the solution phase and trigger the surface stiffness calculation.

[0073] Technical features: It combines human geometric cognition with machine automation capabilities to solve the most complex multi-connected region recognition problem with minimal human intervention (only one surface selection and naming is required), achieving a balance between complexity and automation.

[0074] This embodiment further defines three progressive surface recognition algorithms to handle models of varying complexity. Through the above three-level algorithm system and standardized information transmission mechanism, this invention achieves fully automatic or semi-automatic accurate identification of surface boundaries of finite element models of arbitrary complexity, fundamentally solving the core pain points of traditional methods that rely on manual selection, are time-consuming and error-prone, and cannot handle complex geometry.

[0075] In some embodiments, step S130, "modifying the initial finite element input file to generate a UEL-compatible enhanced input file," is further implemented through the following process: parsing the initial finite element input file using regular expressions to identify the standard element type definition; replacing the standard element type with the UEL element type identifier; inserting user-defined parameters into the element attribute definition section to generate a UEL-compatible enhanced input file; the user-defined parameters include surface elastic constants, surface residual stress, and initial surface energy.

[0076] Here, the initial finite element input file, i.e., the .inp file generated by Abaqus or obtained from mesh conversion, has a format incompatible with the requirements of the UEL subroutine. This embodiment of the invention uses regular expressions to automatically correct the file. Key operations include: replacing ordinary element types (such as CPS4R) with UEL element types (such as U1); and inserting user-defined parameters required by UEL, such as surface elastic constants and surface residual stresses, into the corresponding element definition sections. This step ensures seamless integration between general-purpose modeling tools and dedicated solvers.

[0077] In some embodiments, the surface additional stiffness matrix is ​​calculated through the following process: If the current element is identified as a surface element, then for each marked boundary edge or boundary surface of the current element, the following calculations are performed: extracting the dimension-reduced subset nodes corresponding to the boundary edge or boundary surface; establishing a dimension-reduced local coordinate system and constructing a surface strain-displacement matrix that only relates the displacement and surface strain of the dimension-reduced subset nodes; constructing the surface elasticity matrix based on the Gurtin-Murdoch surface constitutive relation; and performing the following numerical integration calculations on the dimension-reduced geometric domain defined by the boundary edge or boundary surface to obtain the surface additional stiffness matrix: In the formula, To add a stiffness matrix to the surface of a specific boundary edge or boundary surface; This is the surface strain-displacement matrix; The surface elasticity matrix is ​​composed of the surface elastic constants and surface residual stresses. Decide; The geometric domain of the boundary edge or boundary surface. For two-dimensional volume elements, the length of the boundary edge is a infinitesimal element; for three-dimensional volume elements, the area of ​​the boundary surface is a infinitesimal element.

[0078] Here, the boundary surfaces of 3D volume elements correspond to 2D node sets, and the boundary edges of 2D volume elements correspond to 1D node sets. A reduced-dimensional local coordinate system is established for the current surface, and its corresponding surface strain-displacement matrix is ​​constructed. After linearization, The contribution to the stiffness matrix is ​​manifested as a surface-added stiffness matrix. .

[0079] In some embodiments, the material matrices of the matrix element stiffness matrix and the surface additional stiffness matrix are field variable functions. The UEL subroutine receives field variables through the state variable interface, wherein the field variables include temperature, lithium ion concentration, and electric potential, in order to realize thermo-mechanical, lithium ion diffusion-stress, or electro-mechanical coupling analysis.

[0080] Here, the UEL subroutine receives field variables such as temperature, lithium ion concentration, and electric potential through the Solution-Dependent State Variables interface, enabling analysis of ion diffusion, thermal conduction, and stress coupling. It is particularly suitable for predicting the chemical-mechanical coupling fracture of lithium battery nanoelectrode particles during the charging and discharging process.

[0081] The automated finite element simulation method for the surface effects of micro-nano structures described above will be illustrated below with a specific embodiment. However, it is worth noting that this specific embodiment is only for better illustrating the present invention and does not constitute an improper limitation of the present invention.

[0082] This specific embodiment illustrates the fracture behavior of lithium-ion battery nanoelectrode particles as an example. Driven by the pursuit of high power density (fast charging), batteries are often operated under high current (high rate) conditions. This leads to the rapid and uneven insertion and extraction of lithium ions within the electrode particles, generating significant diffusion-induced stress. When this stress exceeds the fracture strength of the particles, it causes particle fragmentation, destroying the integrity of the electrode structure and resulting in a sharp decline in battery capacity and performance. Furthermore, research has shown that reducing particle size to the nanoscale can improve particle performance. However, due to their enormous specific surface area, the surface effect becomes crucial to the mechanical behavior, which traditional continuum mechanics models can no longer accurately describe. Therefore, it is necessary to incorporate surface effects into the calculation system based on traditional analysis.

[0083] Figure 2 A flowchart illustrating a method for predicting the fracture behavior of lithium-ion battery nanoelectrode particles provided in this specific embodiment is shown below. Figure 2 As shown, the prediction method includes the following steps: S210, establish a geometric model of electrode particles containing pre-existing cracks, with particle size in the nanometer range.

[0084] Here, the pre-cracks are located on the particle surface (more susceptible to surface stress modulation) or inside (reflecting bulk failure), covering typical failure modes. The electrode particle material includes nano-silicon, nano-carbon, or silicon-carbon composites. The pre-crack size is 1-20 nm, and the particle characteristic size is 10-200 nm, ensuring significant surface effects. The geometric model is typically two-dimensional axisymmetric or three-dimensional spherical, balancing computational efficiency and physical realism. This step aims to simulate unavoidable micro-defects in real electrode particles, such as synthetic residual cracks and cyclically induced micro-cracks.

[0085] S220, using the above-mentioned automated finite element simulation method or system for surface effects of micro / nano structures, calculates the diffusion-induced stress field considering the surface effects, wherein the surface effects are introduced by superimposing the surface additional stiffness matrix implemented by the UEL subroutine.

[0086] Here, based on the Gurtin-Murdoch surface elasticity theory, the outer surface of the particles and the crack surface are regarded as "zero-thickness elastic membranes" with independent constitutive relations; the superposition of the surface additional stiffness matrix is ​​realized in Abaqus through a custom UEL subroutine; and all boundaries (outer contour + crack surface) that need to be applied to the surface effect are automatically identified by the preprocessing module of the automated finite element simulation system, avoiding manual marking errors.

[0087] S230, calculate the J integral value at the crack tip based on the stress field, and evaluate the degree of surface effect on fracture suppression.

[0088] Here, the J integral value characterizes the energy release rate at the crack tip and is a core fracture driving force indicator in linear elastic / elastoplastic fracture mechanics. It is calculated by integrating the displacement, stress, and concentration fields output by UEL along the path surrounding the crack tip using a post-processing module. This transforms the abstract surface effect into a quantifiable and comparable engineering indicator.

[0089] S240, comparing the J integral values ​​under two working conditions, considering surface effects and not considering surface effects, when the J integral value considering surface effects decreases beyond a preset threshold, it is determined that the surface hardening effect significantly inhibits crack propagation, and the crack resistance performance of particles in charge-discharge cycles is predicted.

[0090] Here, a preset threshold (such as a 20% or 30% decrease in the J integral value) is set. By comparing the J integral values ​​under two working conditions, considering surface effects and not considering surface effects, the crack resistance performance is determined and the cyclic reliability is predicted.

[0091] The core of this specific embodiment lies in extending the classic diffusion-stress coupling model by introducing the surface effects of nanoparticles into the finite element method. In the implementation, a two-dimensional circular plane strain particle model with a radius of 100 nm was constructed, and a 10 nm edge crack was prefabricated to simulate a real defect. Through the custom UEL subroutine and automated pre- and post-processing system integrated into Abaqus provided by this invention, the unidirectional coupling calculation of the mechanical-electrochemical multiphysics field and the Gurtin-Murdoch surface elasticity theory was realized for the first time in a commercial software environment. The pre-processing module automatically identifies all boundaries where surface effects need to be applied to the particle's outer contour and the crack surface through a node-shared element counting algorithm, and embeds parameters characterizing surface elasticity into the model. In the solver, the UEL program accurately accounts for the additional stiffness contribution provided by the crack surface and the particle's outer surface as a "zero-thickness elastic membrane" while calculating the diffusion-induced stress field. The post-processing automatically extracts the crack tip field data and calculates the J integral, a key indicator of the fracture driving force.

[0092] Simulation results show that, under the same load, the crack tip J-integral value calculated by the model considering surface effects is significantly lower than that of the traditional model neglecting surface effects. This qualitatively reveals that the generated surface effects can effectively suppress crack propagation, thus reasonably explaining the microscopic mechanism by which nanoelectrode particles exhibit higher crack resistance. This specific embodiment not only verifies the accuracy and reliability of the invention in handling complex multiphysics coupling and extreme-scale mechanical problems, but also highlights its value as a key tool connecting cutting-edge theory and engineering practice, providing direct theoretical basis and prediction methods for the rational design of high-performance nanoelectrode materials.

[0093] Using this method, the automated finite element simulation system for micro / nano structure surface effects provided by this invention was used to simulate the lithiation / delithiation process of spherical particles of different sizes (especially at the micro / nano scale) and at different charge / discharge rates. Through multi-scale modeling and analysis of lithium-ion battery nanoelectrode particles, the following results can be obtained: Figure 3 The thermograms shown reflect the spatiotemporal distribution of diffusion-induced stress (field distribution at times t=0s and t=300s). A quantitative analysis of how surface effects influence the stress distribution within particles reveals the inhibitory effect of surface effects on crack initiation and propagation. Through parametric studies, the competitive relationship between particle size, charge / discharge rate, and fracture tendency is clarified, elucidating the improvement of battery mechanical properties through particle nanosizing. Figure 4 The figure shows the charging rate-J integral value curves with and without surface effect. This figure reflects the charging rate before and after the introduction of surface effect at different charging rates. The difference in J integral values ​​shows that the smaller J integral value corresponding to the red curve (including surface effect) indicates that the crack is less likely to propagate and the battery performance is better.

[0094] This specific embodiment is the first to quantitatively reveal the significant inhibitory effect of surface effects on the J-integral at the crack tip (reducing it by more than 30%) in the fracture analysis of lithium battery nanoelectrode particles, providing a theoretical basis for the crack-resistant design of nanoelectrodes; it lowers the technical threshold from the expert level to the engineer level, enabling material researchers to use the Gurtin-Murdoch theory for design optimization without being proficient in finite element programming.

[0095] Based on the foregoing embodiments, this invention further provides an automated finite element simulation system for surface effects of micro / nano structures. This system uses Abaqus as its core computing platform and deeply integrates custom functions through its open User Subroutine (UEL) interface and Python scripting interface. Each module transmits data and collaborates using specific file formats (such as hm, inp, for, odb, vtk).

[0096] Figure 5 This is a schematic diagram of the composition structure of an automated finite element simulation system for surface effects of micro / nano structures provided in an embodiment of the present invention, as shown below. Figure 5 As shown, the automated finite element simulation system 500 includes: The preprocessing module 510 is configured to receive mesh data from geometric modeling software, generate a preliminary input file containing volume elements and node information, automatically identify and label surface elements, and generate a UEL-compatible enhanced input file. Solver module 520 is configured to call the finite element software kernel to run the UEL subroutine. The UEL subroutine implements the stiffness matrix calculation, superposition and solution process as described in the above-mentioned automated finite element simulation method for surface effects of micro and nano structures, and writes the calculation results into the result database. The post-processing module 530 is configured to extract nodal displacement and stress field data from the results database and calculate fracture mechanics parameters according to user requirements.

[0097] After identifying surface elements, the preprocessing module 510 automatically assigns a unique label to each surface element and stores the label in a parameter table in association with the corresponding surface elastic parameters. The UEL subroutine in the solver module 520 reads the label during runtime and calls the corresponding surface constitutive model according to the parameter table. The surface elastic parameters include surface Young's modulus, surface Poisson's ratio, and surface residual stress, which can be used to predict the equivalent stiffness of nanoporous metals.

[0098] In this embodiment, the preprocessing module 510 mainly consists of a series of Python scripts. It receives data from open-source software such as AbaqusCAE, Gmsh, and Hypermesh, automatically identifies surface elements, automatically embeds surface parameters, and outputs an enhanced input file—corrected and with enhanced surface information—that can be directly read and executed by the solver module. A flowchart of the preprocessing module 510 is shown below. Figure 6As shown, for the research object, parametric modeling and mesh generation are performed in open-source software such as Gmsh / Hypermesh / CAD using the Model.py program file, outputting .geo / .inp / .hm format files (i.e., the initial finite element input files mentioned above). The Read_data.py program file is called to read the element node information generated in the previous step, including node numbers and coordinates, element numbers and information. The Convert_format.py program file uses regular expressions to automatically correct the data. Key operations include: replacing ordinary element types (such as CPS4R) with UEL element types (such as U1); inserting user-defined parameters required by UEL into the corresponding element definition section, such as surface elastic constants and surface residual stress. Based on the read node and element information and according to the subroutine format specifications, the geometric information of the matching .inp file is generated. The Load.py program file reads the remaining parts of the .inp file, such as loads and material parameters, and adds, deletes, or removes them according to the subroutine format specifications. This program requires additional functionality to be added based on the usage scenario. The Sur_identify.py program reads the node element information from the F_Uel_model file, identifies the surface elements and their corresponding node information based on the algorithm, and sets special identifiers for these elements in the .inp file for subsequent reading. Finally, it outputs the S_Uel_model.inp file (i.e., the enhanced input file mentioned above) for UEL to call.

[0099] The system integrates three progressive surface recognition algorithms to handle models of different complexities, corresponding to simple regular shapes, complex single-connected models, and complex multi-connected or assembly models, respectively.

[0100] In this embodiment, the solver module 520 is an Abaqus UEL subroutine written in Fortran. It reads the INP file generated by the preprocessing module, performs finite element calculations including surface effects under the scheduling of the Abaqus solver kernel, and finally writes the calculation results to the Abaqus results database (odb) file. The solver module 520 mainly performs the following steps: Step 1, Read Element Information and Surface Labels: The UEL subroutine reads the current element number, node coordinates, material parameters, and surface labels (indicating whether the element is a surface element and which edges / faces are surfaces) from the enhanced input file (.inp file) output by the preprocessing module.

[0101] Step 2: Calculate the stiffness matrix of the matrix element. Based on the classical finite element theory, the strain matrix and constitutive matrix of the element are calculated at the numerical integration points based on the nodal coordinates of the element and the material properties of the matrix. Then, they are integrated and assembled into the stiffness matrix of the matrix element.

[0102] Step 3: Calculate the surface additional stiffness matrix For each marked boundary edge or boundary surface of the surface element, a local coordinate system is constructed, and the surface strain-displacement matrix is ​​calculated. and surface elastic matrix This leads to the surface additional stiffness matrix. .

[0103] Step 4, Stiffness Matrix Superposition and Return: Superimpose the matrix stiffness matrix with all surface-attached stiffness matrices to obtain the final total stiffness matrix of the element. Then, the UEL subroutine will generate the total stiffness matrix. The right-hand side (load vector) calculated based on the load is returned to the Abaqus master solver, which assembles it into a global system of equations and solves it.

[0104] It should be noted that the architecture of the UEL subroutine allows for easy extension of multi-field coupling. For example, in computation... and At that time, the material constitutive matrix and surface elastic matrix It can no longer be a constant, but a function of field variables such as current temperature and electric field. By connecting to other user subroutines of Abaqus (such as UMATHT and UELMAT) or implementing multiphysics constitutive models directly within this UEL, coupled analyses such as thermo-mechanical and electro-mechanical analyses can be achieved.

[0105] In this embodiment, the post-processing module 530 is also composed of Python scripts. It actively extracts the raw calculation results data from the .odb file generated by the solver module and performs secondary processing (such as calculating the J-integral and plotting stress-strain curves) and format conversion (such as converting to VTK format) according to user needs. Finally, it outputs the processed data to visualization software such as Paraview for display. Specifically, the script file odb_extractor.py uses the Python API (odbAccess) provided by Abaqus to open the .odb file generated by the solver. Users can specify the extraction of displacement, strain, and stress fields for all nodes, the distribution of field variables along a specific path (for calculating the J-integral), and the load-displacement curves for specific points.

[0106] In some embodiments, the post-processing module 530 includes: The J-integral calculation unit is configured to automatically calculate the fracture driving force based on the crack tip loop integration method. In implementation, the J-integral calculation unit reads the nodal stress and displacement data on a loop defined by the user around the crack tip, performs integration calculations according to the definition formula of J-integral, and outputs the J-integral value as a fracture parameter.

[0107] The VTK format conversion unit is configured to convert ODB format result files into VTK format, which can be read by open-source visualization software. To reduce reliance on specific commercial post-processing software, this unit provides the format conversion script vtk_converter.py, which reorganizes the extracted nodes, cells, and data fields according to the VTK or GMSH .mesh format requirements and writes them to a file. The generated .vtk or .post files can be directly opened in Paraview or GMSH for rich visualizations such as contour plots, vector graphics, and morphing animations.

[0108] In some embodiments, the preprocessing module 510 is further configured to process multi-connected complex geometries, define the inner surface of the porous structure as a surface set through a single region selection, and automatically identify all surface units of the inner surface.

[0109] For porous nanofoam materials (containing hundreds of randomly distributed, interconnected pores), the surface effect must be considered for the inner surface of each pore. In implementation, a porous geometric mesh is generated in Gmsh. During preprocessing, in the modeling stage, all pore inner walls are uniformly defined as a set named INNER_SURF through a single region selection. The system automatically identifies all elements and surfaces contained in this set and passes their parameters to UEL.

[0110] In some embodiments, the finite element software is Abaqus, and the UEL subroutine is written in Fortran and called through the Abaqus / Standard or Abaqus / Explicit solver.

[0111] This system, through a deep customization of Abaqus' UEL interface, is the first to realize the Gurtin-Murdoch surface effect theory with high fidelity in a mainstream engineering simulation platform. At the same time, through the supporting Python pre- and post-processing toolchain, it achieves full automation and intelligence from modeling to analysis, and reserves the ability to expand for multi-physics coupling.

[0112] This invention does not merely provide an isolated UEL subroutine, but rather constructs a seamless, highly automated, and scalable surface effect simulation system that connects theoretical models to engineering applications. Its key technical points and comparison with existing technologies are as follows: Technically, existing fragmented and manually connected code or operations may have a UEL subroutine, but pre- and post-processing rely heavily on manual scripts or software interface operations, resulting in a disjointed workflow. This invention seamlessly integrates the three major modules of pre-processing, solution calculation, and post-processing through standardized data flow and automated scripts, forming a "black box" solution. This solves the fundamental problems of non-automation and inefficiency in the operational process. Users only need to provide initial geometry and parameters, and the system can automatically complete the entire process from modeling to drawing, lowering the threshold for complex surface effect simulation from expert level to engineer level, greatly improving research efficiency and the reliability of results.

[0113] In terms of implementation: Existing methods either only use the software's built-in approximation functions or only use the software as a partial preprocessor or solver caller. This invention modifies and empowers Abaqus's INP file using a preprocessing module, uses a UEL module to take over and enhance Abaqus's core unit calculations, and uses a postprocessing module to extract and transform Abaqus's result data, achieving deep integration of dedicated functions on a general-purpose platform. This solves the problem of the disconnect between theoretical models and software functionality. This invention does not bypass commercial software but utilizes its open interface to embed Gurtin-Murdoch theory into the kernel of industry-standard software, enabling the high-fidelity theoretical model to obtain the computational robustness, parallel efficiency, and rich material and load library support of an industrial-grade solver.

[0114] Theoretical Foundation: Most existing technologies use approximate methods to simulate surface effects, such as using additional layers with thickness or gradient properties, resulting in physical models that do not conform to Gurtin-Murdoch theory. This invention strictly adheres to Gurtin-Murdoch theory: the surface is modeled as a zero-thickness elastic membrane, and the stiffness matrices are calculated separately for the matrix elements and the reduced-dimensional elements (edges / faces) of its surface in UEL, and then precisely superimposed. On the general-purpose Abaqus platform, the classic Gurtin-Murdoch surface effect theory is implemented numerically rigorously and physically accurately, rather than through approximations.

[0115] In terms of scalability: Existing methods or programs typically only consider pure mechanical responses. The architecture of this invention supports multi-field coupling extensions; within the UEL program, the material property matrix can be used as a function of field variables (temperature, potential, etc.). Currently, thermo-mechanical coupling has been implemented, and the architecture design reserves interfaces for multiple physics fields such as electricity and chemistry.

[0116] In terms of data analysis: It is equipped with corresponding post-processing modules and provides Python scripts to extract arbitrary data from ODB files, and seamlessly integrates with open-source scientific computing stacks (such as NumPy and SciPy for calculations, and Matplotlib / Paraview for visualization). It breaks through some limitations of commercial post-processing software, achieving full-process autonomy, controllability, and repeatability from calculation to analysis, and facilitating the integration of post-processing algorithms in professional fields such as J-integral.

[0117] By directly comparing with existing technologies, the following data and examples demonstrate the significant advantages of this invention from four dimensions: computational accuracy, simulation efficiency, ability to handle complex problems, and breadth of application.

[0118] Taking the classic problem of a circular nanopore of radius R under far-field uniaxial tension as an example, this problem has an analytical solution based on the Gurtin-Murdoch theory. Existing methods in Abaqus use a "thick elastic layer" (such as a very thin solid or shell element) to approximate surface effects. However, using the UEL of this system, a zero-thickness elastic surface model is strictly achieved. Regarding the stress concentration factor at the hole edge, existing methods deviate from the analytical solution by approximately 8-15%, and are sensitive to the value of the virtual "layer thickness"; the solution of this invention deviates from the analytical solution by less than 1%. Regarding the strain energy density in the critical region, existing methods systematically overestimate the calculated value, with an error of approximately 10-20%; the solution of this invention is in high agreement with the analytical solution, with a relative error of less than 0.5%.

[0119] Taking a microbeam model containing a complex internal cavity as an example, this paper compares the time consumption and operation steps of the entire process from modeling to obtaining stress contour maps. Traditional manual operation process: Modeling and meshing in Abaqus CAE; manually selecting all elements and corresponding edges of the outer and inner cavity surfaces one by one, creating multiple sets, taking approximately 2-3 hours, and highly prone to omissions or errors; manually writing / modifying the INP file to adapt to UEL and adding parameters, taking approximately 30 minutes, prone to errors; submitting the calculation; manually extracting data and importing it into third-party tools for post-processing such as J-integration, taking approximately 1 hour. Total manual intervention time: approximately 3.5-4.5 hours, with a high risk of error.

[0120] The automated process of this invention is as follows: Model and mesh in GMSH (or use Abaqus CAE), generate a preliminary INP file with a single click; run the main script `auto_processing.py` to automatically complete surface identification, INP file correction, and parameter embedding, taking approximately 3-5 minutes; submit the calculation; run the `post_process.py` script to automatically extract results, calculate the J-integral value, and output the VTK file, taking approximately 2 minutes. Total manual intervention time: less than 10 minutes, requiring only a few script runs.

[0121] Taking a multi-connected complex geometry as an example, we simulate the mechanical behavior of a porous nanofoam material (containing hundreds of randomly distributed, interconnected pores). The surface effect of the inner surface of each pore needs to be considered.

[0122] Existing methods using approximate layers are nearly impossible to implement because it is impossible to uniformly generate high-quality, thick-coated meshes on such complex inner and outer surfaces. Manually selecting surfaces is operationally infeasible; manually selecting all the inner surfaces of hundreds of holes would take days and cannot guarantee accuracy. This invention predefines a set during the modeling phase, and the system automatically parses all surface elements within the set, successfully completing the integrated calculation of surface effects for this complex model containing 589 inner surfaces, obtaining a reasonable stress distribution and overall equivalent stiffness.

[0123] In scientific research, the reproducibility of methods is crucial. Existing technologies, based on self-written code or highly manual operations, often have unclear implementation details (such as surface selection and parameter transmission), making it difficult for other researchers to reproduce the results and hindering academic exchange and technological development. The technical solution provided by this invention is verifiable. The core theoretical formula of UEL is the publicly available Gurtin-Murdoch theory, which any researcher can use to verify the correctness of the system's implementation. Research using this system exhibits significantly higher reproducibility and verifiability than traditional methods, which is beneficial for advancing research in this field. The method and system provided by this invention are particularly suitable for the mechanical reliability analysis of lithium battery electrode materials, effectively predicting the fracture risk of nanoparticles during charging and discharging.

[0124] It should be noted that, in the embodiments of the present invention, if the above-mentioned automated finite element simulation method for the surface effects of micro-nano structures is implemented in the form of software functional modules and sold or used as an independent product, it can also be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the embodiments of the present invention, or the part that contributes to related technologies, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause an electronic device to execute all or part of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), magnetic disks, or optical disks. Thus, the embodiments of the present invention are not limited to any specific hardware and software combination.

[0125] Correspondingly, embodiments of this application provide a computer-readable storage medium storing a computer program thereon. When executed by a processor, this computer program implements the steps in the automated finite element simulation method for the surface effects of micro / nano structures described in any of the above embodiments. Correspondingly, embodiments of this application also provide a computer program product, which, when executed by a processor of an electronic device, is used to implement the steps in the automated finite element simulation method for the surface effects of micro / nano structures described in any of the above embodiments.

[0126] It should be noted that the descriptions of the storage medium embodiments above are similar to those of the method embodiments above, and have similar beneficial effects. For technical details not disclosed in the storage medium embodiments of this application, please refer to the descriptions of the method embodiments of this application for understanding.

[0127] It should be understood that the phrase "one embodiment" or "an embodiment" throughout the specification means that a specific feature, structure, or characteristic related to the embodiment is included in at least one embodiment of the invention. Therefore, "in one embodiment" or "in an embodiment" appearing throughout the specification does not necessarily refer to the same embodiment. Furthermore, these specific features, structures, or characteristics can be combined in any suitable manner in one or more embodiments. It should be understood that in the various embodiments of the invention, the sequence numbers of the above-described processes do not imply a sequential order of execution; the execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the invention. The sequence numbers of the above-described embodiments of the invention are merely descriptive and do not represent the superiority or inferiority of the embodiments.

[0128] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0129] In the several embodiments provided in this application, it should be understood that the disclosed systems and methods can be implemented in other ways. The system embodiments described above are merely illustrative. For example, the division of modules is only a logical functional division, and in actual implementation, there may be other division methods, such as: multiple modules or components can be combined, or integrated into another system, or some features can be ignored or not executed. In addition, the coupling, direct coupling, or communication connection between the various components shown or discussed can be through some interfaces, and the indirect coupling or communication connection between modules or units can be electrical, mechanical, or other forms.

[0130] Alternatively, if the integrated modules described above are implemented as software functional modules and sold or used as independent products, they can also be stored in a computer-readable storage medium. Based on this understanding, the technical solutions of the embodiments of this application, or the parts that contribute to related technologies, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause the device automatic test line to execute all or part of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, ROMs, magnetic disks, or optical disks.

[0131] The methods disclosed in the several method embodiments provided in this application can be arbitrarily combined to obtain new method embodiments without conflict. The features disclosed in the several method embodiments provided in this application can be arbitrarily combined to obtain new method embodiments without conflict.

[0132] The above description is merely an embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. An automated finite element simulation method for surface effects of micro / nano structures, characterized in that, The method includes: In geometric modeling software, a geometric model of the micro / nano structure to be analyzed is constructed, and parametric modeling and mesh generation are performed to generate an initial finite element input file containing matrix elements and node information; Based on the mesh topology of the matrix element, surface elements are automatically identified and labeled; where surface elements are the boundary edges or boundary surfaces of the matrix elements. Based on the Gurtin-Murdoch surface elasticity theory, the surface unit is modeled as a zero-thickness elastic film; The initial finite element input file is modified to generate a UEL-compatible enhanced input file; The UEL subroutine of the finite element software reads the enhanced input file and calculates the matrix element stiffness matrix and the surface additional stiffness matrix respectively. The matrix element stiffness matrix is ​​calculated based on the type of matrix element and the constitutive relation of the matrix material, and the surface additional stiffness matrix is ​​constructed based on the type of surface element and the constitutive relation based on the Gurtin-Murdoch theory. The surface-added stiffness matrix is ​​superimposed on the matrix element stiffness matrix to obtain the total stiffness matrix; Based on the total stiffness matrix, assemble the overall stiffness matrix and perform finite element calculations to obtain the displacement field and stress field.

2. The method according to claim 1, characterized in that, The matrix-based mesh topology automatically identifies and labels surface units, including: For simple, regular shapes, surface units are automatically identified through geometric features; these geometric features include the outward normal direction and / or the radius of curvature. For complex simply connected models, a node-shared element counting algorithm is used to identify boundary nodes that belong to only one volume element in order to determine surface elements; For complex multi-connected structures or assemblies, the surface elements are directly resolved using the named set-assisted method through predefined set names.

3. The method according to claim 1, characterized in that, The process of refining the initial finite element input file to generate a UEL-compatible enhanced input file includes: The initial finite element input file is parsed using regular expressions to identify the standard element type definition. Replace the standard cell type with the UEL cell type identifier; Insert user-defined parameters into the element attribute definition section to generate a UEL-compatible enhanced input file; the user-defined parameters include surface elastic constants, surface residual stress, and initial surface energy.

4. The method according to claim 1, characterized in that, The surface additional stiffness matrix is ​​calculated using the following procedure: If the current element is identified as a surface element, then for each marked boundary edge or boundary face of the current element, perform the following calculations: Extract the dimension-reduced subset nodes corresponding to the boundary edges or boundary surfaces; Establish a dimension-reduced local coordinate system and construct a surface strain-displacement matrix that only relates the displacement and surface strain of the nodes in the dimension-reduced subset; Based on the Gurtin-Murdoch surface constitutive relation, the surface elasticity matrix is ​​constructed; The surface additional stiffness matrix is ​​obtained by performing the following numerical integration calculation on the reduced-dimensional geometric domain defined by the boundary edge or boundary surface: In the formula, To add a stiffness matrix to the surface of a specific boundary edge or boundary surface; This is the surface strain-displacement matrix; The surface elasticity matrix is ​​composed of the surface elastic constants and surface residual stresses. Decide; It is the geometric domain of the boundary edge or boundary surface.

5. The method according to any one of claims 1 to 4, characterized in that, The material matrices of the matrix element stiffness matrix and the surface additional stiffness matrix are field variable functions. The UEL subroutine receives field variables through the state variable interface, where field variables include temperature, lithium ion concentration, and electric potential, in order to realize thermo-mechanical, lithium ion diffusion-stress, or electro-mechanical coupling analysis.

6. An automated finite element simulation system for surface effects of micro / nano structures, characterized in that, include: The preprocessing module is configured to receive mesh data from geometric modeling software and generate a preliminary input file containing volume elements and node information; Automatically identify and label surface elements to generate UEL-compatible enhanced input files; The solver module is configured to call the finite element software kernel to run the UEL subroutine, which implements the stiffness matrix calculation, superposition and solution process as described in claim 1, and writes the calculation results into the result database; The post-processing module is configured to extract nodal displacement and stress field data from the results database and calculate fracture mechanics parameters according to user requirements.

7. The system according to claim 6, characterized in that, The post-processing module includes: J-integral calculation unit is configured to automatically calculate fracture driving force based on crack tip loop integral method; The VTK format conversion unit is configured to convert ODB format result files into VTK format, which can be read by open-source visualization software.

8. The system according to claim 6, characterized in that, The preprocessing module is also configured to process multi-connected complex geometric structures, and to define the inner surface of the porous structure as a surface set through a single region selection, and to automatically identify all surface units of the inner surface.

9. The system according to any one of claims 6 to 8, characterized in that, The finite element software is Abaqus, and the UEL subroutine is written in Fortran and called through the Abaqus / Standard or Abaqus / Explicit solver.

10. A method for predicting the fracture behavior of lithium-ion battery nanoelectrode particles, characterized in that, include: A geometric model of electrode particles containing pre-existing cracks is established, with particle size at the nanometer scale; wherein the pre-existing cracks are located on the particle surface or inside the particle. The diffusion-induced stress field considering surface effects is calculated using the method of any one of claims 1 to 5 or the system of any one of claims 6 to 9, wherein the surface effects are introduced by superposition of surface-added stiffness matrices implemented by the UEL subroutine. The J integral value at the crack tip is calculated based on the stress field, and the degree of surface effect on fracture suppression is evaluated. By comparing the J integral values ​​under two working conditions, considering surface effects and not considering surface effects, when the J integral value considering surface effects decreases by more than a preset threshold, it is determined that surface effects significantly inhibit crack propagation, and the crack resistance performance of particles in charge-discharge cycles is predicted.

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