Computer Methods in Applied Mechanics and Engineering最新文献

Fatigue-constrained topology optimization method for orthotropic materials based on an expanded Tsai-Hill criterion 基于扩展蔡-希尔准则的正交材料疲劳约束拓扑优化方法

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-11-16 DOI: 10.1016/j.cma.2024.117542

Hongling Ye, Yang Xiao, Yongjia Dong, Jialin Xie

Fatigue-constrained topology optimization (FCTO) is a currently research hotspot, and its fatigue constraints have material property dependency, highly nonlinear, and local features, which lead to challenges for the algorithm stability, computational efficiency, and different material application of FCTO. This research provides a FCTO method for structures subjected to variable-amplitude fatigue loading, incorporating the potential orthotropic behavior of materials. Firstly, a fatigue failure function derived from the constitutive model of orthotropic materials and the polynomial form in the Tsai-Hill criterion is proposed to predict multiaxial fatigue failure with a given loading spectrum. Secondly, a FCTO model minimizing structural weight is established based on the independent continuous mapping (ICM) method and constrained by a filtered, scaled, and aggregated fatigue failure function to enhance stability and convergence speed. Thirdly, the sensitivities of objective and constraint in the FCTO model are analyzed, and the optimal model is solved using convolutional filters and the globally convergent method of moving asymptotes (GCMMA) to generate manufacturable design. Finally, numerical examples demonstrate the feasibility of the method for 2D and 3D structures with varying material properties, load spectrums, and design domains. The developed method aims to facilitate the creation of lightweight designs capable of withstanding fatigue loads and to provide a framework and references for the advancement of integrated material-structure-performance designs.

疲劳约束拓扑优化（Fatigue-constrained topology optimization，FCTO）是当前的研究热点，其疲劳约束具有材料属性依赖性、高度非线性和局部性等特点，给FCTO的算法稳定性、计算效率和不同材料的应用带来了挑战。本研究结合材料潜在的各向同性行为，为承受变幅疲劳载荷的结构提供了一种 FCTO 方法。首先，根据正交材料的构成模型和蔡-希尔准则中的多项式形式，提出了一种疲劳破坏函数，用于预测给定加载谱下的多轴疲劳破坏。其次，基于独立连续映射（ICM）方法建立了结构重量最小化的 FCTO 模型，并通过过滤、缩放和聚合疲劳破坏函数进行约束，以提高稳定性和收敛速度。第三，分析了 FCTO 模型中目标和约束的敏感性，并使用卷积滤波器和移动渐近线全局收敛法（GCMMA）求解最优模型，以生成可制造的设计。最后，数值示例证明了该方法对于具有不同材料属性、载荷谱和设计域的二维和三维结构的可行性。所开发的方法旨在促进创建能够承受疲劳载荷的轻质设计，并为材料-结构-性能综合设计的进步提供框架和参考。

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引用次数: 0

Modelling of thermo-mechanical coupling effects in rock masses using an enriched nodal-based continuous-discontinuous deformation analysis method 利用基于丰富节点的连续-非连续变形分析方法模拟岩体的热-机械耦合效应

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-11-16 DOI: 10.1016/j.cma.2024.117543

Yang Xia , Yongtao Yang , Hong Zheng , Shuilin Wang

In this paper, the nodal-based continuous-discontinuous deformation analysis method (NCDDAM) is enriched to simulate the thermo-mechanical coupling effects in rock masses. A distance-based contact potential algorithm is first incorporated into NCDDAM to avoid the dependency of element shape and size on the calculation of contact force between different blocks. Then, three types of heat conduction models, which can deal with heat conduction in continuum and discontinuum, are incorporated into NCDDAM to simulate the heat conduction effects of rock masses. Finally, a two-way staggered algorithm is adopted in the context of NCDDAM to simulate the thermo-mechanical coupling effects in rock masses. Several benchmark examples are used to verify the correctness of the enriched NCDDAM in handling contact problems, heat conduction problems and thermo-mechanical coupling problems. The effects of time step size on the accuracy of NCDDAM for both thermal simulation and mechanical simulation are investigated detailly. In addition, the thermal cracking processes of rock masses for both experiment and engineering scales are simulated by the enriched NCDDAM. The numerical results indicate that the enriched NCDDAM is a powerful tool to simulate the thermo-mechanical coupling processes of rock masses.

本文丰富了基于节点的连续-非连续变形分析方法（NCDDAM），以模拟岩体的热-机械耦合效应。首先在 NCDDAM 中加入了基于距离的接触势算法，以避免元素形状和尺寸对不同岩块之间接触力计算的依赖。然后，在 NCDDAM 中加入了三种热传导模型，可处理连续和非连续热传导，以模拟岩体的热传导效应。最后，在 NCDDAM 中采用了一种双向交错算法来模拟岩体的热机械耦合效应。通过几个基准实例验证了增强型 NCDDAM 在处理接触问题、热传导问题和热机械耦合问题时的正确性。详细研究了时间步长对 NCDDAM 热模拟和机械模拟精度的影响。此外，还利用增强型 NCDDAM 模拟了实验和工程尺度的岩体热裂解过程。数值结果表明，丰富的 NCDDAM 是模拟岩体热机械耦合过程的有力工具。

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引用次数: 0

Adaptive parameter selection in nudging based data assimilation 基于推导的数据同化中的自适应参数选择

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-11-15 DOI: 10.1016/j.cma.2024.117526

Aytekin Çıbık , Rui Fang , William Layton , Farjana Siddiqua

Data assimilation combines (imperfect) knowledge of a flow’s physical laws with (noisy, time-lagged, and otherwise imperfect) observations to produce a more accurate prediction of flow statistics. Assimilation by nudging (from 1964), while non-optimal, is easy to implement and its analysis is clear and well-established. Nudging’s uniform in time accuracy has even been established under conditions on the nudging parameter

χ

and the density of observational locations,

H

, Larios et al. (2019). One remaining issue is that nudging requires the user to select a key parameter. The conditions required for this parameter, derived through á priori (worst case) analysis are severe (Section 2.1 herein) and far beyond those found to be effective in computational experience. One resolution, developed herein, is self-adaptive parameter selection. This report develops, analyzes, tests, and compares two methods of self-adaptation of nudging parameters. One combines analysis and response to local flow behavior. The other is based only on response to flow behavior. The comparison finds both are easily implemented and yields effective values of the nudging parameter much smaller than those of á priori analysis.

数据同化将（不完善的）水流物理规律知识与（噪声、时滞和其他不完善的）观测数据结合起来，以产生更准确的水流统计预测结果。推移同化法（1964 年提出）虽然不是最佳方法，但很容易实现，其分析方法也很明确和成熟。Larios 等人（2019 年）甚至已经确定，在推移参数 χ 和观测点密度 H 的条件下，推移在时间上的精度是一致的。剩下的一个问题是，推算需要用户选择一个关键参数。通过先验（最坏情况）分析得出的该参数所需的条件非常苛刻（本文第 2.1 节），远远超出了计算经验中发现的有效条件。本报告提出的一种解决方案是自适应参数选择。本报告开发、分析、测试并比较了两种自适应推移参数的方法。一种方法结合了分析和对局部流动行为的响应。另一种方法仅基于对流动行为的响应。比较结果表明，这两种方法都很容易实施，而且产生的挤压参数有效值比先验分析法小得多。

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引用次数: 0

Interpretable A-posteriori error indication for graph neural network surrogate models 图神经网络代用模型的可解释 A 后验误差指示

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-11-15 DOI: 10.1016/j.cma.2024.117509

Shivam Barwey , Hojin Kim , Romit Maulik

Data-driven surrogate modeling has surged in capability in recent years with the emergence of graph neural networks (GNNs), which can operate directly on mesh-based representations of data. The goal of this work is to introduce an interpretability enhancement procedure for GNNs, with application to unstructured mesh-based fluid dynamics modeling. Given a black-box baseline GNN model, the end result is an interpretable GNN model that isolates regions in physical space, corresponding to sub-graphs, that are intrinsically linked to the forecasting task while retaining the predictive capability of the baseline. These structures identified by the interpretable GNNs are adaptively produced in the forward pass and serve as explainable links between the baseline model architecture, the optimization goal, and known problem-specific physics. Additionally, through a regularization procedure, the interpretable GNNs can also be used to identify, during inference, graph nodes that correspond to a majority of the anticipated forecasting error, adding a novel interpretable error-tagging capability to baseline models. Demonstrations are performed using unstructured flow field data sourced from flow over a backward-facing step at high Reynolds numbers, with geometry extrapolations demonstrated for ramp and wall-mounted cube configurations.

近年来，随着图神经网络（GNN）的出现，数据驱动的代理建模能力突飞猛进。这项工作的目标是为 GNN 引入一种可解释性增强程序，并将其应用于基于非结构网格的流体动力学建模。给定一个黑盒子基线 GNN 模型，最终结果是一个可解释的 GNN 模型，它在物理空间中分离出与子图相对应的区域，这些区域与预测任务有内在联系，同时保留了基线的预测能力。这些由可解释 GNN 确定的结构会在前向传递中自适应地产生，并作为基线模型架构、优化目标和已知特定问题物理之间的可解释链接。此外，通过正则化程序，可解释 GNN 还可用于在推理过程中识别与大部分预期预测误差相对应的图节点，从而为基线模型增加了一种新颖的可解释误差标记功能。演示使用了非结构化流场数据，这些数据来自高雷诺数条件下流经后向台阶的水流，并演示了斜坡和壁装立方体配置的几何外推。

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引用次数: 0

A novel Hybrid Particle Element Method (HPEM) for large deformation analysis in solid mechanics 用于固体力学大变形分析的新型混合粒子元素法 (HPEM)

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-11-14 DOI: 10.1016/j.cma.2024.117530

Huangcheng Fang, Zhen-Yu Yin

This paper develops a novel Hybrid Particle Element Method (HPEM) to model large deformation problems in solid mechanics, combining the strengths of both mesh-based and particle approaches. In the proposed method, the computational domain is discretized into two independent components: a set of finite elements and a set of particles. The finite elements serve as a temporary tool to compute the spatial derivatives of field variables, while the particles are used for storing history variables and establishing equilibrium equations. Spatial derivatives of field variables on particles are obtained by averaging the surrounding Gauss points of finite elements with a smoothing function. When the finite element mesh becomes distorted, it can be arbitrarily adjusted or completely regenerated. No global variable mapping is required when mesh adjustment or regeneration is performed, thus avoiding irreversible interpolation errors. The proposed method is validated through six typical examples, assessing its accuracy, efficiency, and robustness. The superior performance of the proposed method is comprehensively demonstrated through comparisons with several existing numerical methods.

本文开发了一种新颖的混合粒子元素法（HPEM）来模拟固体力学中的大变形问题，该方法结合了网格法和粒子法的优点。在所提出的方法中，计算域被离散为两个独立的部分：一组有限元和一组粒子。有限元是计算场变量空间导数的临时工具，而粒子则用于存储历史变量和建立平衡方程。粒子上场变量的空间导数是通过对有限元周围的高斯点用平滑函数求平均值得到的。当有限元网格发生扭曲时，可以对其进行任意调整或完全再生。在进行网格调整或再生时，不需要全局变量映射，从而避免了不可逆的插值误差。通过六个典型实例对所提出的方法进行了验证，评估了其准确性、效率和鲁棒性。通过与几种现有数值方法的比较，全面展示了所提方法的优越性能。

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引用次数: 0

Isogeometric topology optimization (ITO) of fiber reinforced composite structures considering stress constraint and load uncertainties 考虑应力约束和载荷不确定性的纤维增强复合材料结构等几何拓扑优化 (ITO)

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-11-14 DOI: 10.1016/j.cma.2024.117537

Jin Cheng , Hengrui Fu , Zhenyu Liu , Jianrong Tan

A novel Isogeometric topology optimization (ITO) method considering stress constraint and load uncertainties is proposed for the fiber reinforced composite structures. Firstly, with the density and fiber orientations at the control points of Non-Uniform Rational B-Splines (NURBS) defined as design variables while the magnitudes and direction angles of uncertain external loads described as interval variables, the ITO model for the fiber reinforced composite structures is constructed to minimize the structural compliance under the constraints on both material usage and global failure coefficient. To accurately calculate the material properties and stress distribution within fiber reinforced composite structures, the Gauss subdivision and the Tsai-Hill criterion combined with the P-norm function are introduced. Further, the critical loads leading to the worst structural performance are determined based on the weighted Sigmoid penalty of the stress constraint for balancing the performance requirements of high stiffness and high strength. Finally, the ITO model is solved by integrating all the proposed innovations with the Method of Moving Asymptotes (MMA). The validity and effectiveness of the proposed ITO method are validated by both numerical and engineering examples.

针对纤维增强复合材料结构，提出了一种考虑应力约束和载荷不确定性的新型等距拓扑优化（ITO）方法。首先，将非均匀有理 B-样条曲线（NURBS）控制点上的密度和纤维方向定义为设计变量，同时将不确定外部载荷的大小和方向角描述为区间变量，构建了纤维增强复合材料结构的 ITO 模型，以在材料用量和全局失效系数的约束下最小化结构顺应性。为精确计算纤维增强复合材料结构的材料属性和应力分布，引入了高斯细分和蔡-希尔准则，并结合 P 正态函数。此外，为了平衡高刚度和高强度的性能要求，还根据应力约束的加权西格莫德惩罚确定了导致最差结构性能的临界载荷。最后，通过移动渐近线法（MMA）整合所有提出的创新方法，求解了 ITO 模型。通过数值和工程实例验证了所提 ITO 方法的有效性和有效性。

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引用次数: 0

Petrov–Galerkin Dynamical Low Rank Approximation: SUPG stabilisation of advection-dominated problems Petrov-Galerkin 动态低等级逼近：平流主导问题的 SUPG 稳定化

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-11-13 DOI: 10.1016/j.cma.2024.117495

Fabio Nobile, Thomas Trigo Trindade

We propose a novel framework of generalised Petrov–Galerkin Dynamical Low Rank (DLR) Approximations in the context of random PDEs. It builds on the standard Dynamical Low Rank Approximations in their Dynamically Orthogonal formulation. It allows to seamlessly build-in many standard and well-studied stabilisation techniques that can be framed as either generalised Galerkin methods, or Petrov–Galerkin methods. The framework is subsequently applied to the case of Streamline Upwind/Petrov–Galerkin (SUPG) stabilisation of advection-dominated problems with small stochastic perturbations of the transport field. The norm-stability properties of two time discretisations are analysed. Numerical experiments confirm that the stabilising properties of the SUPG method naturally carry over to the DLR framework.

我们提出了一种新颖的通用 Petrov-Galerkin 动态低阶近似法（DLR）框架，用于随机 PDEs。它建立在动态正交表述的标准动态低秩逼近基础之上。它允许无缝内置许多标准的、经过充分研究的稳定技术，这些技术可以被归类为广义 Galerkin 方法或 Petrov-Galerkin 方法。该框架随后被应用于流线上风/Petrov-Galerkin（SUPG）稳定输送场小随机扰动的平流主导问题。分析了两种时间离散的规范稳定性。数值实验证实，SUPG 方法的稳定特性可以自然地延续到 DLR 框架中。

引用次数: 0

Modelling high temperature progressive failure in C/SiC composites using a phase field model: Oxidation rate controlled process 利用相场模型模拟 C/SiC 复合材料的高温渐进失效：氧化速率控制过程

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-11-13 DOI: 10.1016/j.cma.2024.117544

Xiaofei Hu , Siyuan Tan , Huiqian Xu , Zhi Sun , Tong Wang , Lang Min , Zilong Wang , Weian Yao

High-temperature oxidation damage in C/SiC composite, alongside mechanical failure, has becoming a focal point of developing high performance motor components. However, most of existing models focus on only one field and thus can hardly to simulate a complete process. To address this, a thermodynamically consistent phase field model tailored specifically for C/SiC composites is proposed. This model offers a long-desired capability to encompass both carbon fiber oxidation in oxidation controlled stage and mechanical fracture, as well as their intricate interactions. Instead of relying on predefined fields or empirical knowledge, our model determines the oxygen field distribution and the evolution of new cracks through the differential equations rigorously, thereby providing a more accurate estimation of the location and extent of the failure process. The validity and reliability of our model have been tested through a few numerical studies. The proposed model has successfully captured the intricate characteristics of micro-crack propagation in C/SiC composites, including the saturation of cracks originating from the SiC matrix and the fracture process of carbon fibers after oxidation. As a result, our research is anticipated to be serving as an invaluable foundation for quantitative investigations into the performance of C/SiC composites, paving the way for the development of more robust and reliable high-temperature C/SiC composites.

C/SiC 复合材料的高温氧化损伤以及机械故障已成为开发高性能电机部件的一个焦点。然而，大多数现有模型只关注一个场，因此难以模拟完整的过程。为了解决这个问题，我们提出了一个专门针对 C/SiC 复合材料的热力学相场模型。该模型提供了一种人们渴望已久的能力，可同时涵盖氧化控制阶段的碳纤维氧化和机械断裂，以及它们之间错综复杂的相互作用。我们的模型不依赖于预定义场或经验知识，而是通过微分方程严格确定氧场分布和新裂纹的演化，从而更准确地估计失效过程的位置和程度。我们通过一些数值研究检验了模型的有效性和可靠性。所提出的模型成功捕捉到了 C/SiC 复合材料中微裂纹扩展的复杂特征，包括源于 SiC 基体的裂纹饱和以及氧化后碳纤维的断裂过程。因此，我们的研究有望为 C/SiC 复合材料性能的定量研究奠定宝贵的基础，为开发更坚固可靠的高温 C/SiC 复合材料铺平道路。

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引用次数: 0

Spherical harmonics-based pseudo-spectral method for quantitative analysis of symmetry breaking in wrinkling of shells with soft cores 基于球谐波的伪频谱方法，用于定量分析软核壳起皱过程中对称性破坏的情况

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-11-13 DOI: 10.1016/j.cma.2024.117529

Jan Zavodnik , Miha Brojan

A complete understanding of the wrinkling of compressed films on curved substrates remains illusive due to the limitations of both analytical and current numerical methods. The difficulties arise from the fact that the energetically minimal distribution of deformation localizations is primarily influenced by the inherent nonlinearities and that the deformation patterns on curved surfaces are additionally constrained by the topology. The combination of two factors – the need for dense meshes to mitigate the topological limitations of discretization in domains such as spheres where there is no spherically-symmetric discretizations, and the intensive search for minima in a highly non-convex energy landscape due to nonlinearity – makes existing numerical methods computationally impractical without oversimplifying assumptions to reduce computational costs or introducing artificial parameters to ensure numerical stability. To solve these issues, we have developed a novel (less) reduced version of shell theory for shells subjected to membrane loads, such as during wrinkling. It incorporates the linear contributions of the usually excluded tangential displacements in the membrane strain energy and thus retains the computational efficiency of reduced state-of-the-art methods while nearly achieving the accuracy of the full Kirchhoff–Love shell theory.

We introduce a Galerkin-type pseudo-spectral method to further reduce computational costs, prevent non-physical deformation distribution due to mesh-induced nucleation points, and avoid singularities at the poles of the sphere. The method uses spherical harmonic functions to represent functions on the surface of a sphere and is integrated into the framework of minimizing the total potential energy subject to constraints. This robust approach effectively solves the resulting non-convex potential energy problem. Our method accurately predicts the transition between deformation modes based solely on the material and geometric parameters determined in our experiments, without the need to introduce artificial parameters for numerical stability and/or additional fitting of the experimental data.

由于分析方法和当前数值方法的局限性，要完全理解曲面基底上压缩薄膜的起皱现象仍是一个未知数。产生这些困难的原因是，变形局部的能量最小分布主要受固有非线性的影响，而且曲面上的变形模式还受到拓扑结构的限制。在球形等没有球形对称离散的领域中，需要密集的网格来缓解离散的拓扑限制，而由于非线性，需要在高度非凸的能量景观中密集搜索最小值，这两个因素的结合使得现有的数值方法在计算上不切实际，而不需要过度简化假设来降低计算成本，或引入人为参数来确保数值稳定性。为了解决这些问题，我们开发了一种新型（较少）简化版壳理论，用于承受膜载荷（如起皱时）的壳。它将通常被排除在外的切向位移的线性贡献纳入膜应变能中，从而在几乎达到完整的 Kirchhoff-Love 壳理论精度的同时，保留了最先进的简化方法的计算效率。

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引用次数: 0

A multi-level adaptive mesh refinement strategy for unified phase field fracture modeling using unstructured conformal simplices 利用非结构共形简约进行统一相场断裂建模的多级自适应网格细化策略

IF 6.9 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2024-11-13 DOI: 10.1016/j.cma.2024.117514

Anshul Pandey, Sachin Kumar

The phase field model (PFM) has emerged as a popular computational framework for analyzing and simulating complex fracture problems. Despite PFM's inherent capacity to model relatively complex fracture phenomena such as nucleation, branching, deflection, etc., the computational costs involved in the analysis are quite high. Hence, a multi-level adaptive mesh refinement framework is proposed for a unified phase field model (PFCZM) to improve the computational efficiency. The proposed adaptive framework can be implemented for structured as well as unstructured meshes, making it suitable for analyzing complex fracture problems. This framework adaptively generates local mesh refinement at the discrete crack tip, based on an active element error indicator, until the damage is initiated, hence completely avoiding the pre-requisite of local mesh refinement. Further, the gradient of energy degradation and the gradient of dissipated fracture energy based error indicators are proposed to capture the fracture domain and regions ahead of the crack tip, respectively. The Newest vertex and Maubach's refinement routines are implemented as the element level-based hierarchical refinement strategies. Unlike recently proposed adaptive strategies for PFCZM involving elements with hanging nodes, the proposed adaptive framework inherently addresses the conformity and reflectivity of the discretized domain efficiently. The robustness and accuracy of the framework is checked against four benchmark fracture problems, demonstrating a significant reduction in computational costs with sufficient accuracy.

相场模型（PFM）已成为分析和模拟复杂断裂问题的常用计算框架。尽管相场模型本身能够模拟成核、分支、偏转等相对复杂的断裂现象，但分析中涉及的计算成本相当高。因此，针对统一相场模型（PFCZM）提出了一种多级自适应网格细化框架，以提高计算效率。所提出的自适应框架既可用于结构化网格，也可用于非结构化网格，因此适用于分析复杂的断裂问题。该框架根据主动元素误差指标，在离散裂纹顶端自适应生成局部网格细化，直到损伤开始，因此完全避免了局部网格细化的前提条件。此外，还提出了基于能量退化梯度和断裂能量耗散梯度的误差指标，以分别捕捉断裂域和裂纹尖端前方区域。最新顶点和毛巴赫细化例程作为基于元素级的分层细化策略得以实施。与最近提出的涉及悬挂节点元素的 PFCZM 自适应策略不同，所提出的自适应框架从本质上有效地解决了离散域的保形性和反射性问题。针对四个基准断裂问题检验了该框架的稳健性和准确性，结果表明在保证足够准确性的前提下显著降低了计算成本。

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引用次数: 0