自适应网格粗化用于高效相场断裂模拟

中文摘要 AI 辅助

相场模型为模拟断裂成核与扩展提供了一个通用框架，无需显式追踪裂纹。其主要计算挑战在于需要用足够细的有限元网格来解析一个较小的正则化长度。这一要求可能使均匀网格模拟变得极其昂贵，尤其是对于三维问题、涉及分布式裂纹成核的问题以及软性近不可压缩材料。自适应网格细化提供了一种降低此成本的天然手段，但现有方法往往依赖启发式细化指示器，主要针对含有预先存在裂纹的问题设计，并且随着裂纹尺寸增长，会保留越来越大的细化区域。本工作提出了一种自适应网格粗化框架以及用于相场断裂的自适应网格细化。粗化策略将裂纹尾迹中的断裂区域替换为一条粗裂纹带，该裂纹带保留了裂纹的基本力学行为，从而使得仅在扩展裂纹尖端附近的小区域内需要细化网格。该方法引入了一个基于物理的细化指示器，该指示器源自材料强度面的违反，这是断裂演化的必要条件。因此，该指示器能够稳健地识别裂纹成核或扩展即将发生的区域，并可应用于任意材料、几何形状和加载条件。该框架在FEniCSx内并行实现；配套的有限元代码已公开。其通用性和显著的计算优势通过涉及准静态和动态加载下软材料和硬材料中裂纹扩展与成核以及热力耦合断裂的基准问题得到了验证。

英文摘要

Phase-field models provide a versatile framework for simulating fracture nucleation and propagation without explicit crack tracking. Their principal computational challenge is the need to resolve a small regularization length with a sufficiently fine finite element mesh. This requirement can render uniform-mesh simulations prohibitively expensive, particularly for three-dimensional problems, problems involving distributed crack nucleation, and soft nearly incompressible materials. Adaptive mesh refinement offers a natural means of reducing this cost, but existing approaches often rely on heuristic refinement indicators, are primarily designed for problems containing pre-existing cracks, and retain increasingly large refined regions as cracks grow in size. This work presents an adaptive mesh coarsening framework along with adaptive mesh refinement for phase-field fracture. The coarsening strategy replaces the fractured region in the crack wake with a coarse crack band that preserves the essential mechanical behavior of a crack, making it necessary to have a refined mesh only in a small region near the tip of the growing crack. The method introduces a physics-based refinement indicator derived from the violation of the material strength surface, which is a necessary condition for fracture evolution. The indicator therefore robustly identifies regions where crack nucleation or propagation is imminent and can be applied across arbitrary materials, geometries, and loading conditions. The framework is implemented in parallel within FEniCSx; the supporting finite element codes are made available. Its generality and substantial computational benefit are demonstrated through benchmark problems involving crack propagation and nucleation under quasi-static and dynamic loading, for soft and hard materials, and for thermomechanical fracture.

发表机构

• Georgia Institute of Technology（佐治亚理工学院）
• Vanderbilt University（范德堡大学）

机构由 AI 辅助整理，请以论文原文为准。