In this article, a novel adaptive mesh refinement scheme based on trimmed hexahedral (TH) meshes is proposed to simulate phase‐field fracture in brittle materials. A regular hexahedral background mesh is adaptively refined using a balanced octree algorithm to resolve the length scale in phase‐field fracture models. Adaptively refined TH meshes are created by cutting octree background meshes with the boundary of an analysis domain. A multithreshold criterion for mesh refinement is proposed to accurately capture the evolution of the damage phase field. Shape functions for transition TH elements are developed to satisfy the compatibility across the interelement boundaries between TH elements with different refinement levels. Numerical results show that the present scheme is very efficient and effective to trace arbitrary evolving phase‐field cracks in three dimensions.

中文翻译：

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用修整的六面体网格模拟相场断裂的新型自适应网格细化方案

在本文中，提出了一种基于修整六面体（TH）网格的新型自适应网格细化方案，以模拟脆性材料的相场断裂。使用平衡八叉树算法自适应调整规则的六面体背景网格，以解决相场裂缝模型中的长度尺度。通过使用分析域的边界切割八叉树背景网格来创建自适应精制的TH网格。提出了一种用于网格细化的多阈值准则，以准确捕获损伤相场的演变。开发了过渡TH元素的形状函数，以满足具有不同细化级别的TH元素之间的元素边界的兼容性。