This paper presents a computationally effective approach for crack propagation under mechanical and thermal loads based on an adaptive mesh refinement (AMR) approach tailored for our recently developed enhanced local damage model. The mesh-dependent issue encountered in the classical local theories is effectively mitigated by incorporation of fracture energy and element characteristic length into the damage evolution function. Our previous research has demonstrated that being equipped by a novel equivalent strain derived from the bi-energy norm concept and a new damage criterion recently proposed by Mazars et al., the model provides results comparable to the reference experimental data as well as other numerical models based on non-local/gradient damage and phase field method. In the framework of computational efficiency using finite elements, we significantly enhance the performance of our enhanced local model by considering adaptive mesh refinement (AMR). The finite element mesh is locally refined in the damaged zone, and the mesh refinement is conducted on-the-fly during the analysis. For that purpose, the damage parameter whose information is stored at integration points is selected as an indicator to mark whether an element should be refined or not after every loading step. For quadrilateral element mesh, a quad-tree technique is utilized, meaning that each marked element is further divided into four smaller quadrilateral elements. The so-called hanging nodes appear during the process, and the elements are thus treated as n-gons and are constructed by the Laplace shape functions, instead of the usual Lagranges shape functions. To show the accuracy and effectiveness of the proposed scheme, several numerical examples involving homogeneous and heterogeneous materials are studied. In these examples, the damage is induced either by only mechanical loads or by both mechanical and thermal loads.

中文翻译：

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一种用于裂纹扩展的自适应网格细化算法，具有增强的热-机械局部损伤模型


本文提出了一种计算有效的机械和热载荷下裂纹扩展的方法，该方法基于为我们最近开发的增强型局部损伤模型量身定制的自适应网格细化 （AMR） 方法。通过将断裂能量和单元特征长度纳入损伤演化函数，可以有效地缓解经典局部理论中遇到的网格依赖性问题。我们以前的研究表明，该模型配备了源自双能范数概念的新型等效应变和 Mazars 等人最近提出的新损伤准则，该模型提供的结果与参考实验数据以及其他基于非局部/梯度损伤和相场法的数值模型相当。在使用有限元的计算效率框架中，我们通过考虑自适应网格细化 （AMR） 显著提高了增强型局部模型的性能。有限元网格在受损区域进行局部细化，网格细化在分析过程中动态进行。为此，选择其信息存储在积分点的损伤参数作为指标，以标记在每个加载步骤后是否应精修元素。对于四边形单元网格，使用了四边形树技术，这意味着每个标记的单元被进一步划分为四个较小的四边形单元。在此过程中会出现所谓的悬挂节点，因此这些单元被视为 n 边形，由拉普拉斯形函数构造，而不是通常的拉格朗日形函数。 为了证明所提出的方案的准确性和有效性，研究了几个涉及均质和非均相材料的数值示例。在这些示例中，损坏要么仅由机械载荷引起，要么由机械载荷和热载荷同时引起。