An adaptive mesh refinement algorithm for crack propagation with an enhanced thermal–mechanical local damage model

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.