In this paper, an adaptive phase-field scaled boundary finite element method for fracture in functionally graded material (FGM) is presented. The model accounts for spatial variation in the material and fracture properties. The quadtree decomposition is adopted for refinement, and the refinement is based on an error indicator evaluated directly from the solutions of the scaled boundary finite element method. This combination makes it a suitable choice to study fracture using the phase field method, as it reduces the mesh burden. A few standard benchmark numerical examples are solved to demonstrate the improvement in computational efficiency in terms of the number of degrees of freedom.

中文翻译：

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自适应相场标度边界有限元法在功能梯度材料中的应用

在本文中，提出了一种用于功能梯度材料（FGM）断裂的自适应相场缩放边界有限元方法。该模型考虑了材料和断裂特性的空间变化。采用四叉树分解进行细化，细化基于直接从缩放边界有限元方法的解评估的误差指标。这种组合使其成为使用相场方法研究断裂的合适选择，因为它减少了网格负担。解决了一些标准的基准数值示例，以证明在自由度数量方面计算效率的提高。