In this manuscript, we expand the conforming to interface structured adaptive mesh refinement (CISAMR) algorithm for modeling complex two-dimensional (2D) crack growth problems involving contact/friction along the crack surface and interaction between multiple cracks. The CISAMR algorithm transforms a structured mesh into a high-quality conforming mesh non-iteratively, which is an attractive feature for modeling the evolution of the crack geometry with minimal changes to the underlying mesh structure. To model such problems, the mesh structure is first adaptively refined and updated near the crack tip to form a spider-web pattern of elements for the accurate approximation of the energy release rate and thereby predicting the new crack path. In each step of the crack advance simulation, a small subset of elements in the vicinity of the crack tip is detected using a tree data structure and then deleted/regenerated to simulate the crack growth. The construction of a high-quality mesh with appropriate element aspect ratios in the algorithm allows the use of an explicit dynamic solver, which is essential to simulate the nonlinear response of the problem caused by contact forces along crack faces. Several benchmark fracture problems are presented to study the accuracy of the proposed algorithm, as well as two more complex problems to demonstrate its ability for modeling interaction of multiple growing cracks with one another and with embedded heterogeneities in the domain.

在这份手稿中，我们扩展了符合界面结构化自适应网格细化 (CISAMR) 算法，用于模拟复杂的二维 (2D) 裂纹扩展问题，包括沿裂纹表面的接触/摩擦以及多个裂纹之间的相互作用。CISAMR 算法以非迭代方式将结构化网格转换为高质量的一致网格，这是模拟裂纹几何对底层网格结构的更改最小。为了模拟此类问题，首先在裂纹尖端附近对网格结构进行自适应细化和更新，以形成元素的蜘蛛网图案，以准确近似能量释放率，从而预测新的裂纹路径。在裂纹扩展模拟的每个步骤中，使用树数据结构检测裂纹尖端附近的一小部分元素，然后删除/重新生成以模拟裂纹扩展。在算法中构建具有适当元素纵横比的高质量网格允许使用显式动态求解器，这对于模拟由沿裂纹面的接触力引起的问题的非线性响应。提出了几个基准断裂问题来研究所提出算法的准确性，以及两个更复杂的问题来证明其对多个生长裂纹相互之间以及在域中嵌入异质性的相互作用进行建模的能力。