Abstract The paper describes a numerical approach to represent cracking along non-pre-established directions, in 2-D structures or domains of quasi-brittle materials such as concrete or rock. The approach is developed on the basis of the FEM with zero-thickness interface elements, combined with the principles of Configurational Mechanics. Interface elements are pre-inserted along all potential crack lines in the mesh, and are equipped with a plasticity-type fracture mechanics-based constitutive model that incorporates fracture energies in mode I and IIa as constitutive parameters. Once an interface element starts cracking, an iterative re-orientation process is triggered according to the direction of configurational forces. After that process has converged, the interface orientation becomes fixed and the surrounding nodes are relocated to preserve mesh quality. The overall procedure developed has the main advantages of a fixed mesh topology (constant number of nodes) and a crack re-orientation criterion based on the minimization of the overall structural energy, as implied by the definition of configurational forces. Various examples of application are presented in which cracks get re-oriented during calculations. The results show good agreement with the crack paths known by symmetry considerations or experimental results, thus illustrating the good performance of the approach proposed.

中文翻译：

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构型力学在准脆性材料裂纹扩展中的应用

摘要 本文描述了一种数值方法来表示在二维结构或准脆性材料（如混凝土或岩石）域中沿非预先确定的方向开裂。该方法是在具有零厚度界面元素的 FEM 的基础上开发的，并结合了配置力学原理。界面元素沿网格中的所有潜在裂纹线预先插入，并配备了基于塑性型断裂力学的本构模型，该模型将模式 I 和 IIa 中的断裂能量作为本构参数。一旦界面元素开始破裂，就会根据构型力的方向触发迭代重新定向过程。在这个过程收敛之后，界面方向变得固定，周围的节点被重新定位以保持网格质量。所开发的整个程序具有固定网格拓扑（节点数恒定）和基于整体结构能量最小化的裂纹重新定向标准的主要优点，正如配置力的定义所暗示的那样。提供了各种应用示例，其中裂纹在计算过程中重新定向。结果表明与通过对称性考虑或实验结果已知的裂纹路径非常吻合，从而说明所提出方法的良好性能。正如配置力的定义所暗示的那样。提供了各种应用示例，其中裂纹在计算过程中重新定向。结果表明与通过对称性考虑或实验结果已知的裂纹路径非常吻合，从而说明所提出方法的良好性能。正如配置力的定义所暗示的那样。提供了各种应用示例，其中裂纹在计算过程中重新定向。结果表明与通过对称性考虑或实验结果已知的裂纹路径非常吻合，从而说明所提出方法的良好性能。