三维脆性断裂：配位力驱动的裂纹扩展
Three-dimensional brittle fracture: configurational-force-driven crack propagation
AI总结：
本文提出了一种三维脆性断裂的计算框架，基于配位力学理论确定裂纹起裂与扩展方向，通过局部网格优化提升精度与鲁棒性，并采用弧长控制技术追踪耗散载荷路径。
摘要：
本文提出了一种用于三维固体准静态脆性断裂的计算框架。该框架基于配位力学理论，确定裂纹起裂与扩展方向，与格里菲斯理论一致。通过限制裂纹到单元面并适应网格以对齐预测裂纹方向，利用有限元网格解决裂纹扩展问题。开发了局部网格优化程序以提高网格质量，从而提升精度和求解鲁棒性，并消除初始网格对裂纹扩展方向的影响。推导了弧长控制技术以追踪耗散载荷路径。实现了分层hp细化策略以提高位移和裂纹几何的近似精度。通过两个数值示例验证了该建模方法的性能，这些示例定性地展示了其预测复杂裂纹路径的能力。所有问题均为三维问题，包括一个扭转问题，其结果准确预测了双曲面裂纹。
英文摘要：
This paper presents a computational framework for quasi-static brittle fracture in three dimensional solids. The paper set outs the theoretical basis for determining the initiation and direction of propagating cracks based on the concept of configurational mechanics, consistent with Griffith's theory. Resolution of the propagating crack by the finite element mesh is achieved by restricting cracks to element faces and adapting the mesh to align it with the predicted crack direction. A local mesh improvement procedure is developed to maximise mesh quality in order to improve both accuracy and solution robustness and to remove the influence of the initial mesh on the direction of propagating cracks. An arc-length control technique is derived to enable the dissipative load path to be traced. A hierarchical hp-refinement strategy is implemented in order to improve both the approximation of displacements and crack geometry. The performance of this modelling approach is demonstrated on two numerical examples that qualitatively illustrate its ability to predict complex crack paths. All problems are three-dimensional, including a torsion problem that results in the accurate prediction of a doubly-curved crack.
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