Abstract A continuous-discontinuous cellular automaton method (CDCA) is developed for dynamic crack propagation. First, a separated time integral scheme is built, in which time difference is divided into two separated time steps: one balances the change of the geometric discretization caused by crack growing, and the other balances the dynamic loading. Second, an adaptive energy conservation strategy is proposed for the CDCA that includes the change in the degree of nodal freedom for the crack tip element, and a new strategy for the inheritance of the degrees of nodal freedom is proposed. This method retains the enrichment scheme for the discontinuity, and the Shepard interpolation method is employed to transform the variables’ values, so as to keeps the energy conservation caused by crack tip location change. Then, the enriched degree of nodal freedom values are easily passed from the crack tip enrichment to the penetrated enrichment and crack tip local coordinate system changing with crack growing. Third, a dynamic crack propagation criterion is developed, which can be used for tensile fractures and compression shear fractures. Based on those theories, a new cellular automaton model is built for dynamic crack propagation. Compared to the extended finite element method (XFEM), the calculation efficiency has been greatly improved, and several numerical examples are given to illustrate accuracy and efficiency of the present method.

中文翻译：

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稳定方案与连续-不连续元胞自动机相结合的动态裂纹扩展分析

摘要 开发了一种用于动态裂纹扩展的连续-不连续元胞自动机方法（CDCA）。首先，建立了分离时间积分方案，将时间差分为两个分离的时间步长：一个平衡裂纹扩展引起的几何离散化的变化，另一个平衡动态载荷。其次，提出了一种包含裂纹尖端单元节点自由度变化的CDCA自适应节能策略，并提出了一种新的节点自由度继承策略。该方法保留了不连续点的富集方案，采用Shepard插值法对变量值进行变换，以保持裂纹尖端位置变化引起的能量守恒。然后，丰富的节点自由度值很容易从裂纹尖端富集传递到渗透富集和裂纹尖端局部坐标系随着裂纹的增长而变化。第三，开发了动态裂纹扩展准则，可用于拉伸断裂和压缩剪切断裂。基于这些理论，为动态裂纹扩展建立了一个新的元胞自动机模型。与扩展有限元法（XFEM）相比，计算效率有了很大的提高，并给出了几个数值例子来说明本方法的准确性和效率。可用于拉伸断裂和压缩剪切断裂。基于这些理论，为动态裂纹扩展建立了一个新的元胞自动机模型。与扩展有限元法（XFEM）相比，计算效率有了很大的提高，并给出了几个数值例子来说明本方法的准确性和效率。可用于拉伸断裂和压缩剪切断裂。基于这些理论，为动态裂纹扩展建立了一个新的元胞自动机模型。与扩展有限元法（XFEM）相比，计算效率有了很大的提高，并给出了几个数值例子来说明本方法的准确性和效率。