中文摘要：

为在易碎的材料为多重裂缝的生长和结合建模的连续不连续的细胞的自动机的一个方法被介绍。水平设置了追踪任意的断绝的方法使用，和计算格子独立于断绝并且不重新协调被要求，裂缝成长。基于 Griffith 破裂理论和 Mohr-Coulumb 标准，为在易碎的材料的多重裂缝生长的一个混合破裂标准被建议。方法对待多重裂缝，和连接标准和结合标准的连接和结合因为易碎的材料也被给。而且，以便为裂缝连接和结合在水平集合近似克服追踪的错误，寻找算法的两分被建议。介绍了上述理论进连续不连续的细胞的自动机，现在的方法能被用于在易碎的材料，和仅仅细胞僵硬解决多重裂缝生长被需要，没有装配全球僵硬被需要。一些数字例子被给证明现在的方法为裂缝连接，结合和过滤有效、精确问题。

英文摘要：

A method of continuous-discontinuous cellular automaton for modeling the growth and coalescence of multiple cracks in brittle material is presented. The method uses the level set to track arbitrary discontinuities, and calculation grids are independent of the discontinuities and no remeshing are required with the crack growing. Based on Grif- fith fracture theory and Mohr-Coulumb criterion, a mixed fracture criterion for multiple cracks growth in brittle mate- rial is proposed. The method treats the junction and coales- cence of multiple cracks, and junction criterion and coales- cence criterion for brittle material are given, too. Besides, in order to overcome the tracking error in the level set ap- proximation for crack junction and coalescence, a dichotomy searching algorithm is proposed. Introduced the above the- ories into continuous-discontinuous cellular automaton, the present method can be applied to solving multiple crack growth in brittle material, and only cell stiffness is needed and no assembled global stiffness is needed. Some numerical examples are given to shown that the present method is efficient and accurate for crack junction, coalescence and percolation problems.