A continuous-discontinuous cellular automaton method for cracks growth and coalescence in brittle material

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 Griffith fracture theory and Mohr–Coulumb criterion,a mixed fracture criterion for multiple cracks growth in brittle material is proposed.The method treats the junction and coalescence of multiple cracks,and junction criterion and coalescence criterion for brittle material are given,too.Besides,in order to overcome the tracking error in the level set approximation for crack junction and coalescence,a dichotomy searching algorithm is proposed.Introduced the above theories into continuous-discontinuous cellular automaton,the present method can be applied to solving multiple crack growth in brittle material,and only cell stifness is needed and no assembled global stifness is needed.Some numerical examples are given to shown that the present method is efcient and accurate for crack junction,coalescence and percolation problems.