Numerical simulation for T-stress for complex multiple branching and intersecting cracks based on continuous-discontinuous cellular automaton

In this work, a discontinuous cellular automaton combined non-singular stress term of T-stress is developed for multiple cracks problems. In order to reflect the influence both singular term of SIFs and nonsingular constant term of T-stress, a new enriched shape function based on crack tip near-field asymptotic functions is proposed, which can simultaneously describe singular and non-singular stress around crack tip. Aimed at non-convergence and internal discontinuity for blending cells, a modified formulation for mathematic description of cellular automaton approximation is employed, in which a mixed uniformly varying function is employed. Besides, mathematic descriptions for strong discontinuities of intersecting and branching cracks are developed in this paper, both opening crack surfaces and close crack surfaces are given in detail respectively. Finally, a comprehensive cellular automaton model considering T-stress is constructed, which includes cell, neighborhood, updating rules and so on. Some numerical examples are given to illustrate that the present method is efficient and accurate, and it can be widely used for some practical engineering.