Continuous-discontinuous cellular automaton method for intersecting and branching crack problems

In this work, a continuous-discontinuous cellular automaton method is developed to simulate crack propagating for multiple intersecting and branching cracks, which can deal with both shearcompression and tensile loading problems. Firstly, the local cell cutting relation and cellular neighbor information are proposed to track multiple discontinuities. Besides, mathematical descriptions of strong discontinuities for intersecting and branching cracks are developed; furthermore, in order to deal with the frictional contact of crack surfaces for intersecting and branching cracks, complex strong discontinuity frictional contact theory for intersecting and branching cracks is also proposed, in which additional enrichment functions for branching cracks are developed. Then, a fast adaptive cellular automaton updating scheme is developed for cells with and without intersecting and branching cracks. Additionally, stress intensity factors for intersecting and branching cracks are studied, and crack propagating processes for multiple intersecting and branching cracks are also discussed. Finally, numerical examples for stress intensity factor and propagation of multiple intersecting and branching cracks are given to examine the accuracy and efficiency of the proposed method.

Automated summary

In this study, a continuous-discontinuous cellular automaton method is developed to simulate the propagation of multiple intersecting and branching cracks, addressing both shear-compression and tensile loading scenarios. The method proposes a local cell cutting relation and cellular neighbor information to track multiple discontinuities, and develops mathematical descriptions as well as a frictional contact theory for intersecting and branching cracks. Furthermore, a fast adaptive cellular automaton updating scheme is devised, considering both cells with and without intersecting and branching cracks. The study also investigates stress intensity factors and the crack propagating processes for multiple intersecting and branching cracks.