Crack propagation in quasi-brittle material such as rock and concrete is studied by a new numerical method, lattice cellular automata. Cellular automaton method is an efficient method that simulates the process of self-organization of the complex system by constructing some simple local rules. It is of the advantage of localization and parallelization. Lattice model can transform a complex triaxial problem into a simpler uniaxial problem as well as consider the heterogeneity of the materials. Lattice cellular automata integrate advantages of both cellular automata and lattice model. In this paper the importance of the study of crack propagation, fundamentals and applications of cellular automata are briefly introduced firstly. Then the cellular automata model is presented, and in order to verify lattice cellular automata, the propagation of mode-I crack in homogeneous material is studied. Results of the numerical simulation are in good accordance with the experimental results and theoretical results of classical fracture mechanics. Furthermore, based on lattice cellular automata, the crack propagation of single crack under uniaxial compression was simulated. During the crack growth the wing crack and secondary cracks were found. The simulation results were consistent with the experimental results.
Thermally induced phases in an Ising Kondo lattice model on a triangular lattice: Partial disorder and Kosterlitz-Thouless state
