3D multi-threaded fast adaptive continuous-discontinuous cellular automaton for crack propagation without remeshing

A three-dimensional fast adaptive continuous-discontinuous cellular automaton method for crack propagation without remeshing is proposed in the present work. Firstly, a novel crack tracking method is developed, which is combined cell space cutting, cell neighbor searching and distance values to crack surface and front, by which the search calculating and data saving are limited to a local area where cracks are located; secondly, a three-dimensional discontinuous cellular automaton is developed, which includes cell automaton model, cell state and updating rules; thirdly, a fast adaptive updating method is proposed, and an adaptive iteration scheme is developed to overcome the difficulty of the choice of the accelerating factor, by which the accelerating factor is updated with the cellular updating processes automatically, and it is finally converged to the optimal accelerating factor; finally, a multi-threaded parallel scheme for the present fast adaptive continuous-discontinuous cellular automaton is developed. By those methods, neither remeshing nor global stiffness assembling is needed for three-dimensional crack propagation, and numbers of updating steps are obviously decreased, computational effectiveness is greatly improved. Numerical examples are given to illustrate that the present method is effective, accurate, and highly convergent.