A nonlinear semi-concurrent multiscale method for fractures

A nonlinear semi-concurrent multiscale method for the modelling of crack propagation evolving from micro-structure for non-linear material behaviour is developed. The present method is based on an asymptotic expansion homogenization combined with the semi-concurrent finite element modelling approach. A modified periodic boundary conditions and sphere grains generation procedure are devised for non-linear material model with post-failure stage. The statistical convergence of the microscale RVE model regarding the RVE characteristic size and composition material distributions is studied. It was found that convergence of the macroscopic material properties is determined by the reproduction of the periodic geometry of the RVEs. The present method is validated by the experimental results for brittle material. The location and sequence of crack initiation captured by the present method is compared with the experimental data. The experimental phenomenon of the wing-cracks initiation location and crack branching pattern are successfully captured by the present method. The results show that the present method is an effective for the modelling of dynamic damage evolution for brittle materials.