A multi-scale rate dependent crack model for quasi-brittle heterogeneous materials

A multi-scale numerical approach for modeling cracking in heterogeneous quasi-brittle materials under dynamic loading is presented. In the model, a discontinuous crack model is used at macro-scale to simulate fracture and a gradient-enhanced damage model has been used at meso-scale to simulate diffuse damage. The traction-separation law for the cohesive zone model at macro-scale is obtained from the meso-scale through the discontinuous computational homogenization method. An implicit time integration is used to solve the dynamic problem at the macro-scale while the meso-scale model is solved as a quasi-static problem. The effect of crack opening rate on the macro cohesive law is taken into account by relating the material properties of the meso-scale model to the macro crack opening rate. The objectivity of the model response with respect to the representative volume element size is demonstrated for wave propagation problems. The model is verified by comparison with a direct numerical simulation.