An enhanced continuous–discontinuous multiscale method for modeling mode-I cohesive failure in random heterogeneous quasi-brittle materials

In this manuscript we present an extension of the computational homogenization scheme for cohesive crack modeling of heterogeneous quasi-brittle materials which has recently been proposed by the authors. The proposed continuous–discontinuous multiscale method is a combination of the standard bulk computational homogenization theory and the recently developed discontinuous homogenization scheme to model the transition of microscopic diffusive damage to macro-cracks for tensile cracking problems. A new evolutionary boundary condition for the microscopic samples is presented. Numerical examples including verification against a direct numerical simulation and crack propagation simulations are given to demonstrate the capabilities of the method. The proposed homogenization scheme allows to define a representative volume for random heterogeneous quasi-brittle materials that show strain localization.