Computational homogenization for adhesive and cohesive failure in quasi-brittle solids

A computational multiscale framework is proposed that incorporates microstructural behaviour in a macroscale discrete fracture model. Homogenization procedures are derived for both adhesive and cohesive failure on the macroscale and are implemented in an FE2-setting. The most important feature of the homogenization procedure is that it implicitly defines a traction-opening relation for the macroscale fracture model. The representativeness of the micro models is studied using a one-dimensional example, which shows that in the softening regime the proposed multiscale scheme behaves different from a bulk homogenization scheme. These results are also observed in a numerical simulation for a micro model with a periodic microstructure. Numerical simulations further demonstrate the applicability of the method.