Numerical analysis of shear bands in solids by means of computational homogenization

A novel fully three–dimensional framework for the numerical analysis of shear bands in solids undergoing large deformations is presented. The effect of micro shear bands on the macroscopic material response is computed by means of a homogenization strategy. More precisely, a strain–driven approach which complies well with displacement–driven finite element formulations is adopted. The proposed implementation is based on periodic boundary conditions for the micro–scale. Details about the implementation of the resulting constraints into a three–dimensional framework are discussed. The shear bands occurring at the micro–scale are modeled by a cohesive zone law, i.e., the tangential component of the traction vector governs the relative shear sliding displacement. This law is embedded into a Strong Discontinuity Approach (SDA). To account for realistic sliding modes, multiple shear bands are allowed to form and propagate in each finite element. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)