Finite element simulation of strain localization in inelastic solids by energy relaxation

Abstract

A new approach for the treatment of strain localization in inelastic material is proposed. It is based on energy minimization principles associated with micro-structure developments. Shear bands are treated as micro-shearing of rank-one laminates.  It is assumed that the thickness of the shear band represented by its volume fraction tends to zero, and the energy inside the shear band is a function of the norm of the strain field. The existence of shear bands in the structure leads to an ill-posed problem which can be solved by means of energy relaxation. The performance of the proposed concept is demonstrated through numerical simulation of tension test under plane strain conditions. Numerical results show that mesh sensitivity can be completely removed.
Keywords:  Energy relaxation, shear band, strain localization.