Numerical simulation of shear band formation in elastic material by energy relaxation

Following up the previous work, 1], a new approach to the problem of shear localization is proposed, based on energy minimization principles associated with micro-structure developments. In this approach, two different material models are included. They represent the behaviour of material at very small strain and very large strain, respectively. Herein, shear bands are treated as the micro-shearing of rank-one laminates. The thickness of a shear band represented by its volume fraction is assumed to tend to zero while the strain inside the shear band tends to infinity. 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 energy relaxation is demonstrated through numerical simulation of a tension test under plane strain conditions. The presented numerical simulation shows that there is no mesh-dependence. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)