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

A theorical framework for the analysis of localized failure in hyperealstic material is presented based on the energy minimization principles associated with micro-structure developments. The theory is predicated upon the assumptions that the thickness of shear band represented by its volume fraction tends to zero as well as that the energy inside shear band is a function of the norm of the deformation gradient. Shear bands are treated as laminates of first order. The existence of shear bands in the structure leads to an ill-posed problem which can be solved by means of energy relaxation. An application of the proposed formulation to Neo-Hookean material is presented. Numerical simulation is shown in order to evaluate the performance of the proposed energy relaxation. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)