Comparison of different finite deformation inelastic damage models within multiplicative elastoplasticity for ductile materials

Abstract

The new contribution of this study is to formulate two wellknown isotropic elastoplastic damage concepts for ductile materials in the framework of ‘geometrically exact’ finite multiplicative elastoplasticity. For the model originally proposed by Lemaitre the damage evolution follows from a dissipation potential and the hypothesis of general associativity. In contrast, the Gurson model takes into account the balance of mass separately to formulate damage evolution. In this contribution both formulations are based on logarithmic Hencky strains leading to a simple application of the so called ‘exponential map’ stress integrator which is the algorithmic counterpart of the multiplicative elastoplastic formulation adopted. Special emphasis is directed towards the numerical implementation of these models within the framework of finite element analysis of inelastic boundary value problems. To compare the results of numerical computations several standard examples within finite elastoplasticity are analysed with both damage models and the results are contrasted to the outcome of an analysis with the classical v. Mises model. thereby, the dramatic influence of damage on the behaviour within necking and localization computations is highlighted. The different behaviour of the two models considered within compression dominated problems is appreciated.