Numerical assessment, implementation and application of an extended Gurson model accounting for void size effects

Using recent results obtained by Dormieux and Kondo (2010) on strength properties of ductile nanoporous media, we aim at investigating the mechanical behaviour of this class of materials. To this end, we first assess and validate the yield criterion proposed by these authors by performing numerical limit-analyses, based on the standard finite element method including elasticity, of an elementary porous cell. This requires special care in order to account for surface stresses at the void's boundary. Then, taking advantage of the normality property for the flow rule to derive the porosity and void size evolution equations, we formulate a complete model for ductile nanoporous materials. Owing to the parametric form of the yield locus, a specific procedure is developed for the numerical implementation of the model. The problem of plastic correction of the elastic stress predictor is reduced to the resolution of two nonlinear equations. Finally, the model is applied to proportional loadings, for different stress triaxialities. The void size appears to have a strong influence on the mechanical behaviour and on the porosity evolution.