The pathological mesh dependence by numerical simulations of localization in time-independent elastic-plastic materials is avoided by using incremental nonlinearity with constitutive rate equations derivable from a velocity-gradient potential. The author considers a yield surface vertex in a transitional regime of strain directions, so that post-critical deformation patterns may be obtained as necking in sheets and shear band formation under plane-strain compression. The Petryk-Thermann computational scheme and Hill’s stationarity principle are employed to minimize the velocity functional together with the total energy increment. This allows to predict plane bands of indeterminate width but with determined volume fractions. The paper includes the constitutive frame of discretized plasticity with bifurcation approach based on energy criterion, and also contains the necking analysis in stretched shear bands under plane strain compression. Different models, principles and governing criterion are illustrated by many diagrams. The results of the paper can be useful for a thorough investigation of material instability.
For the entire collection see [Zbl 0960.00063].