On the impact of the time increment on sensitivity analysis during the elastic-to-viscoplastic transition in metals

Abstract

In many constitutive models of elastoviscoplasticity, like for example overstress models, viscoplastic deformation takes place once the stress state lies outside the yield surface. In most computational implementations of such constitutive laws, the calculation of the viscoplastic deformation increment is performed in a one-step approach by applying the full nominal time increment to the rate-dependent deformation, even if during a part of the increment, purely elastic deformation takes place. This way, time increments affected by the transition from elastic to viscoplastic material behaviour are not properly accounted for, because such time increments exhibit both a purely elastic part and a elastoviscoplastic part. In fact, it has been reported in the literature that errors induced by the use of the conventional one-step approach are insignificant. In the present article, the impact of using the one-step approach, i.e. using the total time increment in case of the elastic-to-viscoplastic transition, on sensitivity analysis is investigated.

Identification of elasto-viscoplastic material parameters by indentation testing and combined finite element modelling and numerical optimization

“…In addition to that, the fast differentiation methods are more accurate, as they do not depend on a numerical perturbation like the finite difference method. However, it should be noted that finite difference and the fast differentiation methods may produce locally poor results in case of non-differentiable evolution equations, as shown in [34][35][36].…”