Elastoplasticity

Abstract

This chapter is devoted to the analysis of a type of behaviour, non-linear by definition, shown by a great variety of materials in response to a great variety of types of loading. The main restrictions will be the assumptions that viscosity can be neglected and that the loading does not damage the material - no cracks or cavitations, for example, are produced. The absence of viscosity does not necessarily mean that the temperatures are low, for if the temperature is low enough for the diffusion mechanisms to be regarded as inhibited then there will in general be a low-temperature viscoplastic regime with other phenomena to be taken into account. It is best to take the view that the validity of the elastoplasticity approximation, introduced as a limiting case of elastoviscoplasticity, holds over a domain which, under suitable temperature conditions, adjoins both that of loads varying infinitely slowly, giving an asymptotically stable response, and that of very rapidly varying loads in which viscosity “has no to act”. In all cases we shall treat plasticity as independent of and velocity - rate-independent plasticity. If a parameter t, called “time” for convenience, appears in an equation this will not be physical but a purely kinematical , enabling us to locate a sequence of events, on an increasing scale; these events will usually be related to changes to the loading and will represent the history of that process, without regard to the rate at which any changes are made. So far as the assumption of no damage is concerned, this is an essential restriction but nevertheless a provisional one which in the end we shall lift when considering the coupling between plasticity and damage. Finally, to avoid unnecessary complications, we shall consider the elastic behaviour as linear; this will enable us to attribute all nonlinear aspects unambiguously to plasticity.