TABLE OF CONTENTS Classical 'plastic' behaviour of solids is characterized by a non-unique stress-strain relationship which is independent of the rate of loading but does depend on loading sequence that may be conveniently represented as a process evolving in time. Indeed, one definition of plasticity is the presence of irrecoverable strains on load removal. If uniaxial behaviour of a material is considered, as shown in Fig. 4.6(a), a non-linear relationship on loading alone does not determine whether non-linear elastic or plastic behaviour is exhibited. Unloading will immediately discover the difference, with an elastic material following the same path and a plastic material showing a history-dependent different path. We have referred to non-linear elasticity already in Sec. 2.4 [see Eq. (2.28)] and will not give further attention to it here as the techniques used for plasticity problems or non-linear elasticity show great similarity. Representation of non-linear elastic behaviour for finite deformation applications is more complex as we shall show in Chapter 5.
Some materials show a nearly ideal plastic behaviour in which a limiting yield stress, Y (or ? y), exists at which the strains are indeterminate. For all stresses below such yield, a linear (or non-linear) elastic relationship is assumed, Fig. 4.6(b) illustrates this. A further refinement of this model is one of a hardening/softening plastic material in which the yield stress...
