6.1 Introduction

In order to complete the finite element development for the finite deformation problem it is necessary to describe how the material behaves when subjected to deformation or deformation histories. In the previous chapter we considered elastic behaviour without introducing details on how to model specific material behaviour. Clearly, restriction to elastic behaviour is inadequate to model the behaviour of many engineering materials as we have already shown in previous applications. The modelling of engineering materials at finite strain is a subject of much research and any complete summary on the state of the art is clearly outside the scope of what can be presented here. In this chapter we present only some classical methods which may be used to model elastic, viscoelastic and elastic-plastic-type behaviours. The reader is directed to literature for details on other constitutive models (e.g. see references 1 and 2).

We first consider some methods which may be used to describe the behaviour of isotropic elastic materials which undergo finite deformation. In this section we restrict attention to those materials in which a stored energy function is used; such behaviour is often called hyperelastic. Later we will extend this to permit the use of viscoelastic and elastic-plastic models and show that much of the material presented in Chapter 4 is here again useful. Finally, to permit the modelling of materials which are not isotropic or cannot be expressed as an extension to elastic behaviour (e.g. generalized plasticity models of Chapter 4) we introduce a...