Nonlinear Elasticity with Application to Soft Fibre-reinforced Materials

Abstract

There are many fibrous materials, both natural and man made, ranging from hard material such as wood and carbon fibre composites to relatively soft materials such as rubber and softer materials such as biological tissues. With particular reference to fibre-reinforced soft materials, this chapter provides the theoretical background for analyzing the elastic properties of such materials based on nonlinear continuum mechanics through so-called structure tensors from which are constructed the deformation invariants that form the independent variables in the elastic constitutive laws. The theory is applied to some simple deformations by way of illustration of the material response. The notion of structure tensor is then used to incorporate residual stresses into the constitutive law and the important effects of residual stresses are illustrated in a prototype boundary-value problem related to the elastic behaviour of arteries.