12.1 Introduction

In the first section of this chapter the (biological) material under consideration can be regarded as a solid. This implies that it is possible to define a reference configuration and local deformations can be related to this reference configuration (see Chapter 10). It is assumed that the deformations (or more precisely, the path along which the actual deformations are reached: the deformation history) fully determine the current stress state (see Chapter 8), except for the special case when we deal with incompressible material behaviour. A number of non-mechanical phenomena are not included, such as the influence of temperature variations.

The constitutive equations discussed in the present chapter address a relation that can be formally written as

with ?( t) the current Cauchy stress tensor at time t and with F( ?) the deformation tensor at the relevant (previous) times ? up to the time t, assuming compressible material behaviour. A specification of this relation (the material behaviour) can only be obtained by means of experimental studies. In the current chapter we restrict our attention to elastic behaviour. In that case the deformation history is not relevant and we can formally write

Further elaboration of this relation will initially be done for the case of small deformations and rotations, so under the condition F ? I. After that, the consequences of including large deformations (and large rotations) will be discussed. In that case it is important to account for...