ABSTRACT
This chapter deals with the basic concepts of continuum mechanics (Malvern, 1969; Marsden and Hughes, 1980). The presence of a specific chapter on this topic is motivated by its use in the wide application of numerical techniques in the field of biomechanics. In particular, the application of the finite element method (Hughes, 1996; Zienkiewicz and Taylor, 1996; Crisfield, 1997) represents a powerful approach to the qualitative and quantitative estimation of the complex mechanical behaviour of both hard and soft tissues, as well as of the interaction between implants and biological tissues. The following topics are given particular attention: anisotropy (Spencer, 1990), finite elasticity (Ogden, 1984) and visco-elasticity (Simo and Hughes, 2000), damage (Kachanov, 1986; Lemaitre, 1996) and poroelasticity (Lewis and Schrefler, 1998). Anisotropic behaviour must be generally taken into account in the modelling of bone tissue (Cowin, 2001), particularly for its cortical portion and it can also regard soft tissues. The concept of finite elasticity is fundamental in describing the mechanical response of soft tissues such as ligaments, intervertebral discs and skin (Maurel et al., 1998). The visco-elastic approach (Christensen, 1982) can provide a sophisticated modelling for a direct formulation of the time dependent behaviour of living tissues. Damage models are also presented since they are commonly adopted to describe inelastic effects on bone (Lee et al., 2000) and, in addition, offer possible approaches to defining a bone remodelling theory (Prendergast and Taylor, 1994; Ramtani and Zidi, 2001). Finally, multi-phase media formulations probably represent the most advanced approach in the analysis of biological tissue mechanics because it is consistent with the micro-mechanical structure of the tissue, including the description of the behaviour of fluid phases and their effects (Mow et al., 1980; Almeida and Spilker, 1998; Cowin, 1999).
