Introduction to nonlinear continuum mechanics

In this chapter we will briefly give the basic introduction to nonlinear continuum mechanics. The reader can find a more detail description of the problems in [Belytschko, T, Liu W. K, and Moran, B. (2000)], [Okrouhlik, M. (ed.). (1995)],[Altenbach, J, Altenbach, H. (1994)]. The most general analysis case is the one in which the material is subjected to large displacements and large strains. The basic problem in a general nonlinear analysis is to find the state of equilibrium of a body corresponding to the applied loads.Continuum mechanics is concerned with models of solids and fluids in which properties and response can be characterised by smooth function of spatial variables. The objective of continuum mechanics is to provide models for macroscopic behaviour of fluids, solids and structures. Three aspects of description of governing equations are classified: 1. the mesh description, 2. the kinetic description determined by the choice of the stress tensor and the form of the momentum equation and 3. The kinematic description determined by the choice of the strain measure.