Basic Equations of Nonlinear Elasticity Theory

The goal of elasticity theory is the computation of deformations of elastic bodies and the corresponding stress forces. These deformations need not necessarily be small. Unfortunately, at present, there is no general nonlinear existence theory available. This makes the study of the literature quite difficult. Lacking this comprehensive general theory, a great number of models are used which are based on different approximation assumptions. These assumptions, however, are often not explicitly formulated and their foundation seems doubtful. Difficulties arise mainly from the fact that often there is no strict distinction between the different regions which correspond to the undeformed and deformed body.