New Existence Theorems in Nonlinear Elasticity

In elasticity theory, the unknown of primary interest from the mechanical and computational viewpoints is often the stress tensor field arising in an elastic body in response to given forces. But the classical approach in elasticity only provides indirect methods for computing the stress field, usually based on models where the deformation field is the primary unknown.In this project, the researchers begin by recasting the nonlinear equations of elasticity as a minimisation problem whose unknown is the right Cauchy-Green strain tensor. Since this tensor necessarily satisfy compatibility conditions in the form of specific nonlinear partial differential equations, this approach gives rise to a constrained minimisation problem whose solution will then provide the stress field by means of the constitutive equation. The basic objective of this project is to seek whether new existence theorems in nonlinear elasticity based on this new formulation can be obtained.