On duality principles for one and three-dimensional non-linear models in elasticity

In this article, we develop duality principles applicable to primal variational formulations found in the non-linear elasticity theory. As a first application, we establish the concerning results in details for one and three-dimensional models. We emphasize such duality principles are applicable to a larger class of variational optimization problems, such as non-linear models of plates and shells and other models in elasticity. Finally, we formally prove there is no duality gap between the primal and dual formulations, in a local extremal context.