ABSTRACT
This chapter develops duality principles applicable to primal variational formulations found in the non-linear elasticity theory. It establishes the concerning results of the primal variational formulation for a one-dimensional model and a three-dimensional model. The chapter describes the main duality principles for the one-dimensional model and the three-dimensional model and emphasizes that such duality principles are applicable to a larger class of variational optimization problems, such as non-linear models of plates and shells as well as other models in elasticity. It also proves formally that there is no duality gap between the primal and dual formulations, in a local extremal context.
