A symplectic Brezis-Ekeland-Nayroles principle for dynamic plasticity in finite strains

In a previous paper, the last author proposed with Buliga a symplectic version of Brezis–Ekeland–Nayroles principle based on the concepts of Hamiltonian inclusions and symplectic polar functions. It was illustrated by application to the standard plasticity in small deformations. The objective of this work is to generalize the previous formalism to dissipative media in finite strains. This aim is reached in three steps. Firstly, we develop a Lagrangian formalism for the reversible media based on the calculus of variation. Next, we propose a corresponding Hamiltonian formalism for such media. Finally, we deduce from it a symplectic minimum principle for dissipative media and we show how to get a minimum principle for plasticity in finite strains.