A reformulation of the Symplectic Brezis-Ekeland-Nayroles principle

The Symplectic Brezis-Ekeland-Nayroles principle (SBEN) is a dissipative version of hamiltonian mechanics [3], [4], [5]. It is named so because it gives a dynamical version of the principles formulated by Brezis-Ekeland [2] for parabolic equations and Nayroles theorems on dissipative systems [10].In this article we continue [6] and reformulate SBEN in a simpler form, which cover non-associated constitutive laws expressed via bipotential theory. We thus obtain a new, dynamical theory for a large class of models which are usually studied in the quasistatic regime.This is the original version of the article written for the preparation of the project ANR-22-CE51-0034.