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.

在之前的一篇论文中，最后一位作者与 Buliga 提出了基于哈密顿夹杂和辛极函数概念的 Brezis-Ekeland-Nayroles 原理的辛版本。它通过应用于小变形中的标准塑性来说明。这项工作的目的是将以前的形式主义推广到有限应变中的耗散介质。这个目标是通过三个步骤来实现的。首先，我们基于变分法为可逆介质开发了拉格朗日形式。接下来，我们为此类媒体提出相应的哈密顿形式主义。最后，我们从中推导出耗散介质的辛最小原理，并展示如何获得有限应变中塑性的最小原理。