A symplectic Brezis-Ekeland-Nayroles principle

TL;DR

This paper introduces a symplectic version of the Brezis-Ekeland-Nayroles principle to extend Hamiltonian formalism for dissipative systems, demonstrated through an application to standard plasticity.

Contribution

It presents a novel symplectic adaptation of a variational principle for dissipative systems, expanding Hamiltonian formalism capabilities.

Findings

Successfully applied to standard plasticity modeling

Provides a new framework for dissipative systems in Hamiltonian formalism

Advances the theoretical foundation for symplectic variational principles

Abstract

We propose a modification of the hamiltonian formalism which can be used for dissipative systems. This work continues arXiv:0810.1419 and advances by the introduction of a symplectic version of the Brezis-Ekeland-Nayroles principle [Brezis Ekeland 1976] [Nayroles 1976]. As an application we show how standard plasticity can be treated in our formalism.