A variational formulation for constitutive laws described by bipotentials

TL;DR

This paper introduces a general variational framework using bipotentials for modeling constitutive laws, inspired by existing algorithms for solving evolution problems in implicit standard materials.

Contribution

It presents a novel variational formulation based on bipotentials, extending previous algorithms to a broader class of constitutive laws.

Findings

Provides a new variational approach for constitutive laws

Links bipotential theory with numerical algorithms

Enhances modeling capabilities for implicit materials

Abstract

Inspired by the algorithm of Berga and de Saxce for solving the discretisation in time of the evolution problem for an implicit standard material, we propose a general variational formulation in terms of bipotentials.