On the relationship between alternative variational formulations of a frictional contact model

TL;DR

This paper explores three different variational formulations of a nonlinear PDE-based frictional contact model, establishing their relationships and methods to recover PDE formulations from mixed variational approaches.

Contribution

It introduces a novel analysis linking three variational formulations of a frictional contact model, including the derivation of PDE formulations from mixed variational forms.

Findings

Established relationships between three variational formulations.

Provided methods to recover PDE formulations from mixed variational forms.

Enhanced understanding of variational approaches in frictional contact modeling.

Abstract

We consider a frictional contact model, mathematically described by means of a nonlinear boundary value problem in terms of PDE. We draw the attention to three possible variational formulations of it. One of the variational formulations is a variational inequality of the second kind and the other two are mixed variational formulations with Lagrange multipliers in dual spaces. As main novelty, we establish the relationship between these three variational formulations. We also pay attention to the recovery of the formulation in terms of PDE starting from the mixed variational formulations.