A concise frictional contact formulation based on surface potentials and isogeometric discretization

TL;DR

This paper develops a simplified yet robust finite element framework for modeling large deformation frictional contact problems using surface potentials and isogeometric discretization, extending existing theories to include friction effects.

Contribution

It introduces a novel friction formulation based on surface potentials that reduces computational complexity and is compatible with isogeometric discretization techniques.

Findings

Accurate modeling of large deformation frictional contact

Reduced computational complexity compared to existing methods

Robustness demonstrated through numerical examples

Abstract

This work presents a concise theoretical and computational framework for the finite element formulation of frictional contact problems with arbitrarily large deformation and sliding. The aim of this work is to extend the contact theory based on surface potentials (Sauer and De Lorenzis, 2013) to account for friction. Coulomb friction under isothermal conditions is considered here. For a consistent friction formulation, we start with the first and second laws of thermodynamics and derive the governing equations at the contact interface. A so-called interacting gap can then be defined as a kinematic variable unifying both sliding/sticking and normal/tangential contact. A variational principle for the frictional system can then be formulated based on a purely kinematical constraint. The direct elimination approach applied to the tangential part of this constraint leads to the so-called moving friction cone approach of Wriggers and Haraldsson (2003). Compared with existing friction formulations, our approach reduces the theoretical and computational complexity. Several numerical examples are presented to demonstrate the accuracy and robustness of the proposed friction formulation.