  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.
