Computational Mechanics

, Volume 64, Issue 4, pp 951–970

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

• Thang X. Duong
• Roger A. Sauer
Original Paper

## 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 in Comput Methods Appl Mech Eng 253:369–395, 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 (Commun Numer Methods Eng 19:285–295, 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.

## Keywords

Contact mechanics Isogeometric analysis Moving friction cone Nonlinear finite element methods Sliding friction Thermodynamical consistency.

## Notes

### Acknowledgements

The authors are grateful to the German Research Foundation (DFG) for supporting this research under Grants GSC 111 and SA1822/8-1.

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