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non-linear friction in FE

Chris W Smith's picture

We are looking at implementing a non-linear model with friction, and at least in the first place for statics. We haven't found much in the literature on non-linear models for friction in FE.

 Anyone any advice on key papers to read ?





Tianlei Li's picture

Y.F. Gao*, "A Peierls perspective on mechanisms of atomic friction."Journal of the Mechanics and Physics of Solids, vol. 58, iss. 12, pp. 2023-2032, 2010 [PDF] [DOI].

fackeldey's picture

 Dear Chris,

 the following might help:

Laursen, T.A. (1992), Formulation and Treatment of Frictional
Problems Using Finite Elements
, Ph.D. Dissertation, Department of
Engineering, Stanford University.

 Kim, T.Y., J.E. Dolbow & T.A. Laursen (2007), "A Mortared Finite
Element Method for Frictional
Contact on Arbitrary Surfaces," Computational Mechanics, 39,

From the mathematical side, a contact problem with Coulomb friction is modelled by variational inequalties. If it is this, what you are interested in, then 

I suggest the following:

Problems in Elasticity: A Study of Variational Inequalities and Finite
Element Methods N.
Kikuchi and J.T. Oden 1988 / xiii + 495 pages / Softcover / ISBN-13:
978-0-898714-68-5 / ISBN-10: 0898714680


 K. Fackeldey, R. Krause:
Solving Frictional Contact Problems with Multigrid Efficiency
, Proc.of
the 16th International Conference on Domain Decomposition Methods,
Widlund, Olof B.; Keyes, David E. (Eds.), Lecture Notes in Computational
Science and Engineering,p. 547-554 Vol. 55 (2007).


 I hope It will help you.







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