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A three-field augmented Lagrangian formulationof unilateral contact problems with cohesive forces

Published online by Cambridge University Press:  27 January 2010

David Doyen ,
Alexandre Ern  and
Serge Piperno
David Doyen
Affiliation:
EDF R&D, 1 avenue du Général de Gaulle, 92141 Clamart Cedex, France. [email protected]
Alexandre Ern
Affiliation:
Université Paris-Est, CERMICS, École des Ponts, 77455 Marne-la-Vallée Cedex 2, France. [email protected]; [email protected]
Serge Piperno
Affiliation:
Université Paris-Est, CERMICS, École des Ponts, 77455 Marne-la-Vallée Cedex 2, France. [email protected]; [email protected]
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Abstract

We investigate unilateral contact problems with cohesive forces, leading tothe constrained minimization of a possibly nonconvex functional. Weanalyze the mathematical structure of the minimization problem. The problem is reformulated in terms of a three-field augmentedLagrangian, and sufficient conditions for the existence of a localsaddle-point are derived. Then, we derive and analyze mixed finiteelement approximations to the stationarity conditions of the three-fieldaugmented Lagrangian. The finite element spaces for the bulk displacement andthe Lagrange multiplier must satisfy a discrete inf-sup condition, whilediscontinuous finite element spaces spanned by nodal basis functions areconsidered for the unilateral contact variable so as to use collocationmethods. Two iterative algorithms are presented and analyzed, namely anUzawa-type method within a decomposition-coordination approach and anonsmooth Newton's method. Finally, numerical results illustrating thetheoretical analysis are presented.

Keywords

Unilateral contactcohesive forcesaugmented Lagrangianmixed finite elementsdecomposition-coordination methodNewton's method
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 44 , Issue 2 , March 2010 , pp. 323 - 346
Copyright
© EDP Sciences, SMAI, 2010

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