Volume 44, Number 2, March-April 2010
|Page(s)||323 - 346|
|Published online||27 January 2010|
A three-field augmented Lagrangian formulation of unilateral contact problems with cohesive forces
EDF R&D, 1 avenue du Général de
Gaulle, 92141 Clamart Cedex, France. firstname.lastname@example.org
2 Université Paris-Est, CERMICS, École des Ponts, 77455 Marne-la-Vallée Cedex 2, France. email@example.com; firstname.lastname@example.org
Revised: 27 July 2009
We investigate unilateral contact problems with cohesive forces, leading to the constrained minimization of a possibly nonconvex functional. We analyze the mathematical structure of the minimization problem. The problem is reformulated in terms of a three-field augmented Lagrangian, and sufficient conditions for the existence of a local saddle-point are derived. Then, we derive and analyze mixed finite element approximations to the stationarity conditions of the three-field augmented Lagrangian. The finite element spaces for the bulk displacement and the Lagrange multiplier must satisfy a discrete inf-sup condition, while discontinuous finite element spaces spanned by nodal basis functions are considered for the unilateral contact variable so as to use collocation methods. Two iterative algorithms are presented and analyzed, namely an Uzawa-type method within a decomposition-coordination approach and a nonsmooth Newton's method. Finally, numerical results illustrating the theoretical analysis are presented.
Mathematics Subject Classification: 65N30 / 65K10 / 74S05 / 74M15 / 74R99
Key words: Unilateral contact / cohesive forces / augmented Lagrangian / mixed finite elements / decomposition-coordination method / Newton's method
© EDP Sciences, SMAI, 2010
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