# A three-field augmented Lagrangian formulation of unilateral contact problems with cohesive forces

David Doyen; Alexandre Ern; Serge Piperno

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 44, Issue: 2, page 323-346
- ISSN: 0764-583X

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topDoyen, David, Ern, Alexandre, and Piperno, Serge. "A three-field augmented Lagrangian formulation of unilateral contact problems with cohesive forces." ESAIM: Mathematical Modelling and Numerical Analysis 44.2 (2010): 323-346. <http://eudml.org/doc/250774>.

@article{Doyen2010,

abstract = {
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.
},

author = {Doyen, David, Ern, Alexandre, Piperno, Serge},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Unilateral contact; cohesive forces; augmented Lagrangian;
mixed finite elements; decomposition-coordination method; Newton's method; mixed finite elements; nonsmooth Newton's method; convergence},

language = {eng},

month = {3},

number = {2},

pages = {323-346},

publisher = {EDP Sciences},

title = {A three-field augmented Lagrangian formulation of unilateral contact problems with cohesive forces},

url = {http://eudml.org/doc/250774},

volume = {44},

year = {2010},

}

TY - JOUR

AU - Doyen, David

AU - Ern, Alexandre

AU - Piperno, Serge

TI - A three-field augmented Lagrangian formulation of unilateral contact problems with cohesive forces

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 44

IS - 2

SP - 323

EP - 346

AB -
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.

LA - eng

KW - Unilateral contact; cohesive forces; augmented Lagrangian;
mixed finite elements; decomposition-coordination method; Newton's method; mixed finite elements; nonsmooth Newton's method; convergence

UR - http://eudml.org/doc/250774

ER -

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