A reduced basis method for frictional contact problems formulated with Nitsche’s method
Niakh, Idrissa1 ; Drouet, Guillaume2 ; Ehrlacher, Virginie3 ; Ern, Alexandre3
1EDF R&D, 7 Boulevard Gaspard Monge, 91120 Palaiseau, France & CERMICS, École des Ponts, 6-8 avenue Blaise Pascal, 77455 Marne-la-Vallée cedex 2, France & INRIA Paris, 2 Rue Simone Iff, 75012 Paris, France
2EDF R&D, 7 Boulevard Gaspard Monge, 91120 Palaiseau, France
3CERMICS, École des Ponts, 6-8 avenue Blaise Pascal, 77455 Marne-la-Vallée cedex 2, France & INRIA Paris, 2 Rue Simone Iff, 75012 Paris, France
The SMAI Journal of computational mathematics, Tome 10 (2024), pp. 29-54

We develop an efficient reduced basis method for the frictional contact problem formulated using Nitsche’s method. We focus on the regime of small deformations and on Tresca friction. The key idea ensuring the computational efficiency of the method is to treat the nonlinearity resulting from the contact and friction conditions by means of the Empirical Interpolation Method. The proposed algorithm is applied to the Hertz contact problem between two half-disks with parameter-dependent radius. We also highlight the benefits of the present approach with respect to the mixed (primal-dual) formulation.

Publié le :
DOI : 10.5802/smai-jcm.105
Classification : 65N99, 65Y20, 68U20
Keywords: model reduction, variational inequalities, reduced basis method, contact problems, Nitsche’s method, Tresca friction, Coulomb friction

Niakh, Idrissa  1   ; Drouet, Guillaume  2   ; Ehrlacher, Virginie  3   ; Ern, Alexandre  3

1 EDF R&D, 7 Boulevard Gaspard Monge, 91120 Palaiseau, France & CERMICS, École des Ponts, 6-8 avenue Blaise Pascal, 77455 Marne-la-Vallée cedex 2, France & INRIA Paris, 2 Rue Simone Iff, 75012 Paris, France
2 EDF R&D, 7 Boulevard Gaspard Monge, 91120 Palaiseau, France
3 CERMICS, École des Ponts, 6-8 avenue Blaise Pascal, 77455 Marne-la-Vallée cedex 2, France & INRIA Paris, 2 Rue Simone Iff, 75012 Paris, France 
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     title = {A reduced basis method for frictional contact problems formulated with {Nitsche{\textquoteright}s} method},
     journal = {The SMAI Journal of computational mathematics},
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     year = {2024},
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Niakh, Idrissa; Drouet, Guillaume; Ehrlacher, Virginie; Ern, Alexandre. A reduced basis method for frictional contact problems formulated with Nitsche’s method. The SMAI Journal of computational mathematics, Tome 10 (2024), pp. 29-54. doi: 10.5802/smai-jcm.105

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