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.
Keywords: model reduction, variational inequalities, reduced basis method, contact problems, Nitsche’s method, Tresca friction, Coulomb friction
Idrissa Niakh 1; Guillaume Drouet 2; Virginie Ehrlacher 3; Alexandre Ern 3
@article{SMAI-JCM_2024__10__29_0, author = {Idrissa Niakh and Guillaume Drouet and Virginie Ehrlacher and Alexandre Ern}, title = {A reduced basis method for frictional contact problems formulated with {Nitsche{\textquoteright}s} method}, journal = {The SMAI Journal of computational mathematics}, pages = {29--54}, publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles}, volume = {10}, year = {2024}, doi = {10.5802/smai-jcm.105}, language = {en}, url = {https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.105/} }
TY - JOUR AU - Idrissa Niakh AU - Guillaume Drouet AU - Virginie Ehrlacher AU - Alexandre Ern TI - A reduced basis method for frictional contact problems formulated with Nitsche’s method JO - The SMAI Journal of computational mathematics PY - 2024 SP - 29 EP - 54 VL - 10 PB - Société de Mathématiques Appliquées et Industrielles UR - https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.105/ DO - 10.5802/smai-jcm.105 LA - en ID - SMAI-JCM_2024__10__29_0 ER -
%0 Journal Article %A Idrissa Niakh %A Guillaume Drouet %A Virginie Ehrlacher %A Alexandre Ern %T A reduced basis method for frictional contact problems formulated with Nitsche’s method %J The SMAI Journal of computational mathematics %D 2024 %P 29-54 %V 10 %I Société de Mathématiques Appliquées et Industrielles %U https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.105/ %R 10.5802/smai-jcm.105 %G en %F SMAI-JCM_2024__10__29_0
Idrissa Niakh; Guillaume Drouet; Virginie Ehrlacher; Alexandre Ern. A reduced basis method for frictional contact problems formulated with Nitsche’s method. The SMAI Journal of computational mathematics, Volume 10 (2024), pp. 29-54. doi : 10.5802/smai-jcm.105. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.105/
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