Unified primal-dual active set method for dynamic frictional contact problems
Abstract In this paper, we propose a semi-smooth Newton method and a primal-dual active set strategy to solve dynamical contact problems with friction. The conditions of contact with Coulomb’s friction can be formulated in the form of a fixed point problem related to a quasi-optimization one thanks...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-08-01
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| Series: | Fixed Point Theory and Algorithms for Sciences and Engineering |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13663-022-00729-4 |
| _version_ | 1798032299893194752 |
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| author | Stéphane Abide Mikaël Barboteu Soufiane Cherkaoui Serge Dumont |
| author_facet | Stéphane Abide Mikaël Barboteu Soufiane Cherkaoui Serge Dumont |
| author_sort | Stéphane Abide |
| collection | DOAJ |
| description | Abstract In this paper, we propose a semi-smooth Newton method and a primal-dual active set strategy to solve dynamical contact problems with friction. The conditions of contact with Coulomb’s friction can be formulated in the form of a fixed point problem related to a quasi-optimization one thanks to the semi-smooth Newton method. This method is based on the use of the primal-dual active set (PDAS) strategy. The main idea here is to find the correct subset A $\mathcal{A}$ of nodes that are in contact (active) opposed to those which are not in contact (inactive). For each case, the nonlinear boundary condition is replaced by a suitable linear one. Numerical experiments on both hyper-elastic problems and rigid granular materials are presented to show the efficiency of the proposed method. |
| first_indexed | 2024-04-11T20:10:24Z |
| format | Article |
| id | doaj.art-846e150c13b64d6c89abc22d0b1d4967 |
| institution | Directory Open Access Journal |
| issn | 2730-5422 |
| language | English |
| last_indexed | 2024-04-11T20:10:24Z |
| publishDate | 2022-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Fixed Point Theory and Algorithms for Sciences and Engineering |
| spelling | doaj.art-846e150c13b64d6c89abc22d0b1d49672022-12-22T04:05:06ZengSpringerOpenFixed Point Theory and Algorithms for Sciences and Engineering2730-54222022-08-012022112210.1186/s13663-022-00729-4Unified primal-dual active set method for dynamic frictional contact problemsStéphane Abide0Mikaël Barboteu1Soufiane Cherkaoui2Serge Dumont3Laboratoire de Mathématiques et Physique, Université de Perpignan Via DomitiaLaboratoire de Mathématiques et Physique, Université de Perpignan Via DomitiaLaboratoire de Mathématiques et Physique, Université de Perpignan Via DomitiaInstitut Montpelliérain Alexander Grothendieck, Université de NîmesAbstract In this paper, we propose a semi-smooth Newton method and a primal-dual active set strategy to solve dynamical contact problems with friction. The conditions of contact with Coulomb’s friction can be formulated in the form of a fixed point problem related to a quasi-optimization one thanks to the semi-smooth Newton method. This method is based on the use of the primal-dual active set (PDAS) strategy. The main idea here is to find the correct subset A $\mathcal{A}$ of nodes that are in contact (active) opposed to those which are not in contact (inactive). For each case, the nonlinear boundary condition is replaced by a suitable linear one. Numerical experiments on both hyper-elastic problems and rigid granular materials are presented to show the efficiency of the proposed method.https://doi.org/10.1186/s13663-022-00729-4Granular mediaElasticityUnilateral constraintFrictionRigid bodyDeformable body |
| spellingShingle | Stéphane Abide Mikaël Barboteu Soufiane Cherkaoui Serge Dumont Unified primal-dual active set method for dynamic frictional contact problems Fixed Point Theory and Algorithms for Sciences and Engineering Granular media Elasticity Unilateral constraint Friction Rigid body Deformable body |
| title | Unified primal-dual active set method for dynamic frictional contact problems |
| title_full | Unified primal-dual active set method for dynamic frictional contact problems |
| title_fullStr | Unified primal-dual active set method for dynamic frictional contact problems |
| title_full_unstemmed | Unified primal-dual active set method for dynamic frictional contact problems |
| title_short | Unified primal-dual active set method for dynamic frictional contact problems |
| title_sort | unified primal dual active set method for dynamic frictional contact problems |
| topic | Granular media Elasticity Unilateral constraint Friction Rigid body Deformable body |
| url | https://doi.org/10.1186/s13663-022-00729-4 |
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