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Article Dans Une Revue Advanced Modeling and Simulation in Engineering Sciences Année : 2015

The inequality level-set approach to handle contact: membrane case

Résumé

Background: Contact mechanics involves models governed by inequality constraints. Even for the simplest contact problem, inequalities arise from the lack of information on the contact zone position. In addition to increasing the difficulty to solve such problems, an unknown contact zone makes it difficult to use an appropriate mesh and to represent efficiently phenomena on the contact zone boundary. Nevertheless these phenomena are often crucial to have an accurate representation of the problem such as weak discontinuity of the displacement.

Methods: In this paper, we propose a method specifically designed to solve inequality constraint problems linked to an unknown domain without remeshing. In order to do so, level sets coupled with X-FEM is used to define the unknown domain and take into account the specific behavior at the contact zone boundary. The key idea of the method is to split the problem involving inequality constraints into two problems. In the first problem, the unknown domain is set and therefore it only involves equalities. Nevertheless, the constraints might be violated, meaning the set domain has to be changed. Then, the other problem is a shape optimization of this domain and leads to an updated set domain. These two problems are iterated up to convergence of the algorithm. Moreover, the addition of adhesion to the problem will be considered.

Results: The studied case in this paper is a membrane in the context of small deformations. First, a 1D example will be given to illustrate the method with and without adhesion. Then 2D cases will be studied. Finally an example with an evolving load will be given. Comparison will be made with a classical active-set method.

Conclusions: The ILS is proved to be an efficient method giving a convincing accuracy for the contact boundary without need of re-meshing. It is also able to naturally handle adhesion.

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Dates et versions

hal-01398280 , version 1 (17-11-2016)

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Matthieu Graveleau, Nicolas Chevaugeon, Nicolas Moes. The inequality level-set approach to handle contact: membrane case. Advanced Modeling and Simulation in Engineering Sciences, 2015, 2 (1), ⟨10.1186/s40323-015-0034-8⟩. ⟨hal-01398280⟩
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