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Stability analysis of rough surfaces in adhesive normal contact

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Abstract

This paper deals with adhesive frictionless normal contact between one elastic flat solid and one stiff solid with rough surface. After computation of the equilibrium solution of the energy minimization principle and respecting the contact constraints, we aim at studying the stability of this equilibrium solution. This study of stability implies solving an eigenvalue problem with inequality constraints. To achieve this goal, we propose a proximal algorithm which enables qualifying the solution as stable or unstable and that gives the instability modes. This method has a low computational cost since no linear system inversion is required and is also suitable for parallel implementation. Illustrations are given for the Hertzian contact and for rough contact.

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Acknowledgements

Support for V.R. from the EPFL Fellows fellowship program co-funded by Marie Skłodowska-Curie, Horizon 2020 Grant Agreement No. 665667 is gratefully acknowledged. The authors would like to thank Professor Jean-François Molinari and Guillaume Anciaux for helpful discussions.

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  1. Valentine Rey

    Present address: Département de physique, GeM - Institut de Recherche en Génie Civil et Mécanique UFR Sciences et techniques, Université de Nantes, 2, rue de la Houssiniére, BP 92208, 44322, Nantes CEDEX 3, France

Authors and Affiliations

  1. Laboratoire de simulation en mécanique des solides, Institut ENAC, Ecole Polytechnique Fédérale de Lausanne (EPFL), Station Z, 1015, Lausanne, Switzerland

    Valentine Rey

  2. Ecole des Ponts ParisTech, Laboratoire Navier (ENPC-IFSTTAR-CNRS UMR 8205), Université Paris-Est, 6-8 av. Blaise Pascal, Cité Descartes, 77455, Champs-sur-Marne, France

    Jeremy Bleyer

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Correspondence to Valentine Rey.

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Rey, V., Bleyer, J. Stability analysis of rough surfaces in adhesive normal contact. Comput Mech 62, 1155–1167 (2018). https://doi.org/10.1007/s00466-018-1556-y

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  • DOI: https://doi.org/10.1007/s00466-018-1556-y

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