Steady sliding frictional contact problem for a 2d elastic half-space with a discontinuous friction coefficient and related stress singularities |
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| Institution: | 1. Laboratoire de Recherche des Monuments Historiques, 29 rue de Paris, 77420 Champs-sur-Marne, France;2. Centre de recherche sur la conservation, Sorbonne Universités, Muséum national d’Histoire naturelle, Ministère de la Culture et de la Communication, Paris, France;1. Università di Trento, DICAM, via Mesiano 77, I-38123 Trento, Italy;2. Russian Academy of Sciences, Steklov Mathematical Institute, Gubkina st. 8, 119991 Moscow, Russia;1. Aix Marseille Univ, CNRS, ISM, Inst Movement Sci, Marseille, France;2. APHM, Sainte-Marguerite Hospital, Institute for Locomotion, Department of Orthopaedics and Traumatology, Marseille, France;3. University of Washington, Seattle, WA, USA |
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| Abstract: | The steady sliding frictional contact problem between a moving rigid indentor of arbitrary shape and an isotropic homogeneous elastic half-space in plane strain is extensively analysed. The case where the friction coefficient is a step function (with respect to the space variable), that is, where there are jumps in the friction coefficient, is considered. The problem is put under the form of a variational inequality which is proved to always have a solution which, in addition, is unique in some cases. The solutions exhibit different kinds of universal singularities that are explicitly given. In particular, it is shown that the nature of the universal stress singularity at a jump of the friction coefficient is different depending on the sign of the jump. |
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| Keywords: | Elasticity Contact Friction Singularity Variational inequality Uniqueness |
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