Abstract
The studies carried out on adhesion by the group “Modeling in Contact Mechanics” at the LMA are reviewed in this paper and recent applications are presented. Based on the introduction of the adhesion intensity variable developed by M. Frémond, different forms of a model coupling adhesion to unilateral contact and friction have been developed. The formulations are given either under the form of implicit variational inequalities or the one of complementarity problems. Both quasi-static and dynamic formulations are considered.
The model is non smooth because we do not use any regularization for the unilateral conditions and for the friction, i.e. Signorini conditions and strict Coulomb law are written. In the thermodynamics analysis, the state and the complementarity laws are then written using sub-differentials and differential inclusions because of the non convexity and non differentiability of the potentials. For the dynamics, the formulation is given in term of differential measures in order to deal with the non continuity of the velocities that may occur in the solutions.
This work therefore owes much to the theories and the numerical scheme developed by J. J. Moreau and M. Jean.
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Raous, M. (2006). Friction and Adhesion. In: Alart, P., Maisonneuve, O., Rockafellar, R.T. (eds) Nonsmooth Mechanics and Analysis. Advances in Mechanics and Mathematics, vol 12. Springer, Boston, MA. https://doi.org/10.1007/0-387-29195-4_9
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DOI: https://doi.org/10.1007/0-387-29195-4_9
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