Quasistatic Signorini Problem with Coulomb Friction and Coupling to Adhesion
In this course, we propose to outline some of the classical results obtained in contact mechanics and to present in addition some contributions resulting from the research carried out in our group “Mécanique et Modélisation du Contact” in the “Laboratoire
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QUASISTATIC SIGNORINI PROBLEM WITH COULOMB FRICTION AND COUPLING TO ADHESION
M. Raous Laboratoire de Mecanique et d' Acoustique, CNRS, Marseille, France
Introd uction In this course, we propose to outline some of the classical results obtained in contact mechanics and to present in addition some contributions resulting from the research carried out in our group "Mecanique et Modelisation du Contact" in the "Laboratoire de Mecanique et d 'Acoustique" in Marseille. These research topics concern : - the study of the dynamic instabilities associated with friction in small or finite elastic deformations, in collaboration with Professor J.A.C. Martins from the IST in Lisbon, with applications to the modelling of stress waves occurring in some sliding contact or squeal phenomena involving ruhber-glass contact ([8] [117]), - the development of models coupling adhesion, unilateral contact and friction with applications to the modeHing of the fiber/matrix interface of composite materials ([17] [88]), - the modelling of frictional unilateral contact in finite plastic deformations conducted
P. Wriggers et al. (eds.), New Developments in Contact Problems © Springer-Verlag Wien 1999
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M. Raous
by P. Chabrand with applications to metal forming ([97] [42] [24] [83]), - the development of accelerating numerical approaches in contact mechanics, using methods such as multigrid or subdomain decomposition methods (Fast Adaptive Composite grids) or Arbitrary Lagrangian Eulerian formulations ([54] [83]), - the study of the mathematical aspects of the previous problems with Professor M. Cocu and E. Pratt. The numerical results presented in this course have been obtained with our finite element codes Gyptis and Euxene written in the Modulef standard and with the Simem3 code first developed for the Renault company. Although it will not be attempted here to give an exhaustive bibliography, we would like to mention a few significant general contributions to contact mechanics. Among the numerous books on the various topics related to contact mechanics, the following are worth noting : - on the modeHing aspects [Jonhson, 1987], [Rabinowicz, 1995], [Kalker, 1990], - on tribology [Dowson, 1979], - on the mathematical aspects (functional and convex and non convex analysis) [DuvautLions, 1972], [Moreau-Panagiotopoulos, Eds, 1988], [Panagiotopoulos, 1985], [Panagiotopoulos, 1993], - on both mathematical and numerical aspects [Kikuchi-Oden, 1988], [Glowinski et al, 1976], [Antes-Panagiotopoulos, 1992]). Numerous references can be found in [Zhong-Mackerle, 1992]. Many papers can also be found in the proceedings of a series of congresses, dealing with contact and unilateral problems, which took place : . in Italy [Del Piero-Maceri, Eds., 1985, 1987, 1991 and 1997], . in Lausanne [Curnier, Ed., 1992], . in Carry-Le-Rouet [Raous-Jean-Moreau, Eds., 1995]. On the tribological aspects, the proceedings of the annual "Leeds-Lyon Symposium on Tribology" (see for example [Dowson et al., Eds., 1996]), and those of the scientific meetings of the "Societe
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