Problems in which a number of elastic bodies are in frictional contact share many features with elastic-plastic problems in that no local deformation [in this case slip] occurs until some critical condition is reached, after which slip occurs at approximately constant load. However, the elementary Coulomb friction law supports a very rich range of different kinds of behaviour including history dependence in the response to periodic loading, occasional elastodynamic events in response to smooth variation in loading conditions, ‘wedging’, meaning that the system is left in a state of stress even when all external loads are removed, and steady cyclic states that satisfy the governing equations but that are unstable to infinitesimal perturbations.
In this talk, I shall discuss attempts to predict the conditions under which these phenomena are possible [e.g. from the stiffness matrix of a finite element discretization] and strategies for describing the evolution of a frictional system.
About the Speaker
J.R.BARBER graduated in Mechanical Sciences from Cambridge University in 1963 and joined British Rail, who later sponsored his research at Cambridge between 1965 and 1968 on the subject of thermal effects in braking systems. In 1969 he became Lecturer and later Reader in Solid Mechanics at the University of Newcastle upon Tyne. In 1981 he moved to the University of Michigan, where he is presently Jon R. and Beverly S. Holt Professor of Engineering and Arthur F. Thurnau Professor of Mechanical Engineering and Applied Mechanics. He is a Chartered Engineer in the U.K., Fellow of the Institution of Mechanical Engineers, and has engaged extensively in consulting work in the field of stress analysis for engineering design.
He is author of three books (‘Elasticity’, ‘Intermediate Mechanics of Materials’ and ‘Contact Mechanics’) and over 200 articles in the fields of Elasticity, Thermoelasticity, Contact Mechanics, Tribology, Heat Conduction and Elastodynamics. He is a recipient of the Drucker Medal, the Ted Belytschko Applied Mechanics Award and the Mayo D. Hersey Award of ASME and the Archie Higdon Distinguished Educator Award of ASEE. He has served as Associate Editor of the ASME Journal of Applied Mechanics, Mathematical Problems in Engineering, and ASME Journal of Tribology, and is co-Editor of the Springer book series Solid Mechanics and its Applications, and a member of the editorial boards of the International Journal of Mechanical Sciences, the Journal of Thermal Stresses and Acta Tribologica.