Friction and Instabilities

The book addresses instability and bifurcation phenomena in frictional contact problems. The treatment of this subject has its roots in previous studies of instability and bifurcation in elastic, thermoelastic or elastic-plastic bodies, and in previous mathematical, mechanical and computational studies of unilateral problems. The salient feature of this book is to put together and develop concepts and tools for stability and bifurcation studies in mechanics, taking into account the inherent non-smoothness and non-associativity (non-symmetry) of unilateral frictional contact laws. The mechanical foundations, the mathematical theory and the computational algorithms for such studies are developed along six chapters written by the lecturers of a CISM course. Those concepts and tools are illustrated not only with enlightening academic examples but also with some demanding industrial applications, related, namely, to the automotive industry.

Preface.- Instability of Thermoelastic Contact (J. R. Barber).- Stability and Critical Points in Large Displacement Frictionless Contact Problems (A. Klarbring).- Some Notes on Frictions and Instabilities (J. A. C. Martins, F. M. F. Simões, A. Pinto da Costa).- Some Examples of Friction-Induced Vibrations and Instabilities (F. Moirot, Q. S. Nguyen).- Contact Friction Models and Stability Problems (Z. Mróz).- Numerical Characterization and Computation of Dynamic Instabilities for Frictional Contact Problems (M. Raous, S. Barbarin, D. Vola)