Instability and ill-posedness in some friction problems

The steady frictional sliding of an elastic half-space in contact with a rigid flat surface is considered. Perturbed solutions in the elastic body are sought which correspond to surface (flutter) instabilities of the steady sliding state. The behavior of these surface solutions for vanishing small values of their arbitrary wavelengths is made clear. The effect of introducing intrinsic length scales in the problem by means of the earlier proposed non-local friction law and normal compliance law or;by means of viscous dissipation in the deformable body is discussed. (C) 1998 Elsevier Science Ltd. All rights reserved.