On uniqueness for frictional contact rate problems

A linear elastic solid having part of the boundary in unilateral frictional contact with a stiffer constraint is considered. Bifurcations of the quasistatic velocity problem are analyzed, making use of methods developed for elastoplasticity. An exclusion principle for bifurcation is proposed which is similar, in essence, to the well-known exclusion principle given by Hill(1958). Sufficient conditions for uniqueness are given for a broad class of contact constitutive equations. The uniqueness criteria are based on the introduction of 'linear comparison interfaces' defined both where the contact rate constitutive equation are piece-wise incrementally linear and where these are thoroughly nonlinear. Structural examples are proposed which give evidence to the applicability of the exclusion criteria. (C) 1999 Elsevier Science Ltd. All rights reserved.