Dynamic stability of finite dimensional linearly elastic systems with unilateral contact and Coulomb friction

Necessary and sufficient conditions are established for the occurrence of d ynamic instabilities in finite dimensional linearly elastic systems in unil ateral frictional contact with a rigid fat surface. These conditions apply, in particular. to the systems that result from the finite element discreti zation of linearly elastic bodies. From a numerical point of view, these co nditions lead to studying eigenproblems relative to a non-symmetric (tangen t) stiffness matrix that incorporates the effect of the current tate of the contact candidate particles. Illustrative small-sized examples are present ed, together with an application to the case of an experimentally tested bl och of polyurethane. where friction induced instability phenomena were obse rved. (C) 1999 Elsevier Science S.A. All rights reserved.