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

Necessary and sufficient conditions are established for the occurrence of dynamic instabilities in finite dimensional linearly elastic systems in unilateral frictional contact with a rigid flat surface. These conditions apply, in particular, to the systems that result from the finite element discretization of linearly elastic bodies. From a numerical point of view, these conditions lead to studying eigenproblems relative to a non-symmetric (tangent) stiffness matrix that incorporates the effect of the current state of the contract candidate particles. Illustrative small-sized examples are presented, together with an application to the case of an experimentally tested block of polyurethane, where friction induced instability phenomena were observed.