Instability of frictional contact states in infinite layers

The research reported in this paper is focused on the instability of equilibrium and steady sliding states of elastic orthotropic layers in the presence of unilateral obstacles with Coulomb friction with emphasis on a divergence type instability called directional instability of frictional contact states that cannot occur in isotropic layers. Analytic expressions and numerical solutions are provided for the instability mode and for the coefficient of friction at the onset of instability. A parametric study is done to investigate how this coefficient of friction and the instability mode vary with changes of the system parameters. For certain combinations of material data, significantly low coefficients of friction were required for the onset of instability. A finite element model that approximates the continuum and a lumped model that captures some of the features of the continuum are presented.