Dynamic anti-plane sliding of dissimilar anisotropic linear elastic solids

The stability of steady, dynamic, anti-plane slipping at a planar interface between two dissimilar anisotropic linear elastic solids is studied. The solids are assumed to possess a plane of symmetry normal to the slip direction, so that in-plane displacements and normal stress changes on the slip plane do not occur. Friction at the interface is assumed to follow a rate and state-dependent law with velocity weakening behavior in the steady state. The stability to spatial perturbations of the form exp(ikx1), where k is the wavenumber and x1 is the coordinate along the interface is studied. The critical wavenumber magnitude, |k|cr, above which there is stability and the corresponding phase velocity, c, of the neutrally stable mode are obtained from the stability analysis. Numerical plots showing the dependence of |k|cr and c on the unperturbed sliding velocity, Vo, are provided for various bi-material combinations of practical interest.