Dynamic anti-plane sliding of dissimilar anisotropic linear elastic solids

TL;DR

This paper analyzes the stability of steady anti-plane sliding between dissimilar anisotropic elastic solids with rate-and-state friction, identifying critical conditions for stability and phase velocity through theoretical analysis and numerical plots.

Contribution

It introduces a stability analysis for anti-plane sliding of dissimilar anisotropic solids considering rate-and-state friction laws, providing critical wavenumber and phase velocity results.

Findings

Critical wavenumber |k|_cr depends on unperturbed velocity V_o

Phase velocity c varies with sliding conditions

Stability thresholds are identified for different material pairs

Abstract

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(ikx_1), where k is the wavenumber and x_1 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, V_o, are provided for various bi-material combinations of practical interest.