Analysis of a statistical stick-slip model

Abstract

We study mathematical details of a statistical stick-slip model of a group of springs. We present the conditions for the steady shear stress σ̄ to be N-shaped and obtain a general viewpoint of the linear stability analysis for a slip model coupled with macroscopic elasticity. Our model can be reduced to an ordinary differential equation under an approximation, and the reduced slip equation is found to be equivalent to a slip equation of a more phenomenological slip model.