Dynamic Surface Solutions in Linear Elasticity and Viscoelasticity With Frictional Boundary Conditions

Abstract

This paper presents a study on the dynamic stability of the steady frictional sliding of a linear elastic or viscoelastic half-space compressed against a rigid plane which moves with a prescribed nonvanishing tangential speed. The system of differential equations and boundary conditions that govern the small plane oscillations of the body about the steady-sliding state of deformation is established. It is shown that for large coefficient of friction and large Poisson’s ratio the steady-sliding of the elastic body is dynamically unstable. This instability manifests itself by growing surface oscillations which necessarily propagate from front to rear and which in a short time lead to situations of loss of contact or stick. Similarly to what has been found with various finite dimensional frictional systems, these flutter type surface instabilities result from the intrinsic nonsymmetry of dry friction contact laws. The effect of viscous dissipation within the deformable body is also assessed: when viscous dissipation is present larger coefficients of friction are required for the occurrence of surface solutions propagating and growing from front to rear.

Rate and state dependent friction and the stability of sliding between elastically deformable solids

“…The problem of stability of steady sliding between dissimilar materials has received much recent attention in theoretical modeling (Renardy, 1992;Martins et al, 1992Adams, 1995;Martins and Simões, 1995;Simões and Martins, 1998;Cochard and Rice, 2000;Ranjith and Rice, 2001). That work has, mostly, neglected rate and state e ects, instead assuming a constant coe cient of friction f, and has focused on the coupling between inhomogeneous slip and alteration of normal stress.…”

Using symbolic computation in the characterization of frictional instabilities involving orthotropic materials

“…5) with an exponentially growing oscillatory motion with respect to the steady sliding solution. The first results of frictional instabilities in half spaces presented by Martins et al (1992;1995) were obtained with no help from symbolic computation. In the cited papers, the authors derived manually the conditions which completely Using symbolic computation in the characterization of frictional instabilities.…”

“…A similar procedure for orthotropic materials is out of question, as will be seen below. The steady sliding solution, whose instability conditions we wish to determine, is defined by σ s yy (x, 0) < 0, v s (x, 0) = 0 (persistent contact) and σ s yx (x, 0) + μσ s yy (x, 0) = 0 (persistent sliding) (see Martins et al, 1995). The upper rigid surface is sliding to the left with a nonvanishing velocity S which is compatible with a shear stress σ frictional boundary conditions at y = 0: σ yx (x, 0, t)+ μσ yy (x, 0, t) = 0.…”

Thermodynamics of surface degradation, self-organization and self-healing for biomimetic surfaces

“…The energy dissipated at the interface can be smaller than the work of the friction force, mP 0 V 0 , which leads to the instabilities found by Adams (1995) and Martins et al (1995). The Adams-Martins instabilities occur during frictional sliding of two rough or smooth elastic half-spaces with a constant coefficient of friction (Nosonovsky & Adams 2004).…”