A further analysis on the analogy between friction and plasticity in Solid Mechanics

A strong analogy between plasticity and friction is commonly admitted in the literature while the question of applicability of plasticity principles to frictional contact problems remains open. Besides, the formulations of various friction laws and associated numerical procedures have been derived, mainly based on this analogy. More recently, the well-known asymptotic mechanisms in plasticity, such as shakedown, cyclic plasticity and ratcheting have been shown to possess analogous asymptotic states under cyclic loading on frictional contact interfaces, the relative slip playing the role of plastic strain. The present paper aims at dealing with the problem of bilateral contact with standard friction in order to show the equivalence of this problem with the one of intermediate volume governed by standard plasticity, when the volume tends towards the contact surface. An equivalence theorem is obtained and mathematically proved by an asymptotic analysis leading to localization of plastic strains on a surface. The outcomes of this equivalence theorem for problems governed by standard friction are then presented and the extension to Coulomb's friction is also discussed. A simple example is finally provided to illustrate the main theoretical results of the proved equivalence between both problems.