Elastoviscoplastic Model and Concept of Slip

Abstract

The model of elastoviscoplastic medium is based on the concept of slip proposed by Batdorf and Budiansky. The conditions of slip on a slip plane take into account the dependence of tangential stresses on slip velocity. But when the viscosity is low, they are almost similar to the dry friction conditions. Under some assumptions we succeeded in integrating the plastic shear rates over all possible slip planes in case of arbitrary three‐dimensional stress state and obtained an expression for the plastic strain rate tensor.

The Integrable Variant of the Theory of Slip

“…In [8] is shown, that in the approximation under consideration 13 1 S ε = + , 1 ε << at the contour the values of the integration limits over ϑ can be depicted as:…”

“…Let's consider them individually. τ − > This condition is thoroughly investigated in [8]. As a result it was obtained that the integration limits over ϑ are given by:…”

“…In the given work, though taking into account the method of [8], is examined the classical variant of the slip condition. Under some assumptions it's possible to fulfill the integration for an arbitrary three-dimensional stress state and to obtain the closed variant of the elastoplastic model, which turns out to be a variant of the plastic flow theory.…”

“…In [7,8] the concept of slip has been used to obtain the equations which describe the behaviour of the elastoviscoplastic medium. In this case there is only one criterion which takes part in formulation of the local condition of slip -the excess of the tangential stress on a slip over some critical level ("the local yield").…”

Wall slip effects in Rayleigh–Bénard convection of viscoplastic materials

“…Previous studies have shown that yield–stress fluids exhibit wall slip, leading to dispersion phenomena adjacent to the walls (Barnes, 1995; Nikitin, 2007; Ballesta et al. , 2012; Damianou and Georgiou, 2014; Jing et al.…”