Uniaxial ratchetting in rate-independent plasticity laws

A discussion of uniaxial ratchetting in linear viscoelasticity is given in [1]. The purpose of this paper is to analyse uniaxial ratchetting in the context of rate-independent plasticity laws. The analysis is referred to constitutive models with kinematic hardening, as well as to sawtooth input functions for stress with constant absolute value for the stress rate. For such loading histories some analytical formulas and explicit expressions concerning the model response for a sufficiently large number of cycles are derived. It turns out that an analogy can be drawn between the constitutive models of linear viscoelasticity and those of rate-independent plasticity with kinematic hardening. The analogy is established by a correspondence between the line representing the elasticity law for the equilibrium stress in viscoelasticity and the axis of kinematic hardening for the plasticity models defined in this paper.