Orthotropic cyclic stress-softening model for pure shear during repeated loading and unloading

TL;DR

This paper develops an orthotropic cyclic stress-softening model for pure shear in rubber, capturing anisotropic effects, hysteresis, stress-relaxation, and residual strain, and shows good agreement with experimental data.

Contribution

It introduces a novel orthotropic model for cyclic stress-softening in rubber, incorporating anisotropy, hysteresis, and residual strains, extending existing isotropic models.

Findings

Model accurately fits experimental stress-strain data.

Captures anisotropic stress response due to strain-induced anisotropy.

Includes effects of hysteresis, stress-relaxation, and residual strain.

Abstract

We derive an orthotropic model to describe the cyclic stress-softening of a carbon-filled rubber vulcanizate through multiple stress-strain cycles with increasing values of the maximum strain. We specialize the deformation to pure shear loading. As a result of strain-induced anisotropy following on from initial primary loading, the material may subsequently be described as orthotropic because in pure shear there are three different principal stretches so that the strain-induced anisotropy of the stress response is different in each of these three directions. We derive non-linear orthotropic models for the elastic response, stress relaxation and residual strain in order to model accurately the inelastic features associated with cyclic stress softening. We then develop an orthotropic version of the Arruda-Boyce eight-chain model of elasticity and then combine it with the ideas previously developed in this paper to produce an orthotropic constitutive relation for the cyclic stress-softening of a carbon-filled rubber vulcanizate. The model developed here includes the widely-occurring effects of hysteresis, stress-relaxation and residual strain. The model is found to compare well with experimental data. } {Mullins effect, stress-relaxation, hysteresis, residual strain, orthotropy.}