A cyclic stress softening model for the Mullins effect

TL;DR

This paper introduces a comprehensive cyclic stress softening model for the Mullins effect in hyperelastic materials, effectively capturing stress relaxation, hysteresis, and residual strains in carbon-filled rubber vulcanizates.

Contribution

It develops a novel model integrating inelastic features with the Arruda-Boyce elasticity framework, uniquely addressing all aspects of cyclic stress-softening in such materials.

Findings

Model accurately fits experimental data

Describes stress-softening and hysteresis effectively

Predicts residual strain and creep reliably

Abstract

In this paper the inelastic features of stress relaxation, hysteresis and residual strain are combined with the Arruda-Boyce eight-chain model of elasticity, in order to develop a model that is capable of describing the Mullins effect for cyclic stress-softening of an incompressible hyperelastic material, in particular a carbon-filled rubber vulcanizate. We have been unable to identify in the literature any other model that takes into consideration all the above inelastic features of the cyclic stress-softening of carbon-filled rubber. Our model compares favourably with experimental data and gives a good description of stress-softening, hysteresis, stress relaxation, residual strain and creep of residual strain. Keywords: Mullins effect, stress-softening, hysteresis, stress relaxation, residual strain, creep of residual strain. MSC codes: 74B20, 74D10, 74L1