Transversely isotropic cyclic stress-softening model for the Mullins effect

TL;DR

This paper develops a transversely isotropic hyperelastic model incorporating stress-softening and Mullins effect, accurately capturing cyclic behavior in rubber materials through advanced constitutive equations.

Contribution

It introduces a novel transversely isotropic stress-softening model combining non-linear elasticity and the Arruda-Boyce framework for the first time.

Findings

Model accurately predicts Mullins effect in rubber vulcanizates.

Captures stress relaxation, residual strain, and creep behaviors.

Applicable to transversely isotropic hyperelastic materials.

Abstract

This paper models stress softening during cyclic loading and unloading of an elastomer. The paper begins by remodelling the primary loading curve to include a softening function and goes on to derive non-linear transversely isotropic constitutive equations for the elastic response, stress relaxation, residual strain and creep of residual strain. These ideas are combined with a transversely isotropic version of the Arruda-Boyce eight-chain model to develop a constitutive relation that is capable of accurately representing the Mullins effect during cyclic stress-softening for a transversely isotropic, hyperelastic material, in particular a carbon-filled rubber vulcanizate. Keywords: Mullins effect, stress-softening, hysteresis, stress relaxation, residual strain, creep of residual strain, transverse isotropy. MSC codes: 74B20, 74D10, 74L15