Transversely isotropic cyclic stress-softening model for the Mullins effect

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