Mullins effect in a filled elastomer under uniaxial tension

Abstract

Modulus softening and permanent set in filled polymeric materials due to cyclic loading and unloading, commonly known as the Mullins effect, can have a significant impact on their use as support cushions. A quantitative analysis of such behavior is essential to ensure the effectiveness of such materials in long-term deployment. In this work we combine existing ideas of filler-induced modulus enhancement, strain amplification, and irreversible deformation within a simple non-Gaussian constitutive model to quantitatively interpret recent measurements on a relevant PDMS-based elastomeric cushion. We find that the experimental stress-strain data is consistent with the picture that during stretching (loading) two effects take place simultaneously: (1) the physical constraints (entanglements) initially present in the polymer network get disentangled, thus leading to a gradual decrease in the effective cross-link density, and (2) the effective filler volume fraction gradually decreases with increasing strain due to the irreversible pulling out of an initially occluded volume of the soft polymer domain.