Disorder, pre-stress and non-affinity in polymer 8-chain models

TL;DR

This paper investigates how pre-stress and non-affinity influence the mechanical response of polymer networks using an extended 8-chain Arruda-Boyce model, revealing significant effects even in linear regimes.

Contribution

It introduces spatial disorder and pre-stress into the 8-chain model, analyzing their impact on non-affinity and mechanical response, and compares nonlinear and linearized models.

Findings

Pre-stress suppresses non-affinity in polymer models.

Full polymer models differ significantly from linearized versions.

Pre-stress causes stiffening of the bulk response.

Abstract

To assess the role of single-chain elasticity, non-affine strain fields and pre-stressed reference states we present and discuss the results of numerical and analytical analyses of modified 8-chain Arruda-Boyce model for cross-linked polymer networks. This class of models has proved highly successful in modeling the finite-strain response of flexible rubbers. We extend it to include the effects of spatial disorder and the associated non-affinity, and use it to assess the validity of replacing the constituent chain's nonlinear elastic response with equivalent linear, Hookean springs. Surprisingly, we find that even in the regime of linear response, the full polymer model gives very different results from its linearized counterpart, even though none of the chains are stretched beyond their linear regime. We demonstrate that this effect is due to the fact that the polymer models are under considerable pre-stress in their ground state. We show that pre-stress strongly suppresses non-affinity in these unit cell models, resulting in a marked stiffening of the bulk response. The effects of pre-stress we discuss may explain why fully affine mechanical models, in many cases, predict the bulk mechanical response of disordered stiff polymer networks so well.