Nonlinear viscoelasticity and generalized failure criterion for polymer gels

TL;DR

This paper develops a nonlinear viscoelastic model for polymer gels that predicts failure behavior and crack growth, validated by experiments, extending durability concepts to soft materials.

Contribution

It introduces a nonlinear integral constitutive equation for polymer gels and couples it with Bailey's criterion to predict failure stress and strain.

Findings

Model accurately predicts gel response up to failure

Crack growth follows a Markovian process

Bailey's criterion applies to soft viscoelastic gels

Abstract

Polymer gels behave as soft viscoelastic solids and exhibit a generic nonlinear mechanical response characterized by pronounced stiffening prior to irreversible failure, most often through macroscopic fractures. Here, we aim at capturing the latter scenario for a protein gel using a nonlinear integral constitutive equation built upon ($i$) the linear viscoelastic response of the gel, here well described by a power-law relaxation modulus, and ($ii$) the nonlinear viscoelastic properties of the gel, encoded into a "damping function". Such formalism predicts quantitatively the gel mechanical response to a shear start-up experiment, up to the onset of macroscopic failure. Moreover, as the gel failure involves the irreversible growth of macroscopic cracks, we couple the latter stress response with Bailey's durability criterion for brittle solids in order to predict the critical values of the stress $\sigma_c$ and strain $\gamma_c$ at the failure point, and how they scale with the applied shear rate. The excellent agreement between theory and experiments suggests that the crack growth in this soft viscoelastic gel is a Markovian process, and that Baileys' criterion extends well beyond hard materials such as metals, glasses, or minerals.