Nonlinear Viscoelasticity and Generalized Failure Criterion for Polymer Gels

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 describe this scenario for a model protein gel using an integral
constitutive equation built upon the linear and the nonlinear viscoelastic
properties of the gel. We show that this formalism predicts quantitatively
the gel mechanical response in shear start-up experiments, up to the
onset of macroscopic failure. Moreover, we couple the computed stress
response with Bailey’s durability criterion for brittle solids
in order to predict the critical values of the stress σc and strain γc at failure. The excellent
agreement between theory and experiments suggests that failure in
this soft viscoelastic gel is a Markovian process and that Bailey’s
failure criterion extends beyond hard materials such as metals, glasses,
or minerals.