Discrete polymer network models for stimuli-responsive, biological, and curing networks via free energy minimization over rotations

Polymer network models allow one to model the constitutive relationships of a broader polymer network from the behavior of a single polymer chain (e.g. viscoelastic response to applied forces, applied electromagnetic fields, etc.). These network models have been used to characterize multiscale phenomena in a variety of contexts such as rubber elasticity, soft multifunctional materials, biological materials, and even the curing of polymers. For decades, a myriad of polymer network models have been developed with different representative volume elements (RVEs). Different RVEs consist of collections of differing numbers of chains that are crosslinked in many different ways. To complicate matters further, there are also competing assumptions for how macroscopic variables (e.g. deformation) are related to individual chains within the RVE.

Here we show how a simple, intuitive assumption for how the RVE rotates relative to applied loading unifies many of the disparate polymer network models and recovers arguably the most successful model for elasticity, the 8-chain model. We then briefly explore some interesting implications of the modified modelling approach for emerging applications in multiphysics, biological, and cure kinetic applications.