  Polymer network models construct 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.). Network
models have been used for 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 differing numbers of chains, arranged in different
ways, and with differing symmetries. To complicate matters further, there are
also competing assumptions for how macroscopic variables (e.g. deformation) are
related to individual chains within the network model. In this work, we propose
a simple, intuitive assumption for how the network locally rotates relative to
applied loading (e.g. stresses, external fields) and show that this assumption
unifies many of the disparate polymer network models--while also recovering one
of the most successful models for rubber elasticity, the Arruda-Boyce $8$-chain
model. The new assumption is then shown to make more intuitive predictions
(than prior models) for stimuli-responsive networks with orientational energies
(e.g. electroactive polymers), which is significant for shape morphing and
designing high degree of freedom actuators (e.g. for soft robotics). Lastly, we
unveil some surprising consequences of the new model for the phases of
multistable biopolymer and semi-crystalline networks.
