Toward rational design of drug delivery substrates: I. Mixture theory for two-scale biocompatible polymers

To rationally design drug release substrates, much as in the rational design of the drugs themselves, the biocompatible polymer physics, chemistry, and biology must be married in a mechanistic fashion via mathematics, and the mathematics must in turn be implemented on the computer for predictive purposes. Here we take a first step in this direction by developing two-scale, thermodynamically consistent, constitutive models for swelling, glassy, biocompatible polymers. Specifically, we apply mixture theory with averaged field equations to obtain thermodynamically consistent constitutive models for both charged and uncharged viscoelastic hydrogels in the glassy state. In Part II of this article we extend these results to a three-scale setting with two fluid phases on the macroscale. We develop constitutive models, insert these into the macroscale field equations, simplify, and solve an imbibition problem by the finite element method.