Non-equilibrium thermodynamics modelling of the stress-strain relationship in soft two-phase elastic-viscoelastic materials

In "soft-soft nanocomposites " based on film formation of latexes with structured particles, the combination of particle structure and interparticle crosslinking leads to materials that behave as nonlinear viscoelastic fluids at small strains and as highly elastic networks at larger strains. Similarly, in studies of flow-induced crystallization in polymers, a two-phase model is often invoked in which a soft viscoelastic component is coupled with a rigid semi-crystalline phase providing stiffness. In the present work, we use the framework of non-equilibrium thermodynamics (NET) to develop stress-strain relationships for such two-phase systems characterized by a viscoelastic and an elastic component by making use of two conformation tensors: the first describes the microstructure of the viscoelastic phase while the second is related to the elastic Finger strain tensor quantifying the deformation of the elastic phase due to strain and is responsible for strain-hardening. The final transport equations are formulated in the context of the generalized bracket formalism of NET and can describe the rheological behavior and mechanical response of a large variety of soft materials ranging from rubbers to artificial tissues.