Nonlinear rheological models for structured interfaces

The GENERIC formalism is a formulation of nonequilibrium thermodynamics ideally suited to develop nonlinear constitutive equations for the stress-deformation behavior of complex interfaces. Here we develop a GENERIC model for multiphase systems with interfaces displaying nonlinear viscoelastic stress-deformation behavior. The link of this behavior to the microstructure of the interface is described by including a scalar and a tensorial structural variable in the set of independent surface variables. We derive an expression for the surface stress tensor in terms of these structural variables, and a set of general nonlinear time evolution equations for these variables, coupling them to the deformation field. We use these general equations to develop a number of specific models, valid for application near equilibrium, or valid for application far beyond equilibrium.