Nonequilibrium thermodynamics of the soft glassy rheology model

The soft glassy rheology (SGR) model is a mesoscopic framework which proved to be very successful in describing flow and deformation of various amorphous materials phenomenologically (e.g., pastes, slurries, foams, etc.). In this paper, we cast SGR in a general, model-independent framework for nonequilibrium thermodynamics called general equation for the nonequilibrium reversible-irreversible coupling. This leads to a formulation of SGR which clarifies how it can properly be coupled to hydrodynamic fields, resulting in a thermodynamically consistent, local, continuum version of SGR. Additionally, we find that compliance with thermodynamics imposes the existence of a modification to the stress tensor as predicted by SGR.

Figure 1

Variable ${\epsilon }_{\text{c}}$ sets a level in the potential-energy landscape. Within the SGR model wells below this level are approximated by harmonic traps with a trap depth $E_i$ drawn from the distribution $\rho (E,\mathit{l})$. Work performed on the system by deforming the material can be stored by the mesoscopic SGR elements. If the stored elastic energy becomes comparable to the energy depth of a well, a yielding event takes place.