A recoverable strain–based constitutive model for complex fluids

We present a thermodynamically consistent, closed constitutive equation for complex fluids based on a continuum-mechanical measure of recoverable elastic strain. The model, inspired by plasticity models, is derived using the nonequilibrium thermodynamic GENERIC framework. The difference with classical rheological models is the treatment of the recoverable strain as internal variable to capture irreversible structural evolution. Using only linear material parameters, the resulting model already captures a remarkably wide range of nonlinear rheological responses and accurately predicts strain-rate–dependent start-up shear experiments for a single-mode wormlike micellar solution. We further permit a statistical interpretation of the internal recoverable-strain variable by introducing a local-field description, which enables a transparent comparison with mesoscopic approaches such as bead–spring chain models and temporary network theories. Using the elastic-strain framework, we re-examine the macroscopic origin of shear thinning without recourse to microscopic relaxation processes or structural kinetics. Rather, shear thinning follows directly from the convective evolution of the elastic strain. Beyond providing a compact constitutive equation, this work contributes to the broader objective of establishing an accessible and didactic framework for complex-fluid modeling. The approach is grounded in a clearly defined internal elastic state variable, the recoverable strain, and a thermodynamically consistent structure, enabling the description of both purely elasto-viscoplastic materials (such as dense suspensions, emulsions and foams, networks, and gels) and key nonlinear features of viscoelastic materials (including surfactant solutions and polymer solutions and melts). • A GENERIC and plasticity based approach to describe complex fluids. • A new simple, closed constitutive equation for the extra stress. • An new angle on the origin of shear thinning.