arXiv2026
Thixotropic yield stress fluids, such as paint or ketchup, are traditionally viewed as elastic structures that, under shear rates, break into viscous liquids with lumps, and reconnect at rest. An alternative framework is presented here: Upon shear, structural destruction is incomplete, leaving sufficient connections. As a result, elasticity fundamentally underlies their non-Newtonian behavior, though they do appear purely viscous under a steady shear, displaying little direct evidence of elastic rebound---same as granular media and polymers. Consequently, all three are described by the same set of evolution equations, differing only in their parameters. These equations are set up by starting from solid dynamics and allowing the elastic strain $\varepsilon^e$ to relax, which in effect interpolates between solid and fluid behavior, appropriate for systems that display both types of behavior. Incorporating in addition a two-temperature framework, tracking how energy is dissipated in two consecutive stages, yields the nonlinear model of Transient Elasticity (TE). It describes an elasticity that is transient in time yet persistent under shear. Previously validated for polymers and granular media, TE is here applied to thixotropic yield-stress fluids. As shown, it successfully accounts for a wide range of characteristic phenomena, including over- and undershoot, viscosity bifurcation, shear banding, and oscillatory rheography. Given its appropriateness across structurally diverse systems, TE offers a unified, surprisingly general account of non-Newtonian phenomena.