A one-dimensional isothermal model of viscoelastic solids in which the viscous stress is carried by an extra balance law with purely local constitutive equations, rather than by a memory integral, so the whole model follows from the universal principles of Rational Extended Thermodynamics: entropy compatibility, convexity, and symmetric hyperbolic form. A student learns how those principles plus Maxwellian iteration fix the system uniquely once the elastic energy, the viscous energy and a deformation-dependent viscosity coefficient are known. In the linear limit the viscous stress obeys the Maxwell equation and the total stress a Zener standard-linear-solid law, and the Shizuta-Kawashima K-condition then guarantees globally smooth solutions for small initial data.
This arxiv paper develops a nonlinear constitutive framework for viscoelastic materials using rational extended thermodynamics, addressing how soft materials with hyperelastic behavior exhibit nonlin…