A symmetric hyperbolic non-isothermal model for viscoelastic solids and non-Newtonian fluids
Year: 2026
Type: article
Abstract: Viscoelastic materials and non-Newtonian fluids often exhibit a pronounced sensitivity to temperature, which significantly influences their mechanical response. Recently, Ruggeri proposed a nonlinear viscoelastic model within the framework of Rational Extended Thermodynamics and showed that, by a suitable modification of the production term, the same structure can also describe non-Newtonian fluids with a finite relaxation time in an isothermal setting. In this paper, we extend these models to non-isothermal processes in one spatial dimension in the absence of heat flux. By coupling the balance laws of momentum and energy with a balance law for an additional nonequilibrium stress variable and enforcing the entropy principle together with convexity, we derive a thermodynamically admissible system of nonlinear evolution equations. The resulting model is symmetric hyperbolic, which guarantees local well-posedness of the Cauchy problem and admits weak solutions, including shocks. For Newtonian production terms, we further verify the Shizuta–Kawashima condition, yielding global-in-time smooth solutions for sufficiently small initial data. A unified framework is thus obtained, capable of describing either nonlinear thermo-viscoelastic behavior or temperature-dependent non-Newtonian rheology in the parabolic (zero-relaxation) limit. The principal-subsystem viewpoint clarifies the nesting of reduced theories: in particular, the previously proposed isothermal model is recovered as a principal subsystem, and classical hyperelastic dynamics emerges as a common principal subsystem of the isothermal and Euler-type limits.
Authors: Takashi Arima, Tommaso Ruggeri
Language: English
Subfield: Mechanics of Materials
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,980
Award: G7495759285
OpenAlex ID: W7127167340