GENERALIZED THERMOELASTICITY

TLDR

Generalized Thermoelasticity refers to hyperbolic thermoelasticity where thermomechanical loads propagate as waves through a solid. The article surveys models of thermoelastic waves in solid bodies. The survey focuses on transient thermoelastic waves, reviewing five key models—L‑S, G‑L, H‑I, G‑N, and C‑T—and their theoretical and practical significance. The review presents domain‑of‑influence theorems, uniqueness results, and one‑dimensional closed‑form solutions, but notes that none of the five models has been experimentally verified except in a limiting rigid‑conductor case, highlighting a challenge for future research.

Abstract

This is a survey article on the modeling of thermoelastic waves in a solid body. The term ''Generalized Thermoelasticity'' stands for a Hyperbolic Thermoelasticity in which a thermomechanical load applied to a body is transmitted in a wave-like manner throughout the body. Only transient thermoelastic waves are included in the survey. The modeling covers: (i) L-S model (Lord and Shulman, 1967), (ii) G-L model (Green and Lindsay, 1972), (iii) H-I model (Hetnarski and Ignaczak, 1996), (iv) G-N model (Green and Naghdi, 1993), and (v) C-T model (Chandrasekharaiah and Tzou, 1998). Attention focuses on the theoretical and practical significance of these models. Theoretical results include the domain of influence theorems, uniqueness as well as one-dimensional closed-form solutions. Except for a limiting case when the models reduce to rigid heat conductors, none of the five models has been verified by a combined thermoelastic experiment up to date, so their applications to real thermoelastic bodies present a challenge for future generations of researchers in the field.