The two-temperature theory is more realistic than the one-temperature theory in the case of generalized thermoelasticity
Baroni, "High-pressure lattice dynamics and thermoelasticity
of MgO," Physical Review B, vol.
(1) The equation of the coupled thermoelasticity
(C-T theory) is obtained when
In particular, electrochemistry , heat conduction process , thermoelasticity
, plasma physics , semiconductor modeling , biotechnology , control theory, and inverse problems .
The classical coupled thermoelasticity
theory proposed by Biot  with the introduction of the strain-rate term in the Fourier heat conduction equation leads to a parabolictype heat conduction equation, called the diffusion equation.
According to thermoelasticity
, the deformation,stress [[delta].sub.def]) of polyurethane elastomers is composed of the enlropic pari and the energetic part .
A survey article of representative theories in the range of generalized thermoelasticity
is due to Hetnarski and Ignaczak .
The different models of thermoelasticity
theory based on the equation of heat convection and the elasticity equations.
of Sidney), experts on fracture mechanics on non-homogeneous materials, introduce basic thermoelasticity
concepts (the mechanics of magneto-electro-elastic coupling), and proceed to fracture problems in layered materials, including transient fractures of a piezoelectric layer bonded to an elastic substrate, thermoelastic fractures of non-homogeneous materials, crack tip fields in media with magneto-electro-elastic coupling, fracture mechanics of non-homogeneous piezoelectric and magneto-electro-elastic materials, thermally induced cracking of piezoelectric materials, and transient thermal fracture of piezoelectric materials' structures.
The classical uncoupled theory of thermoelasticity
predicts two phenomena that are not compatible with physical observations.
Replacing the dots by the deformation gradient F of the finite strain theory in expression (1), we have the standard theory of thermoelasticity
, which is complemented by Fourier's law of heat conduction.
Solutions of Galerkin type and uniqueness theorems in the theory of thermoelasticity
for materials with voids are proved in [11, 12].