Abstract
Our study is concerned with the mixed initial-boundary value problem for a dipolar body in the context of a heat-flux dependent theory for the dipolar thermoelastic bodies. We take into account a set of independent constitutive variables including the heat flux vector. Also, the set of basic equations which govern the behavior of such a body is completed by including an equation of evolution for the components of this vector. The uniqueness result, regarding the solution of the mixed problem, which concludes our study assures the consistency of the constructed theory.
Highlights
In the published studies during the past decades, widespread attention has been given to new continuum theories in order to admit a finite speed for the propagation of waves, which are called the second-sound theories
If the heat flux of components qi is among the independent constituent variables the constitutive equations have the following form τij = ∂εij, σij = ∂γij, μijk = ∂ χijk, η = − ∂θ, (8)
We introduce E from (7) in (4), take into account that the function Φ has the independent variables εij, γij, χijk, θ, θ,i, qi and we carry out the differentiation with respect to these variables
Summary
In the published studies during the past decades, widespread attention has been given to new continuum theories in order to admit a finite speed for the propagation of waves, which are called the second-sound theories. By using some thermodynamical considerations, we deduce the constitutive equations which characterize our heat-flux dependent dipolar thermoelasticity theory. If the heat flux of components qi is among the independent constituent variables the constitutive equations have the following form τij = ∂εij , σij = ∂γij , μijk = ∂ χijk , η = − ∂θ , (8)
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