Spatial behavior of the dual-phase-lag deformable conductors

Abstract

The purpose of the present article is to investigate about the spatial behavior question for a thermoelastic model describing the intrinsic coupling between the high-order effects of thermal lagging and the ultrafast deformation. The main achievements of this study consist of four types of results concerning the spatial behavior, namely: I) when the orders of approximation in the constitutive equation for the heat flux differ by one and (i) when short elapsed times are considered we establish a result describing the domain of influence that characterizes the wave like-behavior, while (ii) when long elapsed times are considered then we establish in the inside of the influence domain, some appropriate exponential decay estimates with uniform in time decay rate and II) when approximations of the same order are considered and (iii) when short elapsed times are considered we establish some exponential decaying estimates of Saint Venant type with decay rate depending on time, while (iv) when long elapsed times are considered then we establish some appropriate Saint Venant exponential estimates with uniform in time decaying rate or Phragmén-Lindelöf alternative (for a semi-infinite cylinder). The last two results characterize the diffusion like-behavior of the model. The reported spatial behavior is established for a large class of constitutive equations for the heat flux under mild assumptions upon the characteristics of the high-order thermal lagging and for both finite and semi-infinite cylinders.

Keywords:

• Deformable conductors
• heat transfer
• lagging behavior of high order
• spatial behavior
• spatial decaying estimates of Saint Venant type
• theorem of influence domain

Acknowledgments

This article is dedicated to Professor Richard B. Hetnarski on the occasion of his 90th birthday and to the 40th anniversary of the Journal of Thermal Stresses.

Disclosure statement

No potential conflict of interest was reported by the authors.