On a theory of thermoelasticity with the second gradient of temperature
Abstract
Abstract This paper deals with a linear theory of non-simple thermoelastic materials based on Green–Naghdi thermomechanics. We use an entropy production inequality, a thermal displacement and the entropy flux tensor to establish a theory of thermoelasticity in which the second displacement gradient and the second temperature gradient are included in the classical set of independent constitutive variables. The reciprocity theorem, a variational theorem, a uniqueness and a structural stability result are established. The existence and the impossibility of localization are also investigated. In the equilibrium theory, the deformation of an elastic space with a spherical cavity is studied.
Fields of Study & Subjects
Nonlocal and gradient elasticity in micro/nano structures
Thermoelastic and Magnetoelastic Phenomena
Contact Mechanics and Variational Inequalities
Publication details
- Journal / source
- Zeitschrift für angewandte Mathematik und Physik
- Publisher
- Springer Science and Business Media LLC
- Volume
- 77
- Issue
- 6
- Publication date
- 29 May 2026
- Language
- EN