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<p>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.</p>

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On a theory of thermoelasticity with the second gradient of temperature

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月29日

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  • D. Ieşan,
  • R. Quintanilla

摘要

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.