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From Generalized Theories of Media with Fields of Defects to Closed Variational Models of the Coupled Gradient Thermoelasticity and Thermal Conductivity

  • Sergey LurieEmail author
  • Petr Belov
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 120)

Abstract

A gradient theory of the coupled theory of elasticity, thermoelasticity and thermal conductivity based on a generalized model of media with fields of defects is developed. Defectiveness is defined only by free dilatation and the tensor of incompatible distortions is determined by the spherical tensor. In the general case, the unified model includes scale parameters that are responsible for mechanical and temperature scale effects. In the particular case the proposed model describes the gradient thermoelasticity, in which effects are controlled by a mechanical scale parameter, and in the limit case, it describes the classical thermoelasticity, when this parameter tends to zero. The analysis of boundary problems of the general model is given. Particular cases are considered, and it is shown that gradient thermal conductivity and thermoelasticity make it possible to simulate thermal resistance and size effects.

Keywords

Generalized Mindlin’s medium Free dilatations Gradient thermoelasticity Reversible thermal conductivity Cohesive interactions Scale effects 

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Notes

Acknowledgements

The authors are deeply grateful to Professor Holm Altenbach for professional and useful discussions of our research. This work was carried out with support from the Russian Government Foundation of Institute of Applied Mechanics of RAS, Project -AAAA-A-19-119012290177-0 and particularly supported by the Russian Foundation for Basic Research grant 18-01-00553-1.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of Applied Mechanics of Russian Academy of SciencesMoscowRussia

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