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On the spatial behavior of thermal signals in generalized thermoelasticity with memory-dependent derivative

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Abstract

In this article, a novel mathematical model is theoretically developed by incorporating a memory-dependent derivative (MDD) into the temperature-rate-dependent thermoelasticity theory (Green–Lindsay) on three mathematical aspects in order to study the spatial behavior of the thermal signals in an isotropic, homogeneous, thermoelastic continuum. Firstly, to ensure the thermodynamic consistency of the proposed model, the constitutive equations involving MDD are derived from the principle of thermodynamics or continuum mechanics in conjunction with the corresponding kinematic assumptions. Secondly, to prove the finite propagation speeds of the thermal signals of the proposed model, a domain of influence theorem is established. Finally, to analyze the spatial propagation of the thermal signals inside the domain of influence, a spatial decay theorem is established. As an immediate outcome of this theoretical analysis, a uniqueness theorem of the proposed model is also derived.

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Acknowledgements

The authors are grateful to the Editor and the Reviewers for their valuable comments and suggestions for the improvement of the quality of the article. This research work is financially supported by Council of Scientific and Industrial Research (CSIR), New Delhi, via Grant Number 08/003(0116)/2016-EMR-I.

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  1. Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Shibpur, Howrah, West Bengal, 711103, India

    Indranil Sarkar & Basudeb Mukhopadhyay

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  1. Indranil Sarkar
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Correspondence to Indranil Sarkar.

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Sarkar, I., Mukhopadhyay, B. On the spatial behavior of thermal signals in generalized thermoelasticity with memory-dependent derivative. Acta Mech 231, 2989–3001 (2020). https://doi.org/10.1007/s00707-020-02687-7

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  • DOI: https://doi.org/10.1007/s00707-020-02687-7

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