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Generalized thermo-viscoelasticity with memory-dependent derivative: uniqueness and reciprocity

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Abstract

This article theoretically demonstrates the reciprocity and uniqueness theorems for generalized theory of thermo-viscoelasticity involving memory-dependent derivative (MDD). To prove the theorems, a thermo-viscoelastic initial-boundary value problem under the domain of three-phase-lag (TPL) model is taken into consideration for an isotropic, homogeneous medium. The theorems are proved with the help of the Laplace transform of the thermophysical quantities. Finally, a few special cases in the generalized theory of thermo-elasticity and thermo-viscoelasticity with MDD and without MDD are derived from the present model.

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Acknowledgements

We are grateful to the reviewers for their valuable comments and suggestions to improve the quality of the paper and Council of Scientific and Industrial Research (CSIR), New Delhi (Grant No. 08/003(0116)/2016-EMR-I), for the financial support to carry out this research work.

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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. Generalized thermo-viscoelasticity with memory-dependent derivative: uniqueness and reciprocity. Arch Appl Mech 91, 965–977 (2021). https://doi.org/10.1007/s00419-020-01799-9

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