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Variational principle and reciprocity theorem on the temperature-rate-dependent poro-thermoelasticity theory

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Abstract

The present work is concerned with the temperature-rate-dependent theory of poro-thermoelasticity for anisotropic homogeneous medium and aims to establish the variational principle based on this theory for the fluid-saturated poro-thermoelastic medium. Here, the principle of virtual work is applied to derive the expressions for the generalized strain energy, Biot’s free energy, and the total work done by the system during the thermo-mechanical process. Further in view of this, the variational principle is established in the context of the temperature-rate-dependent poro-thermoelasticity. We also prove that a reciprocity theorem results for a general problem of poro-thermoelasticity of an anisotropic medium.

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Acknowledgements

The authors thankfully acknowledge the constructive suggestions by reviewers and the editor to improve the quality of the present paper.

Funding

One of the authors, Om Namha Shivay, thankfully acknowledges the full financial assistance of the SRF Fellowship (Roll Number 433492, Reference Number 21/06/2015 (i) EU-V) by the University Grant Commission (UGC), India, to carry out the present work.

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  1. Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, 221005, India

    Om Namha Shivay & Santwana Mukhopadhyay

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  1. Om Namha Shivay
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Correspondence to Om Namha Shivay.

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Shivay, O.N., Mukhopadhyay, S. Variational principle and reciprocity theorem on the temperature-rate-dependent poro-thermoelasticity theory. Acta Mech 232, 3655–3667 (2021). https://doi.org/10.1007/s00707-021-02996-5

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  • DOI: https://doi.org/10.1007/s00707-021-02996-5

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