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Continuum Mechanics and Thermodynamics
Published in: Continuum Mechanics and Thermodynamics 1/2023

26-10-2022 | Original Article

Thermodynamic consistency of nonclassical continuum theories for solid continua incorporating rotations

Authors: K. S. Surana, S. S. C. Mathi

Published in: Continuum Mechanics and Thermodynamics | Issue 1/2023

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Abstract

In this paper, we present derivations of three micropolar nonclassical continuum theories in which a material point always has displacements \( \pmb {\varvec{u }} \) as degrees of freedom. Additionally, (i) in the first nonclassical continuum theory (NCCT) we consider internal or classical rotations \({}_i \pmb {\varvec{\varTheta }}\) (known) due to skew symmetric part of the deformation gradient tensor; (ii) in the second NCCT, we consider both internal rotations \({}_i \pmb {\varvec{\varTheta }}\) and external or Cosserat or microrotations \({}_e \pmb {\varvec{\varTheta }}\) (unknown degrees of freedom); (iii) in the third NCCT, we consider Cosserat rotations \({}_e \pmb {\varvec{\varTheta }}\) only; hence, \({}_i \pmb {\varvec{\varTheta }}\) are neglected in this NCCT. We examine consistent choice of kinematic variables, modifications of conservation and balance laws of classical continuum theories (CCTs) due to the presence of new physics of rotations and determine whether the consideration of rotations requires additional balance laws. NCC theories derived here are examined for thermodynamic and mathematical consistency and are compared with published works. Model problem studies are also presented.
previous article A model of dual-phase-lag thermoelasticity for a Cosserat body
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Metadata
Title
Thermodynamic consistency of nonclassical continuum theories for solid continua incorporating rotations
Authors
K. S. Surana
S. S. C. Mathi
Publication date
26-10-2022
Publisher
Springer Berlin Heidelberg
Published in
Continuum Mechanics and Thermodynamics / Issue 1/2023
Print ISSN: 0935-1175
Electronic ISSN: 1432-0959
DOI
https://doi.org/10.1007/s00161-022-01163-y

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