Surana, K.S., and Mathi, S.S.C.  (2022) Thermodynamic consistency of nonclassical continuum theories for solid continua incorporating rotations.  Continuum Mechanics and Thermodynamics, 35, 17-59.

Abstract

In this paper, we present derivations of three micropolar nonclassical continuum theories in which a material point always has displacements u as degrees of freedom. Additionally, (i) in the first nonclassical continuum theory (NCCT) we consider internal or classical rotations iΘ (known) due to skew symmetric part of the deformation gradient tensor; (ii) in the second NCCT, we consider both internal rotations iΘ and external or Cosserat or microrotations eΘ (unknown degrees of freedom); (iii) in the third NCCT, we consider Cosserat rotations eΘ only; hence, iΘ 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.