Surana, K.S. and Carranza, C.H. (2022).  Nonclassical continuum theories for fluent media incorporating rotation rates and their thermodynamic consistency.  ZAMM- Journal of Applied Mathematics and Mechanics/Zeitschrift fr Angewandte Mathematik und Mechanik, 103, 1.

Abstract

In this paper, we present three micropolar nonclassical continuum theories (NCCT) for fluent medium in which a material point always has velocities 𝑣¯ as degrees of freedom, additionally, we consider (i) in the first NCCT, we consider classical or internal rotations rates 𝑖𝑟⁢𝛩¯ (known) due to skew-symmetric part of velocity gradient tensor; (ii) in the second NCCT, we consider rotation rates 𝑖𝑟⁢𝛩¯ and Cosserat or microrotation rates 𝑒𝑟⁢𝛩¯ (unknown degrees of freedom); (iii) in the third NCCT, we consider Cosserat or microrotation rates 𝑒𝑟⁢𝛩¯ only, hence 𝑖𝑟⁢𝛩¯ are neglected. Conservation and balance laws (CBL) and the constitutive theories are derived for all three NCCT. We examine consistent choice of kinematic variables, modification of the CBL of classical continuum theories (CCT) due to new physics and determine if the new physics of rotation rates requires additional balance law. All three NCCT derived here are examined for thermodynamic and/or mathematical consistency and are compared with published works. Model problem studies are also presented.