Journal of Pure and Applied Mathematics: Advances and ApplicationsAuthor's: K. S. Surana, M. Powell and J. N. Reddy
Pages: [89] - [150]
Received Date: September 29, 2015
Submitted by:
DOI: http://dx.doi.org/10.18642/jpamaa_7100121545
In recent papers [1, 2] the authors presented an internal polar
continuum theory for solid continua (under the name a polar
continuum theory) in which varying internal rotations and
conjugate moments between neighboring material points that exist in
all deforming homogeneous and isotropic solid continua were
incorporated in the derivations of the conservation and balance laws.
It was shown that this theory leads to a more complete thermodynamic
framework as it incorporates the additional physics due to varying
internal rotations that is completely neglected in the currently used
thermodynamic framework. The currently used thermodynamic framework
for solid continua is a subset of the internal polar continuum theory
presented in [1, 2].
Just as in non-internal polar thermoelastic solid continua, in
internal polar thermoelastic solid continua also (both compressible
and incompressible), the mechanical deformation is reversible, hence
in such continua there is no mechanism of conversion of mechanical
energy into any other forms, hence the rate of mechanical work does
not contribute to the rate of entropy production. Thus, in internal
polar thermoelastic solid continua the rate of mechanical work
equilibrates with the rate of change of kinetic energy and the rate of
change of strain energy. In this paper, this aspect of the physics is
utilized to derive alternate forms of the first and second laws of
thermodynamics applicable to internal polar thermoelastic solid
continua. In these derivations of the alternate forms, the strain
energy density is removed from the entropy inequality so that the
resulting entropy inequality is purely a statement of the rates of
entropies. This form is meritorious in demonstrating that the
constitutive theories for the stress tensor and moment tensor are
independent of the entropy inequality, hence the constitutive theories
for the stress tensor and moment tensor have no thermodynamic
restrictions. In this paper we consider both forms of the entropy
inequality, the entropy inequality containing strain energy density
and the one in its absence and other approaches and their
applicability in the derivations of the constitutive theories for
internal polar thermoelastic solid continua. The solid continua is
assumed homogeneous and isotropic. The deformation and strain are
assumed to be small.
Internal polar thermoelastic solid continua, constitutive theories, generators and invariants, strain energy density, complementary strain energy density.
