Author's: K. S. Surana, A. D. Joy and J. N. Reddy
Pages: [1] - [41]
Received Date: June 21, 2016
Submitted by:
DOI: http://dx.doi.org/10.18642/jpamaa_7100121677
This paper presents a non-classical internal polar continuum theory
for finite deformation of isotropic, homogeneous compressible and
incompressible solid continua. The classical continuum theories only
incorporate partial physics of deformation in the thermodynamic
framework. Since the Jacobian of deformation J is
fundamental measure of deformation in solid continua, J
in its entirety must be incorporated in the thermodynamic framework.
Polar decomposition of J into right stretch tensor
and pure rotation tensor R
shows that entirety of J implies entirety of
and R. The classical
continuum theories for isotropic and homogeneous solid continua
are derived purely using
thus ignoring the influence of
R altogether. The purpose of this research is to present
a new and more complete thermodynamic framework for finite deformation
of solids that incorporates complete deformation physics described by
J. This can be accomplished by incorporating the
additional physics due to R in the current theories as
these theories already contain the physics due to
We note that the rotation tensor
R results due to deformation of solid continua, hence
arises in all deforming solid continua. Thus, this theory can be
referred to as internal polar non-classical theory for
solid continua. The use of internal polar non-classical is
appropriate as the theory considers internal rotations. If the varying
internal rotations and the rotation rates are resisted by the solid
continua, then there must exist internal moments that are conjugate to
the rotations which together with rotations and rotation rates can
result in additional energy storage, dissipation, and memory.
Derivations of conservation and balance laws are presented for
internal polar non-classical continuum theory for solid continua for
finite deformation. Necessity of additional conservation and balance
laws is discussed and their derivations are presented. The resulting
mathematical model is compared with the mathematical models resulting
from the current continuum theories for finite deformation to
illustrate the differences in them due to incorporating the additional
physics associated with R and thereby incorporating
J in its entirety. The non-classical continuum theory
for solid continua presented here is not to be confused with the
micropolar theories, stress-couple theories, or strain gradient
theories as demonstrated in this paper. The objective of the theory
presented here is to present new thermodynamic framework for solid
continua with finite deformation that is consistent with the
deformation physics, which necessitates that J in its
entirety must form the basis for derivation of conservation and
balance laws. Since this internal polar non-classical continuum theory
considers additional physics due to R, the resulting
thermodynamic framework is more complete and consistent with the
physics of deformation compared to the currently used thermodynamic
framework.
non-classical continuum theory, internal polar continuum theory, solid continua, Jacobian of deformation, polar decomposition, stretch tensor, rotation tensor, finite deformation.