Mathematical Problems in Engineering
Volume 2003 (2003), Issue 4, Pages 153-171
doi:10.1155/S1024123X03212011
Thermomechanical constraints and constitutive formulations in thermoelasticity
Department of Mechanical Engineering, Texas A&M University, College Station, 77843, TX, USA
Received 7 December 2002
Copyright © 2003 S. Baek and A. R. Srinivasa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We investigate three classes of constraints in a thermoelastic
body: (i) a deformation-temperature constraint, (ii) a
deformation-entropy constraint, and (iii) a deformation-energy
constraint. These constraints are obtained as limits of
unconstrained thermoelastic materials and we show that
constraints (ii) and (iii) are equivalent. By using a limiting
procedure, we show that for the constraint (i), the entropy plays
the role of a Lagrange multiplier while for (ii) and (iii), the
absolute temperature plays the role of Lagrange multiplier. We
further demonstrate that the governing equations for materials
subject to constraint (i) are identical to those
of an unconstrained material whose internal energy is an affine
function of the entropy, while those for materials subject to
constraints (ii) and (iii) are identical to those of an
unstrained material whose Helmholtz potential is affine in the
absolute temperature. Finally, we model the thermoelastic
response of a peroxide-cured vulcanizate of natural
rubber and show that imposing the constraint in which the
volume change depends only on the internal energy leads to very
good predictions (compared to experimental results) of the stress
and temperature response under isothermal and isentropic
conditions.