(1) Department of Mathematics, Illinois Institute of Technology, Chicago
Abstract:
Thermodynamics is developed for a class of thermo-hypo-elastic materials. It is shown that materials of this class obey the laws of thermodynamics, but are not elastic.
Table of Symbols
Latin Letters
Aijkl
tensor-valued function of tij appearing in hypo-elastic constitutive relation
-
Bijkl
another tensor-valued function. See equation (4.2)
-
B
the square of
-
dij
rate of deformation tensor
-
dij
deviator of rate of deformation
-
f, k
functions of pressure, p
-
g, h
functions of the invariant
-
p
pressure
-
qi
heat flux vector
-
sij
stress deviator
-
ij
co-rotational derivative of stress deviator
-
t
time
-
t1t2
specific values of time
-
tij
stress tensor
-
tij0
a specific value of stress
-
T
Temperature
-
T0
a specific value of temperature
-
ui
velocity
-
V(t)
a material volume as a function of time, t
-
V0
a material volume at a reference configuration
-
W
work (W = work done in a deformation—section 5)
Sript Letters
Specific internal energy
-
Specific Helmholtz free energy
-
G
Specific Gibbs function
Greek Letters
an invariant of the stress deviator—see eq. (2.4)
-
ij
kroneker delta
-
(W = work done in a deformation—section 5)
-
specific entropy
-
hypo-elastic potential
-
hypo-elastic potential
-
mass density
-
0
mass density in a reference configuration
-
specific volume = 1/
-
a function of p
-
ijkl
a constant tensor—see eq. (2.5)
-
–G/
-
ij
rate of rotation tensor
This work is dedicated to Jerald L. Ericksen, without whose influence it would not have been possible