Paper presented at the 5th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, South Africa, 1-4 July, 2007.
It has been observed that classical thermomechanics
can be founded upon the requirement that the total energy
equation is to be consistent with the first axiom of
Newton. Then, since the boost velocity in Galilean transformations
is arbitrary, a balance of forces must result.
Mass invariance is then a consistency requirement.
Newtonian continuum mechanics is not totally consistent
since material response to applied forces is not
constrained by the first axiom of Newton: the larger Euclidean
group must be adopted for all constitutive aspects
of the theory. This dichotomy allows the Cauchy stress
tensor symmetry to be explored from the thermal energy
equation covariance under Eu. This scalar equation must
be covariant under rigid body motion as a reflection of
material response being independent of observer motion.
The angular momentum equation holds for consistency.