On a dichotomy in Newtonian continuum mechanics : a survey

Abstract

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.