A Fundamental Structure of Continuum Mechanics I. Elastic Systems
Bernward Stuke · Zeitschrift für Naturforschung A · 1996
Abstract Continuum mechanics and thermodynamics are complementary areas of classical field theory. Their fundamental structure, however, is rather different according to the present view: on the one hand there is the equation of motion or the equivalent balance of momentum, on the other there is Gibbs' fundamental equation. In a preceding paper it has been shown that systems having a potential of acceleration possess a structure of continuum mechanics which corresponds to the one of thermodynamics. This discussion is extended to elastic systems. In this case a tensorial potential of acceleration must be introduced. The equation of motion derived for this extended structure contains two additional terms (reactive forces) not present in the conventional balance of forces.