A Fundamental Structure of Continuum Mechanics I. Elastic Systems

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.