The Thermodynamics of Irreversible Processes. IV. The Theory of Elasticity and Anelasticity

Abstract

The traditional theory of the solid state rests on two false assumptions. One is the principle of a constant relaxed (or standard) state. The other is the principle of relaxability-in-the-large, first formulated mathematically by de Saint-Venant. His equations are essentially identical with Riemann's equations expressing the condition that a geometry be Euclidean-in-the-large. It is shown that a principle of relaxability-in-the-small is sufficient for the geometry of strain—which then becomes a three-dimensional Riemannian geometry. The kinematics of strain is next developed without introducting the principle of a constant relaxed state.