Fluxes and Flux-Conjugate Stresses

Abstract

The work presented here is concerned with stress theory on differentiable manifolds. In addition to the theoretical interest as to the geometrical structure needed for the formulation of stress theory, such a general geometrical setting is used in theories of materials with microstructure to model the space where the “order parameters” are valued (see [2]). This sequel to our previous work on this subject (see [5], [6], [7], [8], [9]) follows [11] and focuses on two aspects of stress theory:

• (a) the stresses are associated with bodies whose material structure is induced by an extensive property rather than assumed a priori;

• (b) considering the electric charge as the extensive property, the general setting allows us to study the Maxwell stress tensor of electromagnetism for the case where a metric structure is not available on spacetime and without any reference to a constitutive relation for the electromagnetic fields (e.g., the aether relations).