On the relation between generalized stress theory and electrodynamics

Abstract eng:
A mathematical formulation of continuum mechanics is proposed which includes an extension of the basic equations of electrodynamics as a special case. In the continuum mechanics context, we present a weak Eulerian formulation of the fundamentals of continuum mechanics on differentiable manifolds. Forces and stresses are considered in the framework of the theory of de Rham currents and some extensions thereof. In particular, stresses maybe as irregular as Borel measures. Considering generalized velocities represented by differential forms and interpreting such a form as generalized potential field, we present a weak formulation of pre-metric, p-form electrodynamics as a natural example of the foregoing theory in which the current density may be the distributional derivative of a measure. Finally, it is shown that the assumptions leading to p-form electrodynamics may be replaced by the condition that the force functional is continuous with respect to the flat topology.

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