  This paper offers an informal instructive introduction to some of the main
notions of geometric continuum mechanics for the case of smooth fields. We use
a metric invariant stress theory of continuum mechanics to formulate a simple
generalization of the fields of electrodynamics and Maxwell's equations to
general differentiable manifolds of any dimension, thus viewing generalized
electrodynamics as a special case of continuum mechanics. The basic kinematic
variable is the potential, which is represented as a $p$-form in an
$n$-dimensional spacetime. The stress for the case of generalized
electrodynamics is assumed to be represented by an $(n-p-1)$-form, a
generalization of the Maxwell $2$-form.
