  In the setting of an $n$-dimensional Euclidean space, the duality between
velocity fields on the class of admissible bodies and Cauchy fluxes is studied
using tools from geometric measure theory. A generalized Cauchy flux theory is
obtained for sets whose measure theoretic boundaries may be as irregular as
flat $(n-1)$-chains. Initially, bodies are modeled as normal $n$-currents
induced by sets of finite perimeter. A configuration space comprising Lipschitz
embeddings induces virtual velocities given by locally Lipschitz mappings. A
Cauchy flux is defined as a real valued function on the Cartesian product of
$(n-1)$-currents and locally Lipschitz mappings. A version of Cauchy's
postulates implies that a Cauchy flux may be uniquely extended to an $n$-tuple
of flat $(n-1)$-cochains. Thus, the class of admissible bodies is extended to
include flat $n$-chains and a generalized form of the principle of virtual
power is presented. Wolfe's representation theorem for flat cochains enables
the identification of stress as an $n$-tuple of flat $(n-1)$-forms.
