  In this work, the principles of Homological Integration Theory are applied to
the mathematical formulation of continuum mechanics. A central guideline in the
currently acceptable formulation of continuum mechanics is that an admissible
body is represented by a set of finite perimeter. The proposed framework is
shown to enable the inclusion of a class of generalized bodies for which a
corresponding stress theory is properly formulated and a generalized principle
of virtual power is presented.
