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

Application of Geometric measure Theory in Continuum Mechanics: The  Configuration Space, Principle of Virtual Power and Cauchy's Stress Theory  for Rough Bodies