Application of Geometric measure Theory in Continuum Mechanics: The Configuration Space, Principle of Virtual Power and Cauchy's Stress Theory for Rough Bodies
arXiv:1305.4286
Abstract
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.
arXiv admin note: substantial text overlap with arXiv:1303.4104