Reuven Segev - Department of Mechanical Engineering, Ben-Gurion University of the Negev, P.O.Box 653, Beer-Sheva, 84105, Israel (email)
Abstract: In the context of stress theory of the mechanics of continuous media, a generalization of the boundary operator for de Rham currents---the co-divergence operator---is introduced. While the boundary operator of de Rham's theory applies to real valued currents, the co-divergence operator acts on vector valued currents, i.e., functionals dual to differential forms valued in a vector bundle. From the point of view of continuum mechanics, the framework presented here allows for the formulation of the principal notions of continuum mechanics on a manifold that does not have a Riemannian metric or a connection while at the same time allowing irregular bodies and velocity fields.
Keywords: de Rham currents, vector valued currents, boundary operator, Continuum
mechanics, balance equations, differential operators.
Received: June 2010; Revised: July 2011; Published: December 2011.
2011 Impact Factor.921