Cauchy's Theorem on Manifolds |
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Authors: | R Segev G Rodnay |
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Institution: | (1) Department of Mechanical Engineering, Ben Gurion University of the Negev, P.O. Box 653, Beer Sheva, 84105, Israel. E-mail |
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Abstract: | A generalization of the Cauchy theory of forces and stresses to the geometry of differentiable manifolds is presented using
the language of differential forms. Body forces and surface forces are defined in terms of the power densities they produce
when acting on generalized velocity fields. The normal to the boundary is replaced by the tangent space equipped with the
outer orientation induced by outward pointing vectors. Assuming that the dimension of the material manifold is m, stresses are modelled as m − 1 covector valued forms. Cauchy's formula is replaced by the restriction of the stress form to the tangent space of the
boundary while the outer orientation of the tangent space is taken into account. The special cases of volume manifolds and
Riemannian manifolds are discussed.
This revised version was published online in August 2006 with corrections to the Cover Date. |
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Keywords: | continuum mechanics forces stresses manifolds differential forms balance laws Cauchy's theorem |
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