Skip to Main content Skip to Navigation
Journal articles

Cauchy's Flux Theorem in Light of Geometric Integration Theory

Abstract : This work presents a formulation of Cauchy's flux theory of continuum mechanics in the framework of geometric integration theory as formulated by H. Whitney and extended recently by J. Harrison. Starting with convex polygons, one constructs a formal vector space of polyhedral chains. A Banach space of chains is obtained by a completion process of this vector space with respect to a norm. Then, integration operators, cochains, are defined as elements of the dual space to the space of chains. Thus, the approach links the analytical properties of cochains with the corresponding properties of the domains in an optimal way. The basic representation theorem shows that cochains may be represented by forms. The form representing a cochain is a geometric analog of a flux field in continuum mechanics.
Document type :
Journal articles
Complete list of metadata

Cited literature [22 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00956979
Contributor : Christian Cardillo <>
Submitted on : Friday, March 7, 2014 - 4:24:53 PM
Last modification on : Monday, July 22, 2019 - 11:46:01 AM
Long-term archiving on: : Saturday, June 7, 2014 - 11:41:42 AM

File

CAUCHYS_FLUX_THEOREM_IN_LIGHT_...
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00956979, version 1

Citation

Guy Rodnay, Reuven Segev. Cauchy's Flux Theorem in Light of Geometric Integration Theory. Journal of Elasticity, Springer Verlag, 2003, 71 (1-3), pp.183-203. ⟨hal-00956979⟩

Share

Metrics

Record views

178

Files downloads

396