On norms of force functionals and stress representations

R. Segev; G. Debotton

doi:10.1177/1081286505040402

On norms of force functionals and stress representations

R. Segev, G. Debotton

Department of Mechanical Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

Forces in continuum mechanics are analyzed as 0-currents of geometric measure theory. The representation of forces by stresses is discussed and the flat norm of a force is expressed in terms of stress fields. An analogous treatment expresses the Sobolev norm of a force in terms of stress fields. In both cases, one obtains bounds on the stress fields that are in equilibrium with a given force. The analysis is universal in the sense that it is independent of any constitutive relation.

Original language	English
Pages (from-to)	229-250
Number of pages	22
Journal	Mathematics and Mechanics of Solids
Volume	11
Issue number	3
DOIs	https://doi.org/10.1177/1081286505040402
State	Published - 1 Jun 2006

Keywords

Continuum mechanics
Divergence measures
Flat chains
Forces
Norms
Sobolev norms
Stresses

ASJC Scopus subject areas

Mathematics (all)
Materials Science (all)
Mechanics of Materials

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AB - Forces in continuum mechanics are analyzed as 0-currents of geometric measure theory. The representation of forces by stresses is discussed and the flat norm of a force is expressed in terms of stress fields. An analogous treatment expresses the Sobolev norm of a force in terms of stress fields. In both cases, one obtains bounds on the stress fields that are in equilibrium with a given force. The analysis is universal in the sense that it is independent of any constitutive relation.

KW - Continuum mechanics

KW - Divergence measures

KW - Flat chains

KW - Forces

KW - Norms

KW - Sobolev norms

KW - Stresses

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On norms of force functionals and stress representations

Abstract

Keywords

ASJC Scopus subject areas

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