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On Norms of Force Functionals and Stress Representations

Department of Mechanical Engineering, Ben-Gurion University, P.O. Box 653, Beer-Sheva 84105 Israel

G. Debotton

Department of Mechanical Engineering, Ben-Gurion University, P.O. Box 653, Beer-Sheva 84105 Israel

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.

Key Words: Continuum mechanics • forces • stresses • norms • flat chains • divergence measures • Sobolev norms

This version was published on June 1, 2006

Mathematics and Mechanics of Solids, Vol. 11, No. 3, 229-250 (2006)
DOI: 10.1177/1081286505040402


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