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On Norms of Force Functionals and Stress Representations

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.
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  • HAL Id : hal-01064978, version 1

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Reuven Segev, Gal de Botton. On Norms of Force Functionals and Stress Representations. Mathematics and Mechanics of Solids, SAGE Publications, 2006, 11 (3), pp.229-250. ⟨hal-01064978⟩

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