On Norms of Force Functionals and Stress Representations

Reuven Segev (1) , Gal de Botton (1)

1 Department of Mechanical Engineering [Beer-Sheva]

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.

Domaines: Mécanique [physics.med-ph]

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