Edge effects in Hypar nets

Edge effects in hyperbolic paraboloidal nets are analyzed using a model that features elastic resistance of the fibers of the net to flexure and twist in addition to the extensional elasticity of the conventional membrane theory of networks.; Les effets de bord dans les réseaux paraboloïdaux hyperboliques sont analysés à l'aide d'un modèle présentant la résistancé elastique des fibres du réseaù a la flexion et à la torsion, en plus de l'élasticité en extension de la théorie conventionnelle des membranes pour les réseaux

Mechanically equivalent elastic-plastic deformations and the problem of plastic spin

The problem of plastic spin is phrased in terms of a notion of mechanical equivalence among local intermediate configurations of an elastic/ plastic crystalline solid. This idea is used to show that, without further qualification, the plastic spin may be suppressed at the constitutive level. However, the spin is closely tied to an underlying undistorted crystal lattice which, once specified, eliminates the freedom afforded by mechanical equivalence. As a practical matter a constitutive specification of plastic spin is therefore required. Suppression of plastic spin thus emerges as merely one such specification among many. Restrictions on these are derived in the case of rate-independent response

Koiter’s Shell Theory from the Perspective of Three-dimensional Nonlinear Elasticity

Abstract Koiter’s shell model is derived systematically from nonlinear elasticity theory, and shown to furnish the leading-order model for small thickness when the bending and stretching energies are of the same order of magnitude. An extension of Koiter’s model to finite midsurface strain emerges when stretching effects are dominant

Asymptotic finite-strain thin-plate theory for elastic solids

AbstractWe offer some observations on recent efforts to extract models for the stretching and bending of thin plates from three-dimensional finite elasticity. Using an asymptotic argument like that advanced by Ciarlet and his school, we show that recent work purporting to derive a non-standard bending theory generates instead a correction to membrane theory of order thickness squared