Mechanics of materially uniform thin films

A rigorous pure-bending model for thin films, accurate to leading order in film thickness, is established on the basis of the three-dimensional theory of materially uniform elastic bodies. An extension of the model, accounting for both stretching and bending and incorporating a generalization of Koiter’s theory, is proposed. One conclusion is that the classical Kirchhoff–Love hypothesis, i.e., the assumption that material lines normal to the film remain so in the course of deformation, does not obtain. The model is applicable to materials that have undergone prior plastic deformation, diffusion, or growth

Linear Pantographic Sheets: Existence and Uniqueness of Weak Solutions

The well-posedness of the boundary value problems for second gradient elasticity has been studied under the assumption of strong ellipticity of the dependence on the second placement gradients (see, e.g., Chambon and Moullet in Comput. Methods Appl. Mech. Eng. 193:2771–2796, 2004 and Mareno and Healey in SIAM J. Math. Anal. 38:103–115, 2006). The study of the equilibrium of planar pantographic lattices has been approached in two different ways: in dell’Isola et al. (Proc. R. Soc. Lond. Ser. A 472:20150, 2016) a discrete model was introduced involving extensional and rotational springs which is also valid in large deformations regimes while in Boutin et al. (Math. Mech. Complex Syst. 5:127–162, 2017) the lattice has been modelled as a set of beam elements interconnected by internal pivots, but the analysis was restricted to the linear case. In both papers a homogenized second gradient deformation energy, quadratic in the neighbourhood of non deformed configuration, is obtained via perturbative methods and the predictions obtained with the obtained continuum model are successfully compared with experiments. This energy is not strongly elliptic in its dependence on second gradients. We consider in this paper also the important particular case of pantographic lattices whose first gradient energy does not depend on shear deformation: this could be considered either a pathological case or an important exceptional case (see Stillwell et al. in Am. Math. Mon. 105:850–858, 1998 and Turro in Angew. Chem., Int. Ed. Engl. 39:2255–2259, 2000). In both cases we believe that such a particular case deserves some attention because of what we can understand by studying it (see Dyson in Science 200:677–678, 1978). This circumstance motivates the present paper, where we address the well-posedness of the planar linearized equilibrium problem for homogenized pantographic lattices. To do so: (i) we introduce a class of subsets of anisotropic Sobolev’s space as the most suitable energy space E relative to assigned boundary conditions; (ii) we prove that the considered strain energy density is coercive and positive definite in E; (iii) we prove that the set of placements for which the strain energy is vanishing (the so-called floppy modes) must strictly include rigid motions; (iv) we determine the restrictions on displacement boundary conditions which assure existence and uniqueness of linear static problems. The presented results represent one of the first mechanical applications of the concept of Anisotropic Sobolev space, initially introduced only on the basis of purely abstract mathematical considerations

Esthetic Buccal Flap for Correction of Buccal Fenestration Defects During Flapless Immediate Implant Surgery

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/141057/1/jper0517.pd

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

The Alpha Magnetic Spectrometer (AMS): search for antimatter and dark matter on the International Space Station

The AMS is a state of the art detector for extraterrestrial study of antimatter, matter and missing matter. After a precursor flight on STS91 in May 1998, AMS will be installed on the International Space Station where it will operate for three years. In this paper the AMS experiment is described and is physics potential reviewed.Comment: Invited talk to S. Miniato 1997, to be published on N.I.M., 8 pages 7 figures, LATEX, espcvc2.sty include