One-dimensional modeling of necking in rate-dependent materials

This paper presents an asymptotically rigorous one-dimensional analytical formulation capable of accurately capturing the stress and strain distributions that develop within the evolving neck of bars and sheets of rate-dependent materials stretched in tension. The work is an extension of an earlier study by the authors on necking instabilities in rate-independent materials. The one-dimensional model accounts for the gradients of the stress and strain that develop as the necking instability grows. Material strain-rate dependence has a significant influence on the strain that can be imposed on a bar or sheet before necking becomes pronounced. The formulation in this paper enables a quantitative assessment of the interplay in necking retardation due to rate-dependence and that due to the development of hydrostatic tension in the neck. The connection with a much simpler long-wavelength approximation which does not account for curvature induced hydrostatic tension in the neck is also emphasized and extended

Photo-Motile Structures

Actuation remains a signifcant challenge in soft robotics. Actuation by light has important advantages: objects can be actuated from a distance, distinct frequencies can be used to actuate and control distinct modes with minimal interference and signifcant power can be transmitted over long distances through corrosion-free, lightweight fiber optic cables. Photo-chemical processes that directly convert photons to configurational changes are particularly attractive for actuation. Various researchers have demonstrated light-induced actuation with liquid crystal elastomers combined with azobenzene photochromes. We present a simple modeling framework and a series of examples that studies actuation by light. Of particular interest is the generation of cyclic or periodic motion under steady illumination. We show that this emerges as a result of a coupling between light absorption and deformation. As the structure absorbs light and deforms, the conditions of illumination change, and this in turn changes the nature of further deformation. This coupling can be exploited in either closed structures or with structural instabilities to generate cyclic motion

Twisting instabilities in elastic ribbons with inhomogeneous pre-stress: a macroscopic analog of thermodynamic phase transition

We study elastic ribbons subject to large, tensile pre-stress confined to a central region within the cross-section. These ribbons can buckle spontaneously to form helical shapes, featuring regions of alternating chirality (phases) that are separated by so-called perversions (phase boundaries). This instability cannot be described by classical rod theory, which incorporates pre-stress through effective natural curvature and twist; these are both zero due to the mirror symmetry of the pre-stress. Using dimension reduction, we derive a one-dimensional (1D) 'rod-like' model from a plate theory, which accounts for inhomogeneous pre-stress as well as finite rotations. The 1D model successfully captures the qualitative features of torsional buckling under a prescribed end-to-end displacement and rotation, including the co-existence of buckled phases possessing opposite twist, and is in good quantitative agreement with the results of numerical (finite-element) simulations and model experiments on elastomeric samples. Our model system provides a macroscopic analog of phase separation and pressure-volume-temperature state diagrams, as described by the classical thermodynamic theory of phase transitions.Comment: 29 pages; 11 figure

Flambage capillaire d'un film mince adhérant sur une sphère

Nous étudions théoriquement et expérimentalement le flambement sous l'action de forces capillaires d'un film mince enrobant une sphère. La sphère est rigide et mouillée, et recouverte par un film mince de forme initiale cylindrique. L'équilibre du film est gouverné par les effets antagonistes de l'élasticité, qui tend à garder la forme développable, et de la capillarité, qui tend à courber le film dans ses deux directions de façon à maximiser l'aire de contact avec la sphère. Expérimentalement, la région de contact entre le film est la sphère est à symétrie cylindrique aux faibles rayons de la sphère, puis se déstabilise en une forme ondulante quand le rayon dépasse une valeur critique. Nous adaptons les équations de Donnell pour les coques quasi-cylindriques de manière à prendre en compte la condition unilatérale de contact avec la sphère et les forces capillaires agissant le long du bord de la région mobile de contact. Une solution non-linéaire décrivant les configurations axi-symétriques est obtenue. Une analyse stabilité est ensuite présentée, qui prédit correctement l'instabilité d'ondulation, la symétrie du mode instable, le seuil d'instabilité et la longueur d'onde au seuil