Large deformations of thin elastic plates usually lead to the formation of singular structures which are either linear (ridges) or pointlike (developable cones). These structures are thought to be generic for crumpled plates, although they have been investigated quantitatively only in simplified geometries. Previous studies have also shown that a large number of singularities are generated by successive instabilities. Here we study, experimentally and numerically, a generic situation in which a plate is initially bent in one direction into a cylindrical arch, then deformed in the other direction by a load applied at its centre. This induces the generation of pairs of singularities; we study their position, their dynamics and the corresponding resistance of the plate to deformation. We solve numerically the equations describing large deformations of plates; developable cones are predicted, in quantitative agreement with the experiments. We use geometrical arguments to predict the observed patterns, assuming that the energy of the plate is given by the energy of the singularities.

The interaction between two disks immersed in a 2D nematic is investigated (i) analitically using the tensor order parameter formalism for the nematic configuration around isolated disks and (ii) numerically using finite element methods with adaptive meshing to minimize the corresponding Landau-de Gennes free energy. For strong homeotropic anchoring, each disk generates a pair of defects with one-half topological charge responsible for the 2D quadrupolar interaction between the disks at large distances. At short distance, the position of the defects may change, leading to unexpected complex interactions with the quadrupolar repulsive interactions becoming attractive. This short range attraction in all directions is still anisotropic. As the distance between the disks decreases their preferred relative orientation with respect to the far-field nematic director changes from oblique to perpendicular.PACS numbers: 77.84.Nh Liquids, emulsions, and suspensions; liquid crystals -61.30.cz Theory and models of liquid crystal structure -61.30.Jf Defects in liquid crystals.

We characterize the elastic contribution to the surface free energy of a nematic liquid crystal in the presence of a sawtooth substrate. Our findings are based on numerical minimization of the Landau-de Gennes model and analytical calculations on the Frank-Oseen theory. The nucleation of disclination lines ͑characterized by nonhalf-integer winding numbers͒ in the wedges and apexes of the substrate induces a leading order proportional to q ln q to the elastic contribution to the surface free-energy density, with q being the wave number associated with the substrate periodicity.

Abstract:We describe a novel, low-cost and low-tech method for the fabrication of elastomeric Janus particles with diameters ranging from micrometers to millimeters. This consists of UV-irradiating soft urethane/urea elastomer spheres, which are then extracted in toluene and dried. The spheres are thus composed of a single material: no coating or film deposition steps are required. Furthermore, the whole procedure is carried out at ambient temperature and pressure. Long, labyrinthine corrugations ("wrinkles") appear on the irradiated portions of the particles' surfaces, the spatial periodicity of which can be controlled by varying the sizes of particles. The asymmetric morphology of the resulting Janus particles has been confirmed by scanning electron microscopy, atomic force microscopy, and optical microscopy. We have also established that the spheres behave elastically by performing bouncing tests with dried and swollen spheres. Results can be interpreted by assuming that each sphere consists of a thin, stiff surface layer ("skin") lying atop a thicker, softer substrate ("bulk"). The skin's higher stiffness is hypothesized to result from the more extensive cross-linking of the polymer chains located near the surface by the UV radiation. Textures then arise from competition between the effects of bending the skin and compressing the bulk, as the solvent evaporates and the sphere shrinks.