Les Sudak

A cross-linking model for estimating Young's modulus of artificial bone tissue grown on carbon nanotube scaffold

Carbon nanotubes (CNTs) provide a suitable environment for growth and proliferation of bone cells. The elastic properties exhibited by CNTs can enhance mechanical characteristics of bone mineral phase, hydroxyapatite (HAp), precipitated on such a scaffold. In this article, a simplified model for estimating the axial Youngs modulus of a representative volume element (RVE) of CNT-HAp composite is presented. The model is based on the idea of HAp formation on functionalized sites on CNTs as cross-links between HAp matrix and CNT. Modeling results show that the reinforcement role contributed by CNT in the RVE causes a significant increase in the Youngs modulus of the composite material which is a direct consequence of transferring stresses from the HAp matrix to the CNT through the cross-links. Similar conclusions may be suggested regarding the improvement of overall mechanical properties of the material. The prediction made by the model lies reasonably well within the limits proposed by conventional Rule-of-Mixtures, and sliding below Voigts model. The Youngs modulus predicted by the model lies adjacent to the Hashin-Shtrikman upper bound as a function of the RVE length (or equivalently CNT aspect ratio). The model simulation indicates that an increase in the CNT aspect ratio and/or number of cross-links in the RVE, results in the prediction to move closer to the estimation made by Voigt as the assumption of perfect bonding between composite phases is approached.

Design Procedure for Tubular Lattice Towers for Small Wind Turbines

Despite having been used for a long time, tubular lattice towers with three or four legs have not been systematically analysed for use with small wind turbines. We present a design procedure based on modelling the towers as either tripods or quadrapods to allow analytic approximations to the tower stresses. Following the IEC standard for small wind turbine design, the critical load occurs at the 50-year extreme wind speed acting on a stationary turbine and tower. To avoid buckling in the downwind leg, three separate methods of estimating the critical buckling resistance are shown to give very similar results. The analytic models also allow the tower-top deflection to be simply approximated. We use an arbitrary limit on deflection as 5% of the tower height, to ensure linear, static behaviour for extreme wind loads. Two example tower designs are considered: an 18 m tower for a 5 kW turbine and a 12 m tower for a 500 W turbine.

Wrinkles and creases in the bending, unbending and eversion of soft sectors

We study what is clearly one of the most common modes of deformation found in nature, science and engineering, namely the large elastic bending of curved structures, as well as its inverse, unbending, which can be brought beyond complete straightening to turn into eversion. We find that the suggested mathematical solution to these problems always exists and is unique when the solid is modelled as a homogeneous, isotropic, incompressible hyperelastic material with a strain-energy satisfying the strong ellipticity condition. We also provide explicit asymptotic solutions for thin sectors. When the deformations are severe enough, the compressed side of the elastic material may buckle and wrinkles could then develop. We analyse, in detail, the onset of this instability for the Mooney–Rivlin strain energy, which covers the cases of the neo-Hookean model in exact nonlinear elasticity and of third-order elastic materials in weakly nonlinear elasticity. In particular, the associated theoretical and numerical treatment allows us to predict the number and wavelength of the wrinkles. Guided by experimental observations, we finally look at the development of creases, which we simulate through advanced finite-element computations. In some cases, the linearized analysis allows us to predict correctly the number and the wavelength of the creases, which turn out to occur only a few per cent of strain earlier than the wrinkles.