Some solutions for a compressible isotropic elastic material

In this article we obtain closed-form solutions for the combined inflation and axial shear of an elastic tube in respect of the compressible isotropic elastic material introduced by Levinson and Burgess. Several other boundary-value problems are also examined, including the bending of a rectangular block and straightening of a cylindrical sector, both coupled with stretching and shearing, and an axially varying twist deformation. Some of the solutions appear in closed form, others are expressible in terms of elliptic functions.     

On nonlinear universal relations in nonlinear elasticity

In the theory of nonlinear elasticity universal relations are relationships connecting the components of stress and deformation tensors that hold independently of the constitutive equation for the considered class (or sub-class) of materials. They are classified as linear or nonlinear according as the components of the stress appear linearly or nonlinearly in the relations. In this paper a general scheme is developed for the derivation of nonlinear universal relations and is applied to the constitutive law of an isotropic Cauchy elastic solid. In particular, we consider examples of quadratic and cubic universal relations. In respect of universal solutions our results confirm the general result of Pucci and Saccomandi [1] that nonlinear universal relations are necessarily generated by the linear ones. On the other hand, for non-universal solutions we develop a general method for generating nonlinear universal relations and illustrate the results in the case of cubic relations. (Received: November 9, 2005)     

Reflection of plane waves from the boundary of a pre-stressed compressible elastic half-space

The effect of pre-stress on the propagation and reflection ofplane waves in an incompressible isotropic elastic half-spacehas been examined recently by the authors (Ogden & Sotiropoulos,1997). In the present paper the corresponding analysis for compressiblematerials is detailed. In the two-dimensional context consideredfor incompressible materials the (homogeneous) plane waves werenecessarily shear waves. By contrast, in the compressible contextpure shear waves can propagate only in specific directions inthe considered principal plane and, in a general direction,a quasi-shear wave may be accompanied by a quasi-longitudinalwave, as is the case in the anisotropic linear theory. The dependenceof the (in-plane) slowness section on the pre-stress (and finitedeformation) and on the choice of constitutive law is elucidated.This information is used to determine the reflection coefficientsfor reflection of either a (quasi-) shear wave or a (quasi-)longitudinal wave from the boundary of the half-space and tocharacterize the different cases which arise depending on thegeometry of the slowness section. The theoretical results are illustrated by numerical calculationsfor the range of possible types of behaviour with referenceforms of strain-energy function and different states of finitedeformation and to the question of stability of the half-space.     

A "plug-and-play" approach to the preparation of transparent luminescent hybrid materials based on poly(methyl methacrylate), a calix[4]arene cross-linking agent, and terbium ions

A novel methodology to prepare transparent luminescent hybrid materials is reported. Using a calixarene ionophore as a PMMA cross-linker avoids problems, such as phase segregation, and produces a polymer monolith that can be loaded with the metal ion required for luminescence post-synthesis. This approach is versatile and will simplify the production of such materials.     

Initial stresses in elastic solids: Constitutive laws and acoustoelasticity

On the basis of the nonlinear theory of elasticity, the general constitutive equation for an isotropic hyperelastic solid in the presence of initial stress is derived. This derivation involves invariants that couple the deformation with the initial stress and in general, for a compressible material, it requires 10 invariants, reducing to 9 for an incompressible material. Expressions for the Cauchy and nominal stress tensors in a finitely deformed configuration are given along with the elasticity tensor and its specialization to the initially stressed undeformed configuration. The equations governing infinitesimal motions superimposed on a finite deformation are then used to study the combined effects of initial stress and finite deformation on the propagation of homogeneous plane waves in a homogeneously deformed and initially stressed solid of infinite extent. This general framework allows for various different specializations, which make contact with earlier works. In particular, connections with results derived within Biot's classical theory are highlighted. The general results are also specialized to the case of a small initial stress and a small pre-deformation, i.e. to the evaluation of the acoustoelastic effect. Here the formulas derived for the wave speeds cover the case of a second-order elastic solid without initial stress and subject to a uniaxial tension [Hughes and Kelly, Phys. Rev. 92 (1953) 1145] and are consistent with results for an undeformed solid subject to a residual stress [Man and Lu, J. Elasticity 17 (1987) 159]. These formulas provide a basis for acoustic evaluation of the second- and third-order elasticity constants and of the residual stresses. The results are further illustrated in respect of a prototype model of nonlinear elasticity with initial stress, allowing for both finite deformation and nonlinear dependence on the initial stress.     

Extraction of small boat harmonic signatures from passive sonar

This paper investigates the extraction of acoustic signatures from small boats using a passive sonar system. Noise radiated from a small boats consists of broadband noise and harmonically related tones that correspond to engine and propeller specifications. A signal processing method to automatically extract the harmonic structure of noise radiated from small boats is developed. The Harmonic Extraction and Analysis Tool (HEAT) estimates the instantaneous fundamental frequency of the harmonic tones, refines the fundamental frequency estimate using a Kalman filter, and automatically extracts the amplitudes of the harmonic tonals to generate a harmonic signature for the boat. Results are presented that show the HEAT algorithms ability to extract these signatures.     

Non-affine strain measures for continuum models of network materials

Based on stretch averaging, two non-affine strain measures for materials with random network microstructure are suggested. The first concept provides a scaling between affine and non-affine behaviour that is predefined by the network functionality. The second approach applies to fibres that experience strong reorientation upon macroscopic deformation of the network. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Maintaining particle size in the transformation of anatase to rutile titania nanostructures

We study the temperature-dependent transformation of two distinctly synthesized TiO₂ nanoparticles from the anatase to the rutile phase. These studies are carried out over the temperature range extending from room temperature to an excess of 800 °C where the anatase to rutile conversion is found to occur. Results obtained for both a sol-gel-generated nanocolloid (3-20 nm) and a sol-gel-generated micelle nanostructure (∼40 nm) are evaluated. While the TiO₂ nanocolloid structures aggregate to form larger crystallites as a function of increasing temperature with sizes comparable to the sol-gel-generated micelle structures, the resulting anatase crystallites, which are of a diameter 40-50 nm, appear to transform to comparable or slightly smaller rutile structures at 800 °C. This is in contrast to the transformation to larger rutile structures, observed for larger anatase particles. The importance of kinetic effects is considered as it enhances the rate of anatase to rutile conversion. These characteristics are established using a combination of Raman spectroscopic, X-ray diffraction, and scanning electron microscopy. The relative playoffs of the Raman and X-ray diffraction techniques are considered as they are used for the analysis of particles at the nanoscale, especially when phase transformations are evaluated.