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 helical shear of a compressible elastic circular cylindrical tube

In this paper we examine the combined azimuthal and axial shear of a compressible isotropic elastic circular cylindrical tube of finite extent, otherwise referred to as helical shear (which is an isochoric deformation). The equilibrium equations are formulated in terms of the principal stretches, and explicit necessary and sufficient conditions on the strain-energy function for the material to support this deformation are obtained and compared with those obtained previously for this problem. Several classes of strain-energy functions are derived and in some general cases complete solutions of the equilibrium equations are obtained. Existing results are recovered as special cases and some new results for the strain-energy functions derived are determined and discussed.

A comparison of stability and bifurcation criteria for inflated spherical elastic shells

The nonlinear stability analysis introduced by Chen and Haughton [1] is employed to study the full nonlinear stability of the non-homogeneous spherically symmetric deformation of an elastic thick-walled sphere. The shell is composed of an arbitrary homogeneous, incompressible elastic material. The stability criterion ultimately requires the solution of a third-order nonlinear ordinary differential equation. Numerical calculations performed for a wide variety of well-known incompressible materials are then compared with existing bifurcation results and are found to be identical. Further analysis and comparison between stability and bifurcation are conducted for the case of thin shells and we prove by direct calculation that the two criteria are identical for all modes and all materials.

On extension and torsion of a compressible elastic circular cylinder

In this paper we examine the combined extension and torsion of a compressible isotropic elastic cylinder of finite extent. The equilibrium equations are formulated in terms of the principal stretches and then applied to the special case of pure torsion superimposed on a uniform extension (an isochoric deformation). Explicit necessary and sufficient conditions on the strain-energy function for the material to support this deformation with vanishing traction on the lateral surfaces of the cylinder are obtained. Some strain-energy functions satisfying these conditions are considered, existing results are recovered as special cases and new results are obtained. We also point out how the strain-energy functions generated from the considered isochoric deformation considered (of a compressible material) can be used to generate energy functions and corresponding solutions for the incompressible theory.

Physisorption-induced electron scattering on the surface of carbon-metal core-shell nanowire arrays for hydrogen sensing

Palladium is sputtered on multi-walled carbon nanotube forests to form carbon-metal core-shell nanowire arrays. These hybrid nanostructures exhibited resistive responses when exposed to hydrogen with an excellent baseline recovery at room temperature. The magnitude of the response is shown to be tuneable by an applied voltage. Unlike the charge-transfer mechanism commonly attributed to Pd nanoparticle-decorated carbon nanotubes, this demonstrates that the hydrogen response mechanism of the multi-walled carbon nanotube-Pd core-shell nanostructure is due to the increase in electron scattering induced by physisorption of hydrogen. These hybrid core-shell nanostructures are promising for gas detection in hydrogen storage applications.

A linear-elastic model of anisotropic tumour growth

This paper examines the effect of anisotropic growth on the evolution of mechanical stresses in a linear-elastic model of a growing, avascular tumour. This represents an important improvement on previous linear-elastic models of tissue growth since it has been shown recently that spatially-varying isotropic growth of linear-elastic tissues does not afford the necessary stress-relaxation for a steady-state stress distribution upon reaching a nutrient-regulated equilibrium size. Time-dependent numerical solutions are developed using a Lax-Wendroff scheme, which show the evolution of the tissue stress distributions over a period of growth until a steady-state is reached. These results are compared with the steady-state solutions predicted by the model equations, and key parameters influencing these steady-state distributions are identified. Recommendations for further extensions and applications of this model are proposed.

Towards improved precision in the quantification of surface-enhanced Raman scattering (SERS) enhancement factors: A renewed approach

This paper demonstrates a renewed procedure for the quantification of surface-enhanced Raman scattering (SERS) enhancement factors with improved precision. The principle of this method relies on deducting the resonance Raman scattering (RRS) contribution from surface-enhanced resonance Raman scattering (SERRS) to end up with the surface enhancement (SERS) effect alone. We employed 1,8,15,22-tetraaminophthalocyanato-cobalt(II) (4α-CoIITAPc), a resonance Raman- and electrochemically redox-active chromophore, as a probe molecule for RRS and SERRS experiments. The number of 4α-CoIITAPc molecules contributing to RRS and SERRS phenomena on plasmon inactive glassy carbon (GC) and plasmon active GC/Au surfaces, respectively, has been precisely estimated by cyclic voltammetry experiments. Furthermore, the SERS substrate enhancement factor (SSEF) quantified by our approach is compared with the traditionally employed methods. We also demonstrate that the present approach of SSEF quantification can be applied for any kind of different SERS substrates by choosing an appropriate laser line and probe molecule.

Revisiting borehole stresses in anisotropic elastic media : comparison of analytical versus numerical solutions

We present a rigorous validation of the analyticalAmadei solution for the stress concentration around arbitrarily orientated borehole in general anisotropic elastic media. First, we revisit the theoretical framework of the Amadei solution and present analytical insights that show that the solution does indeed contain all special cases of symmetry, contrary to previous understanding, provided that the reduced strain coefficients β11 and β55 are not equal. It is shown from theoretical considerations and published experimental data that the β11 and β55 are not equal for realistic rocks. Second, we develop a 3D finite-element elastic model within a hybrid analyticalnumerical workflow that circumvents the need to rebuild and remesh the model for every borehole and material orientation. Third, we show that the borehole stresses computed from the numerical model and the analytical solution match almost perfectly for different borehole orientations (vertical, deviated and horizontal) and for several cases involving isotropic and transverse isotropic symmetries. It is concluded that the analytical Amadei solution is valid with no restrictions on the borehole orientation or elastic anisotropy symmetry.

Novel non-linear elastic structural analysis with generalised transverse element loads using a refined finite element

In the finite element modelling of structural frames, external loads such as wind loads, dead loads and imposed loads usually act along the elements rather than at the nodes only. Conventionally, when an element is subjected to these general transverse element loads, they are usually converted to nodal forces acting at the ends of the elements by either lumping or consistent load approaches. In addition, it is especially important for an element subjected to the first- and second-order elastic behaviour, to which the steel structure is critically prone to; in particular the thin-walled steel structures, when the stocky element section may be generally critical to the inelastic behaviour. In this sense, the accurate first- and second-order elastic displacement solutions of element load effect along an element is vitally crucial, but cannot be simulated using neither numerical nodal nor consistent load methods alone, as long as no equilibrium condition is enforced in the finite element formulation, which can inevitably impair the structural safety of the steel structure particularly. It can be therefore regarded as a unique element load method to account for the element load nonlinearly. If accurate displacement solution is targeted for simulating the first- and second-order elastic behaviour on an element on the basis of sophisticated non-linear element stiffness formulation, the numerous prescribed stiffness matrices must indispensably be used for the plethora of specific transverse element loading patterns encountered. In order to circumvent this shortcoming, the present paper proposes a numerical technique to include the transverse element loading in the non-linear stiffness formulation without numerous prescribed stiffness matrices, and which is able to predict structural responses involving the effect of first-order element loads as well as the second-order coupling effect between the transverse load and axial force in the element. This paper shows that the principle of superposition can be applied to derive the generalized stiffness formulation for element load effect, so that the form of the stiffness matrix remains unchanged with respect to the specific loading patterns, but with only the magnitude of the loading (element load coefficients) being needed to be adjusted in the stiffness formulation, and subsequently the non-linear effect on element loadings can be commensurate by updating the magnitude of element load coefficients through the non-linear solution procedures. In principle, the element loading distribution is converted into a single loading magnitude at mid-span in order to provide the initial perturbation for triggering the member bowing effect due to its transverse element loads. This approach in turn sacrifices the effect of element loading distribution except at mid-span. Therefore, it can be foreseen that the load-deflection behaviour may not be as accurate as those at mid-span, but its discrepancy is still trivial as proved. This novelty allows for a very useful generalised stiffness formulation for a single higher-order element with arbitrary transverse loading patterns to be formulated. Moreover, another significance of this paper is placed on shifting the nodal response (system analysis) to both nodal and element response (sophisticated element formulation). For the conventional finite element method, such as the cubic element, all accurate solutions can be only found at node. It means no accurate and reliable structural safety can be ensured within an element, and as a result, it hinders the engineering applications. The results of the paper are verified using analytical stability function studies, as well as with numerical results reported by independent researchers on several simple frames.

A homogeneous surface-enhanced Raman scattering platform for ultra-trace detection of trinitrotoluene in the environment

A facile and sensitive surface-enhanced Raman scattering substrate was prepared by controlled potentiostatic deposition of a closely packed single layer of gold nanostructures (AuNS) over a flat gold (pAu) platform. The nanometer scale inter-particle distance between the particles resulted in high population of ‘hot spots’ which enormously enhanced the scattered Raman photons. A renewed methodology was followed to precisely quantify the SERS substrate enhancement factor (SSEF) and it was estimated to be (2.2 ± 0.17) × 105. The reproducibility of the SERS signal acquired by the developed substrate was tested by establishing the relative standard deviation (RSD) of 150 repeated measurements from various locations on the substrate surface. A low RSD of 4.37 confirmed the homogeneity of the developed substrate. The sensitivity of pAu/AuNS was proven by determining 100 fM 2,4,6-trinitrotoluene (TNT) comfortably. As a proof of concept on the potential of the new pAu/AuNS substrate in field analysis, TNT in soil and water matrices was selectively detected after forming a Meisenheimer complex with cysteamine.

Molecular recognition of 2,4,6-trinitrotoluene by 6-aminohexanethiol and surface-enhanced Raman scattering sensor

2,4,6-trinitrotoluene (TNT) is one of the most commonly used nitro aromatic explosives in landmine, military and mining industry. This article demonstrates rapid and selective identification of TNT by surface-enhanced Raman spectroscopy (SERS) using 6-aminohexanethiol (AHT) as a new recognition molecule. First, Meisenheimer complex formation between AHT and TNT is confirmed by the development of pink colour and appearance of new band around 500 nm in UV-visible spectrum. Solution Raman spectroscopy study also supported the AHT:TNT complex formation by demonstrating changes in the vibrational stretching of AHT molecule between 2800-3000 cm−1. For surface enhanced Raman spectroscopy analysis, a self-assembled monolayer (SAM) of AHT is formed over the gold nanostructure (AuNS) SERS substrate in order to selectively capture TNT onto the surface. Electrochemical desorption and X-ray photoelectron studies are performed over AHT SAM modified surface to examine the presence of free amine groups with appropriate orientation for complex formation. Further, AHT and butanethiol (BT) mixed monolayer system is explored to improve the AHT:TNT complex formation efficiency. Using a 9:1 AHT:BT mixed monolayer, a very low detection limit (LOD) of 100 fM TNT was realized. The new method delivers high selectivity towards TNT over 2,4 DNT and picric acid. Finally, real sample analysis is demonstrated by the extraction and SERS detection of 302 pM of TNT from spiked.

Multimodal imaging of the collagen and elastic fibre networks in the bovine intervertebral disc

INTRODUCTION. The intervertebral disc is the largest avascular structure in the human body, withstanding transient loads of up to nine times body weight during rigorous physical activity. The key structural elements of the disc are a gel-like nucleus pulposus surrounded by concentric lamellar rings containing criss-crossed collagen fibres. The disc also contains an elastic fiber network which has been suggested to play a structural role, but to date the relationship between the collagen and elastic fiber networks is unclear. CONCLUSION. The multimodal transmitted and reflected polarized light microscopy technique developed here allows clear differentiation between the collagen and elastic fiber networks of the intervertebral disc. The ability to image unstained specimens avoids concerns with uneven stain penetration or specificity of staining. In bovine tail discs, the elastic fiber network is intimately associated with the collagen network.

Graphene quantum dots and the resonance light scattering technique for trace analysis of phenol in different water samples

A novel, highly selective resonance light scattering (RLS) method was researched and developed for the analysis of phenol in different types of industrial water. An important aspect of the method involved the use of graphene quantum dots (GQDs), which were initially obtained from the pyrolysis of citric acid dissolved in aqueous solutions. The GQDs in the presence of horseradish peroxidase (HRP) and H2O2 were found to react quantitatively with phenol such that the RLS spectral band (310 nm) was quantitatively enhanced as a consequence of the interaction between the GQDs and the quinone formed in the above reaction. It was demonstrated that the novel analytical method had better selectivity and sensitivity for the determination of phenol in water as compared to other analytical methods found in the literature. Thus, trace amounts of phenol were detected over the linear ranges of 6.00×10−8–2.16×10−6 M and 2.40×10−6–2.88×10−5 M with a detection limit of 2.20×10−8 M. In addition, three different spiked waste water samples and two untreated lake water samples were analysed for phenol. Satisfactory results were obtained with the use of the novel, sensitive and rapid RLS method.

Scattering of electromagnetic waves from chirally coated cylinders

The problem of electromagnetic scattering from an isotropic homogeneous chirally coated conducting cylinder is analysed. The cylinder is assumed to be illuminated by either a transverse magnetic or a transverse electric wave. Mie's analysis is used to evaluate the scattering characteristics. The computed results include the evaluation of the normalized scattering width and the absorption efficiency. The results show that there is a significant reduction in the normalized scattering width as compared to a RAM coated cylinder. This reduction has been attributed to increased absorption.