Non-existence of a massive scalar field for the Marder universe in Lyra and Riemannian geometries

In this paper, we have studied a massive scalar field for a Marder type universe in the context of Lyra and Riemannian geometries. From the exact solutions obtained we show that the massive scalar field does not survive in Lyra and Riemannian geometries for an anisotropic Marder type universe. Therefore we have solved the massless scalar field problem in Lyra and Riemann geometries for two cases. Also we have obtained vacuum solutions for homogeneous and anisotropic Marder space-time in Lyra geometry and the solutions obtained are compared by considering Lyra and Riemann geometries. Finally, some physical and kinematical properties are discussed by using graphics.     

Depth and orientational dependencies of MRI T(2) and T(1ρ) sensitivities towards trypsin degradation and Gd-DTPA(2-) presence in articular cartilage at microscopic resolution

Depth and orientational dependencies of microscopic magnetic resonance imaging (MRI) T(2) and T(1ρ) sensitivities were studied in native and trypsin-degraded articular cartilage before and after being soaked in 1 mM Gd-DTPA(2-) solution. When the cartilage surface was perpendicular to B(0), a typical laminar appearance was visible in T(2)-weighted images but not in T(1ρ)-weighted images, especially when the spin-lock field was high (2 kHz). At the magic angle (55°) orientation, neither T(2)- nor T(1ρ)-weighted image had a laminar appearance. Trypsin degradation caused a depth- and orientational-dependent T(2) increase (4%-64%) and a more uniform T(1ρ) increase at a sufficiently high spin-lock field (55%-81%). The presence of the Gd ions caused both T(2) and T(1ρ) to decrease significantly in the degraded tissue (6%-38% and 44%-49%, respectively) but less notably in the native tissue (5%-10% and 16%-28%, respectively). A quantity Sensitivity was introduced that combined both the percentage change and the absolute change in the relaxation analysis. An MRI experimental protocol based on two T(1ρ) measurements (without and with the presence of the Gd ions) was proposed to be a new imaging marker for cartilage degradation.     

The Effect of Rotation on the Onset of Double Diffusive Convection in a Horizontal Anisotropic Porous Layer

The effect of rotation and anisotropy on the onset of double diffusive convection in a horizontal porous layer is investigated using a linear theory and a weak nonlinear theory. The linear theory is based on the usual normal mode technique and the nonlinear theory on the truncated Fourier series analysis. Darcy model extended to include time derivative and Coriolis terms with anisotropic permeability is used to describe the flow through porous media. The effect of rotation, mechanical and thermal anisotropy parameters, and the Prandtl number on the stationary and overstable convection is discussed. It is found that the effect of mechanical anisotropy is to allow the onset of oscillatory convection instead of stationary. It is also found that the existence of overstable motions in case of rotating porous medium is not restricted to a particular range of Prandtl number as compared to the pure viscous fluid case. The finite amplitude analysis is performed to find the thermal and solute Nusselt numbers. The effect of various parameters on heat and mass transfer is also investigated.     

Large deformation of anisotropic austenitic stainless steel sheets at room temperature: Multi-axial experiments and phenomenological modeling

A newly developed multi-axial testing technique for sheet materials is employed to investigate the inelastic response of a temper-rolled stainless steel 301LN under isothermal quasi-static loading conditions at room temperature. The experimental technique consists of a flat sheet specimen, which is subject to combinations of shear and normal loading using a custom-made dual-actuator system. The large deformation behavior under monotonic loading is determined along more than 20 distinct radial paths in the stress space. The experimental results indicate that Hill's quadratic yield function along with an associated flow rule provides a good approximation of the initial yield behavior of this anisotropic two-phase FCC/BCC sheet material. Based on the experimental data for radial monotonic loading, it is concluded that conventional isotropic-kinematic hardening models cannot successfully describe the strain hardening of this austenitic steel. Instead, a non-associated anisotropic hardening model is proposed that relates the increase in yield strength to an isothermal martensitic transformation kinetics law. The comparison of the model predictions with the experimental results shows very good agreement for all biaxial and uniaxial experiments.     

Conditions for Strong Ellipticity of Anisotropic Elastic Materials

We consider the problem of finding the transversely isotropic elasticity tensor closest to a given elasticity tensor with respect to the Frobenius norm. A similar problem was considered by other authors and solved analytically assuming a fixed orientation of the natural coordinate system of the transversely isotropic tensor. In this paper we formulate a method for finding the optimal orientation of the coordinate system—the one that produces the shortest distance. The optimization problem reduces to finding the absolute maximum of a homogeneous eighth-degree polynomial on a two-dimensional sphere. This formulation allows us a convenient visualization of local extrema, and enables us to find the closest transversely isotropic tensor numerically.      

The plane problem of an elliptically reinforced circular hole in an anisotropic plate or laminate

Summary  Within the scope of linear elasticity, the in-plane problem of an anisotropic plate or laminate with a circular hole and an elliptical hole reinforcement is considered. Arbitrary anisotropic elastic stiffnesses are allowed for the base plate and the reinforcement material, and for the reinforcement there is no restriction for its elliptical shape and size. The analysis of the problem is performed by the complex potential method with appropriately chosen series representations inside and outside the reinforcement region. The derived closed-form solution provides all resultant in-plane stresses and deformations within and around the hole reinforcement with little computational effort and at high accuracy. The determined solution allows a proper and effective assessment of hole reinforcements for many technical applications. Received 26 June 2000; accepted for publication 26 September 2000     

Segmental orientations of trains versus loops and tails: the adsorbed polymethylmethacrylate system when the surface coverage is incomplete

We measure, for the first time, the separate surface coverage-dependent orientations of trains and of loops/tails in the structure of an adsorbed polymer, and show that these have different average orientations. The system was PMMA (atactic polymethylmethacrylate) adsorbed onto oxidized silicon from dilute solution in carbon tetrachloride at 25.0°C. The method was FTIR-ATR (infrared spectroscopy in attenuated total reflection). With increasing surface coverage, train segments were observed to maintain constant average anisotropy with respect to the solid surface. Free segments were preferentially flattened when the surface coverage was low, but with increasing surface coverage became progressively more random in orientation. Free and bound segments were separated according to shifts of the vibrational frequencies of carbonyl segments upon hydrogen-bonding to the surface silanol groups. The dependence of segmental orientation on molecular weight of the chain is also discussed.     

Evolution of subsequent yield surfaces and elastic constants with finite plastic deformation. Part-I: A very low work hardening aluminum alloy (Al6061-T6511)

In the present study, the initial and subsequent yield surfaces in Al 6061-T6511, based on 10 με deviation from linearity definition of yield, are presented. The subsequent yield surfaces are determined during tension, free end torsion, and combined tension–torsion proportional loading paths after reaching different levels of strains. The yield surfaces are also obtained after linear, bi-linear and non-linear unloading paths after finite plastic deformation. The initial yield surface is very close to the von-Mises yield surface and the subsequent yield surfaces undergo translation and distortion. In the case of this low work hardening material, the size of the yield surfaces is smaller and negative cross-effect is observed with finite plastic deformation. The subsequent yield have a usual “nose” in the loading direction and flattened shape in the reverse loading direction; the observed nose is more dominant in the case of tension and combined tension–torsion loading than in torsional loading. The size of the yield surfaces after unloading is smaller than the initial yield surface but larger than subsequent yield surfaces obtained during prior loading, show much smaller cross-effect, and the shape of these yield surfaces depends strongly on the loading and unloading paths. Elastic constants (Young’s and shear moduli) are also measured within each subsequent yield surfaces. Evolution of these constants with finite deformation is also presented. The decrease of the two moduli is found to be much smaller than reported earlier in tension by Cleveland and Ghosh [Cleveland, R.M., Ghosh, A.K., 2002. Inelastic effects on springback in metals. Int. J. Plast. 18, 769–785]. Part-II and III [(Khan et al., 2009a) and (Khan et al., 2009b)] of the papers will include experimental results on annealed 1100 Al (a very high work hardening material) and on both Al alloys (Al6061-T6511 and annealed 1100 Al) in tension- tension stress space, respectively. The results for both cases are quite different than the ones that are presented in this paper.     

On the Dynamic Interaction and Cross-Interaction of 2D Rigid Structures with Orthotropic Elastic Media Possessing General Principal Axes Orientation

A direct boundary element method (BEM) implementation for the dynamic interaction analysis in the frequency domain of 2D rigid structures with elastic orthotropic media is presented. The BEM implementation is based on non-singular full-space influence functions. The rigid structure response is obtained by applying equilibrium and kinetic compatibility conditions. The method is applied to the analysis of the dynamic response of a rigid tunnel in a half-space with various elasticity principal axes inclinations and to the analysis of two rigid rectangular galleries in a half space with various distances between them.