On the use of universal relations in the modeling of transversely isotropic materials

A material is of coaxial type   if the Cauchy stress tensor T$\mathit{T}$ and the strain tensor B$\mathit{B}$ are coaxial for all deformations. Clearly a hyperelastic material is of coaxial type if and only if it is isotropic. Here we present a weaker definition of materials of coaxial type. Anisotropic materials may be of a coaxial type in a weak sense if for a given specific  B$\mathit{B}$ we have that TB=BT$\mathit{TB}=\mathit{BT}$. We denote these materials B$\mathit{B}$-coaxial. We show that for transverse isotropic materials weak coaxial constitutive equations may be characterized using universal relations. We discuss the impact of B$\mathit{B}$-coaxial materials in the modeling of soft tissues. We conclude that B$\mathit{B}$-coaxial materials are a strong evidence that in real world materials two anisotropic invariants are always necessary to model in a meaningful and correct way single fiber reinforced materials.     

Finite elastic deformations of transversely isotropic circular cylindrical tubes

We consider the finite radially symmetric deformation of a circular cylindrical tube of a homogeneous transversely isotropic elastic material subject to axial stretch, radial deformation and torsion, supported by axial load, internal pressure and end moment. Two different directions of transverse isotropy are considered: the radial direction and an arbitrary direction in planes normal locally to the radial direction, the only directions for which the considered deformation is admissible in general. In the absence of body forces, formulas are obtained for the internal pressure, and the resultant axial load and torsional moment on the ends of the tube in respect of a general strain-energy function. For a specific material model of transversely isotropic elasticity, and material and geometrical parameters, numerical results are used to illustrate the dependence of the pressure, (reduced) axial load and moment on the radial stretch and a measure of the torsional deformation for a fixed value of the axial stretch.     

A novel beam–spin asymmetry in double-hadron inclusive lepto-production

We show that a new beam–spin asymmetry appears in deep inelastic inclusive lepto-production at low transverse momenta when a hadron in the target fragmentation region is observed in association with another hadron in the current fragmentation region. The beam leptons are longitudinally polarized while the target nucleons are unpolarized. This asymmetry is a leading-twist effect generated by the correlation between the transverse momentum of quarks and the transverse momentum of the hadron emitted by the target. Experimental signatures of this effect are discussed.     

Influence of transverse field on the spin-3/2 Blume–Capel model on rectangular lattice

Transverse field effect on thermodynamic properties of the spin-3/2 Blume–Capel model on rectangular lattice in which the interactions in perpendicular directions differ in signs is studied within the mean field approximation. Phase diagrams in the (transverse field, temperature) plane are constructed for various values of single-ion anisotropy.     

A higher order finite element including transverse normal strain for linear elastic composite plates with general lamination configurations

This paper describes a higher-order global-local theory for thermal/mechanical response of moderately thick laminated composites with general lamination configurations. In-plane displacement fields are constructed by superimposing the third-order local displacement field to the global cubic displacement field. To eliminate layer-dependent variables, interlaminar shear stress compatibility conditions have been employed, so that the number of variables involved in the proposed model is independent of the number of layers of laminates. Imposing shear stress free condition at the top and the bottom surfaces, derivatives of transverse displacement are eliminated from the displacement field, so that C⁰ interpolation functions are only required for the finite element implementation. To assess the proposed model, the quadratic six-node C⁰ triangular element is employed for the interpolation of all the displacement parameters defined at each nodal point on the composite plate. Comparing to various existing laminated plate models, it is found that simple C⁰ finite elements with non-zero normal strain could produce more accurate displacement and stresses for thick multilayer composite plates subjected to thermal and mechanical loads. Finally, it is remarked that the proposed model is quite robust, such that the finite element results are not sensitive to the mesh configuration and can rapidly converge to 3-D elasticity solutions using regular or irregular meshes.     

Theoretical validation on the existence of two transverse surface waves in piezoelectric/elastic layered structures

In this paper, we analytically study the dispersion behavior of transverse surface waves in a piezoelectric coupled solid consisting of a transversely isotropic piezoelectric ceramic layer and an isotropic metal or dielectric substrate. This study is a revisit to the stiffened Love wave propagation done previously. Closed-form dispersion equations are obtained in a very simple mathematical form for both electrically open and shorted cases. From the viewpoint of physical situation, two transverse surface waves (i.e., the stiffened Love wave and the FDLW-type wave) are separately found in a PZT-4/steel system and a PZT-4/zinc system. All the observed dispersion curves are theoretically validated through the discussion on the limit values of phase velocity using the obtained dispersion equations. Those validation and discussion give rise to a deeper understanding on the existence of transverse surface waves in such piezoelectric coupled structures. The results can be used as a benchmark for the study of the wave propagation in the piezoelectric coupled structures and are significant in the design of wave propagation in the piezoelectric coupled structures as well.     

Role of anisotropy on the domain wall properties of ferromagnetic nanotubes

In this paper we investigate the role of magneto-crystalline anisotropy on the domain wall (DW) properties of tubular magnetic nanostructures. Based on a theoretical model and micromagnetic simulations, we show that either cubic or uniaxial magneto-crystalline anisotropies have some influence on the domain wall properties (wall size, propagation velocity and energy barrier) and then on the overall magnetization reversal mechanism. Besides the characterization of the transverse and vortex domain wall sizes for different anisotropies, we predict an anisotropy dependent transition between the occurrence of transverse and vortex domain walls in tubular nanowires. We also discuss the dynamics of the vortex DW propagation gradually increasing the uniaxial anisotropy constant and we found that the average velocity is considerably reduced. Our results show that different anisotropies can be considered in real samples in order to manipulate the domain wall behavior and the magnetization reversal process.     

Low temperature radio-frequency transverse susceptibility measurements using a CMOS oscillator circuit

A transverse susceptibility (TS) measurement system based on a simple inverter CMOS cell oscillator cross-coupled to a LC tank is presented. The system has been implemented to operate at a Quantum Design Physical Properties Measurement System (PPMS). We introduce several improvements with respect to similar currently operating TS measurement equipments. The electronics have been redesigned to use CMOS transistors as active devices, which simplifies the circuit design and enlarge the tuning range, thus making the proposed electronic block more feasible, predictable, and precise. Additionally, we propose a newly designed sample holder, which facilitates the procedure to change a sample and improves reproducibility of the circuit. Our design minimizes the thermal leak of the measuring probe by one order of magnitude, allowing to measure from 1.8 K in standard PPMS systems, thanks to the use of a low temperature beryllium–copper coaxial cable instead of the conventional RG402 Cu coaxial cable employed in the insert for the PPMS in similar systems. The data acquisition method is also simplified, so that the measuring sequences are implemented directly in the PPMS controller computer by programming them in the Quantum Design MultiVu software that controls the PPMS. We present the test measurements performed on the system without sample to study the background signal and stability of the circuit. Measurements on a Gd₂O₃ calibrating sample yield to the estimation of the system sensitivity, which is found to be on the order of 10⁻⁶ emu. Finally, measurements on a TmCo₂ Laves phase sample with a ferrimagnetic transition temperature around 4 K are described, demonstrating that the developed system is well suited to explore interesting magnetic phenomena at this temperature scale.     

Effect of dispersion on the diffusion zone in two-phase laminar flows in microchannels

Aim of the present work is to investigate the reaction–diffusion process of a two species system under laminar flow in a T-shaped microchannel. A zone formed at the interface between the aqueous solutions of these two species is affected by advection and diffusion. Through theoretical analyses and experimental results, the effect of dispersion has been shown to influence this diffusion zone. We have defined a parameter called effective diffusivity, to account for the dispersion effects and observed it to be a function of the channel Peclet number. In the limiting case of low Peclet number, this parameter is constant and turns out to be equal to the molecular diffusivity. We have also related effective diffusivity and the dispersion coefficient through scaling estimates.