A macroscopic consitutive model on induced anisotropy for polymers with weighting functions

The alignment of polymer chains is a well known microstructural evolution effect due to straining of polymers. This has a drastic influence on the macroscopic properties of the initially isotropic material, such as a pronounced strength in the loading direction of stretched films. Experiments on strain induced anisotropy at room temperature are analyzed by optical measurements. For modeling the effect of strain induced anisotropy a macroscopic constitutive model is presented. As a key idea, weighting functions are introduced to represent a strain-softening/hardening-effect to account for induced anisotropy. These functions represent the ratio between the total strain rate and a structural tensor. In this way, material parameters are used as a sum of weighted direction related quantities. In the finite element examples we simulate the cold-forming of amorphous thermoplastic films below the glass transition temperature subjected to different re-loading directions. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Plasma transport coefficients: An application of SO(3) group

The appearance of anisotropy in certain properties such as conductivity and diffusion coefficients could be induced by the application of external magnetic fields. Using the matricial representation of SO(3) group it was possible to demonstrate that this anisotropy is characterized by a rotation of plasma current. This work presented in a didatical way the relation between the external magnetic field and some plasma parameters with the rotation angle.     

Homogenization of Linear Elastic Properties of Silicon Nitride

The effective linear elastic properties of silicon nitride (Si₃N₄) are estimated based on first–, third–, and fifth–order bounds of the strain energy density. This specific type of material is a mixture of two linear elastic materials with different material symmetries. The β-Si₃N₄ grains have a hexagonal symmetry with significant amount of anisotropy, whereas the glassy phase is approximately isotropic. The results are as follows: i) The fifth–order upper and lower bounds are almost identical. Therefore, these bounds are sufficient for estimating the effective elastic properties. ii) For fixed elastic constants of the hexagonal β-Si₃N₄ grains, the effective properties of Si₃N₄ are determined as a function of properties of the glassy phase and its volume fraction. The corresponding diagrams allow for the inverse identification of the elastic properties of the glassy phase. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Determination of the thermoelastic characteristics of spatially reinforced fibrous media in the case of general anisotropy of their components

A model of spatially reinforced media whose constituents possess the general anisotropy is proposed, which allows one to determine the effective thermomechanical characteristics of a hybrid composite and the stress-strain state in phase materials.     

Structure and magnetic properties of nanocrystalline ferromagnets (II)

The role of magnetoelastic coupling effects in nanocrystalline ferromagnets is investigated by means of high-field magnetization and Doppler-broadening spectrum measurements. For the nanocrystalline Fe_{73 5}Cu₁Nb₃Si_13.5B₉ alloy, the results show that the pinning effects resulting from the quasidislocation dipole intensely influence the movement of domain wall; by coupling with the magnetostriction the defects-induced stress fields determine the magnetic properties at the early stage of crystallization. In view of the effective anisotropy and magnetoelastic coupling energy the optimal annealing conditions of alloys are discussed.     

Indirect interaction between nuclear spins in easy-axis antiferromagnets

We consider two atoms with nuclear spins I = 1/2 belonging to a regular chain (spin register) of isotopes substituting basic nuclear-spin-free atoms in a plate of an antiferromagnet with the easy anisotropy axis. A constant external magnetic field is assumed to be directed along the easy axis perpendicular to the plate plane and to have a constant gradient along the register direction. For a simple model, we diagonalize the spin Hamiltonian in a spin-wave approximation using the Bogoliubov-Tyablikov transformation. We show that in the presence of a nonuniformity of the external magnetic field, the indirect interaction between nuclear spins caused by the hyperfine interaction of nuclear spins with virtual spin waves in the antiferromagnet can increase and even oscillate depending on the distance between the considered spins if the local field at the midpoint between them is close to the field of the orientational phase transition to the spin-flop phase in a homogeneous antiferromagnet.     

The effects of strong magnetic fields and rotation on soliton stars at finite temperature

We study the effects of strong magnetic fields and uniform rotation on the properties of soliton stars in Lee-Wick model when a temperature dependence is introduced into this model. We first recall the properties of the Lee-Wick model and study the properties of soliton solutions, in particular, the stability condition, in terms of the parameters of the model and in terms of the number of fermions N inside the soliton (for very large N) in the presence of strong magnetic fields and uniform rotation. We also calculate the effects of gravity on the stability properties of the soliton stars in the simple approximation of coupling the Newtonian gravitational field to the energy density inside the soliton, treating this as constant throughout. Following Cottingham and Vinh Mau, we also make an analysis at finite temperature and show the possibility of a phase transition which leads to a model with parameters similar to those considered by Lee and his colleagues but in the presence of magnetic fields and rotation. More specifically, the effects of magnetic fields and rotation on the soliton mass and transition temperature are computed explicitly. We finally study the evolution on these magnetized and rotating soliton stars with the temperature from the early universe to the present time.     

The NMR line shape of a system of nuclear spins with equal spin-spin coupling constants

We obtain an expression for the NMR line at low temperatures for a system of nuclear spins described by a Hamiltonian with equal spin-spin coupling constants. We show that in the case of “easy axis” anisotropy, the line has a logarithmic low-frequency singularity and an exponentially decreasing high-frequency asymptotic behavior at the temperature of an anomalous peak of heat capacity. In the case of “easy plane” anisotropy, the line has the traditional Gaussian form. We discuss the possibility of using NMR data to discover specific thermodynamic and magnetic properties of the considered model system.     

New exact multi-coated ellipsoidal inclusion model for anisotropic thermal conductivity of composite materials

The present study deals with a new micromechanical modeling of the thermal conductivity of multi-coated inclusion-reinforced composites. The proposed approach has been developed in the general frame of anisotropic thermal behavior per phase and arbitrary ellipsoidal inclusions. Based on the Green's function technique, a new formulation of the problem of multi-coated inclusion is proposed. This formulation consists in constructing a system of integral equations, each associated to the thermal conductivity of each coating and the reference medium. Thanks to the concept of interior- and exterior-point Eshelby's conduction tensors, the exact solution of the problem of multicoated inclusion is obtained. Analytical expressions of the intensity in each phase and the effective thermal conductivity of the composite, through homogenizations schemes such as Generalized self-consistent and Mori-Tanaka models are provided. Results of the present model are successfully compared with those issued from both analytical models and finite elements methods for composites with doubly coated inclusions. Moreover, the developed micromechanical model has been applied to a three phase composite materials in order to analyze combined effects of the aspect ratio and the volume fraction of the ellipsoidal inclusions, the anisotropy of the thermal conductivity of interphase, the thermal conductivity contrast between local phases on the predicted effective thermal conductivity.     

Modeling of skin anisotropy directions for identifying stress free reference configuration of the female breast

Biomechanical simulations of the female breast are important for surgical applications such as implants augmentation, tumorectomy and reconstruction after the tumor removal. One of the main challenges for such breast simulations is to define its reference configuration which can be considered as a stress free state. Indeed, MRI (Magnetic Resonance Imaging) scans of the breast can be obtained only under gravitational load which introduces a considerable stress and strains level for any position of the patient. Moreover, realistic material properties especially anisotropy of skin should be taken into account. This anisotropy can play an important role but has not so far been considered in biomechanical simulations of the breast. In the current contribution, we implement an iterative method to define the reference configuration of the breast model according to MRI data of certain individuals in the prone position by taking into account the anisotropy directions of skin. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An effective permeability model to predict field-dependent modulus of magnetorheological elastomers

Magnetorheological elastomers (MREs) are composites where magnetic particles are suspended in a non-magnetic solid or a gel-like matrix. MREs are shown to have a controllable, field-dependent shear modulus. Most of conventional MREs models are based on magnetic dipole interactions between two adjacent particles of the chain. These models can predict the field-dependent properties of MREs with simple chain-like structures. In this paper, an effective permeability model is proposed to predict the field-induced modulus of MREs. Based on the effective permeability rule and taking into account the particle’s saturation, the model is proposed to predict the mechanical performances of MREs with complex structure and components. The effectiveness of the model is justified by a designed novel MREs.     

Solid State Amorphisation in Magnetic Multilayers: the Interface Structure and the Electrical Transport Properties

The structure and electrical conductivity properties of the R.F. sputtered FeZr and FeTi multilayers with ultrathin layer thicknesses, in as-deposited states, have been studied using X-ray diffraction, low-angle X-ray and neutron reflectometry, conversion electron Mössbauer spectroscopy (CEMS), resistivity and magnetoresistivity measurements. The thickness ratio (β=d_Fed_Zr and d_Fed_Ti) of analysed multilayers was 0.5 and 1, the values of the bilayer thickness (λ=d_Fe+d_Ti,Zr) was varied from 9 Å to 600 Å, maintaining constant the total thickness of the samples by controlling the number of bilayers. The results obtained from CEM-spectroscopy and X-ray diffraction show that Fe layers of the thickness below 20 Å are alloyed forming an amorphous phase during deposition. This amorphous phase is distributed in the plane between the crystalline sublayers as well as in the grain boundaries according with the proposed model of the interpretation of the electrical conductivity as a function of the bilayer thickness (λ).     

Effect of homogeneous and heterogeneous chemical reactions on peristaltic transport of an MHD micropolar fluid with wall effects

In this paper, the influence of magnetic field on the dispersion of a solute in peristaltic flow of an incompressible micropolar fluid is studied as a model of fluid transport in the human intestinal system with wall properties. Long wavelength approximation, Taylor's limiting condition, and dynamic boundary conditions at the flexible walls are used to obtain the average effective dispersion coefficient in the presence of combined homogeneous and heterogeneous chemical reactions. The effects of various pertinent parameters on the effective dispersion coefficient are discussed. Average effective dispersion coefficient increases with amplitude ratio, which implies that dispersion is more in the presence of peristalsis. It also increases with the cross‐viscosity coefficient, heterogeneous chemical reaction rate, and wall parameters. Further, dispersion decreases with micropolar parameter, magnetic parameter, and homogeneous chemical reaction rates. Copyright © 2015 John Wiley & Sons, Ltd.     

Theoretical model of the anisotropy of low-cycle deformability of glass-fiber reinforced plastics

Conclusion A theoretical model is suggested for the anisotropy of low-cycle deformability of glass plastics determined by the anisotropy of the deformational properties of the material in short-term static tension (compression). The effect of the anisotropy of cyclic loss of strength of the deformational properties is taken into account by the introduction of the characterizing function which is taken to be independent of the mechanical properties of the material and of the conditions of low-cycle loading.Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 437–442, May–June, 1985.     

Dynamics of Bianchi Type I Solutions of the Einstein Equations with Anisotropic Matter

We analyze the global dynamics of Bianchi type I solutions of the Einstein equations with anisotropic matter. The matter model is not specified explicitly but only through a set of mild and physically motivated assumptions; thereby our analysis covers matter models as different from each other as, e.g., collisionless matter, elastic matter and magnetic fields. The main result we prove is the existence of an ‘anisotropy classification’ for the asymptotic behaviour of Bianchi type I cosmologies. The type of asymptotic behaviour of generic solutions is determined by one single parameter that describes certain properties of the anisotropic matter model under extreme conditions. The anisotropy classification comprises the following types. The convergent type A₊: Each solution converges to a Kasner solution as the singularity is approached and each Kasner solution is a possible past asymptotic state. The convergent types B₊ and C₊: Each solution converges to a Kasner solution as the singularity is approached; however, the set of Kasner solutions that are possible past asymptotic states is restricted. The oscillatory type D₊: Each solution oscillates between different Kasner solutions as the singularity is approached. Furthermore, we investigate non-generic asymptotic behaviour and the future asymptotic behaviour of solutions. Submitted: October 28, 2008.; Accepted: January 26, 2009.     

Flow-induced anisotropic viscosity in short fiber reinforced polymers

The commonly used flow models for fiber reinforced polymers often neglect the flow induced mechanical anisotropy of the suspension. With an increasing fiber volume fraction, this plays, however, an important role. There are some models which count on this effect, they are, however, phenomenological and require a fitted model parameter. In this paper, a micromechanically based constitutive law is proposed which considers the flow induced anisotropic viscosity of the fiber suspension. The introduced viscosity tensor can handle arbitrary anisotropy of the fluid-fiber mixture depending on the actual fiber orientation distribution. A homogenization method for unidirectional structures in contribution with orientation averaging is used to determine the effective viscosity tensor. The motion of rigid ellipsoidal fibers induced by the flow of the matrix material is described by Jeffery's equation. A numerical implementation of the introduced model is applied to representative flow modes. The calculated stress values are analyzed in transient and stationary flow cases. They show a less pronounced anisotropic viscous behaviour in every investigated case compared to the results obtained by the use of the Dinh-Armstrong constitutive law. The reason for the qualitative difference is that the presented model depends on the complete orientation information, while the other one is linear in the fourth-order fiber orientation tensor. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spectral and dispersion properties of pair soliton states in a quasi-one-dimensional anisotropic antiferromagnet withS=1/2

By solution of the Schrödinger equation in the continuum approximation, it is shown analytically that there exist excited eigenstates of the quasi-one-dimensional Ising antiferromagnet with spinS=1/2 in the form of spatially localized quantum states. Computer modeling of a discrete model of interacting solitons with allowance for the symmetry of the solutions gives eigenvalues of the Sturm sequence that differ from the solutions of the continuum approximation. The spectral and dispersion properties of the nonlinear bound states of lowest energy and the selection rules in resonance transitions in an external magnetic field applied parallel to and perpendicular to the axis of magnetic anisotropy are calculated.L. V. Kirenski Physics Institute, Siberian Branch, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 91, No. 1, pp. 112–119, April, 1992.     

Hybrid Simulation of Space Plasmas: Models with Massless Fluid Representation of Electrons. IV. Kelvin–Helmholtz Instability

This is a survey of the literature on hybrid simulation of the Kelvin–Helmholtz instability. We start with a brief review of the theory: the simplest model of the instability—a transition layer in the form of a tangential discontinuity; compressibility of the medium; finite size of the velocity shear region; pressure anisotropy. We then describe the electromagnetic hybrid model (ions as particles and electrons as a massless fluid) and the main numerical schemes. We review the studies on two-dimensional and three-dimensional hybrid simulation of the process of particle mixing across the magnetopause shear layer driven by the onset of a Kelvin–Helmholtz instability. The article concludes with a survey of literature on hybrid simulation of the Kelvin–Helmholtz instability in finite-size objects: jets moving across the magnetic field in the middle of the field reversal layer; interaction between a magnetized plasma flow and a cylindrical plasma source with zero own magnetic field.