Neutral Inhomogeneity Research Articles

Neutral inhomogeneity in circular cylinder subjected to prescribed boundary displacement

In this paper a single circular inhomogeneity embedded within a solid circular cylinder whose curved boundary surface is subjected to a given boundary displacement in axial direction is considered. The displacement neutrality of the coupled system of host body and inclusion is studied. The neutral inhomogeneity (inclusion) does not disturb the displacement, strain and stress fields in the host body. In this paper the deformation of the considered inhomogeneous cylinder is a linear antiplane shear deformation.

Suppressing thermal stress in the vicinity of a circular nano-inhomogeneity via the mechanism of size effects

Thermal stress is one of the main factors threatening the reliability of nanocomposites. In this paper, we propose a set of interfacial conditions to simulate the interfacial phonon scattering and interfacial elasticity in the nanocomposite, and then obtain closed-form solutions for the thermal-elastic fields around the circular nano-inhomogeneity. The results show that the interfacial thermal stress within matrix is more sensitive to interfacial phonon scattering than that in nano-inhomogeneity, while the size change of inhomogeneity has greater impact on the stress of nano-inhomogeneity than that of the matrix. In view of the significant effects of thermal conductivities and thermal expansion coefficients on the thermal stress around inhomogeneity, the maximum von Mises stress is reduced up to three orders of magnitude by adjusting these parameters. More importantly, the thermal stresses within matrix and inhomogeneity can be, respectively, designed as “zero” even though the nanocomposite is subjected to a large thermal loading, which is viewed as an update mechanism of “neutral inhomogeneity.” Our work provides guidance for the design of nanocomposites and has important potential applications.

Neutral Inhomogeneities in a Two-dimensional Steady-state Heat Conduction Problem

A steady-state heat conduction problem is considered in a two-dimensional solid body which is filled up composite circular inclusions. The composite circular inclusions consist of a core and a coating both of which are cylindrically orthotropic. In this paper the neutral inhomogeneity is defined as a foreign body (inclusion) which can be introduced into the host body (matrix) without distributing the temperature field in the originally homogeneous body. The perfect thermal contacts are assumed to be between the different components of nonhomogeneous bodies.

Discharge characteristics and increased electron current during azimuthally nonuniform propellant supply in an anode layer Hall thruster

Discharge current components, such as electron, ion beam, and lost-to-wall currents, are obtained as functions of azimuthal propellant inhomogeneity in a Hall thruster. Discharge characteristics are discussed based on discharge current oscillation and radial–azimuthal discharge photography. A highly oscillative operation regime is found to be accompanied by radially enlarged expansion of discharge under limited electron currents. Further increases in neutral inhomogeneity lead to quiescent discharge combined with enhanced electron currents and an azimuthally separated ionization region. An axial one-dimensional classical view of electron flow is found to explain the observed electron current evolution only until moderate propellant inhomogeneity occurs. Through discharge image analysis, it is shown that plasma inhomogeneity increases linearly with respect to the input neutral particle inhomogeneity. The evolution of the inhomogeneity does not capture a stepwise increase in the electron current during discharge mode changes; however, the monotonic increase featured in each discharge regime shows that the azimuthal gradient of plasma properties can contribute to increased electron current. Lastly, the weakened magnetic barrier to electron flow resulting from axial–azimuthal variation in plasma structures is presented as another possible cause of increased electron current in nonuniform propellant operations.

Design of a neutral elastic inhomogeneity via thermal expansion

A neutral elastic inhomogeneity does not affect the existing stress field when inserted into an elastic body. It has been shown that no such inhomogeneity can exist under the classical assumption of a perfectly bonded interface between the inhomogeneity and the surrounding material. We show that by introducing a suitable temperature field inside the inhomogeneity it is indeed possible to achieve neutrality regardless of the perfect bonding assumption. Specifically, we show that a nonuniform internal temperature field can induce neutrality in an inhomogeneity in the form of an elastic ring with concentric internal and external boundaries of arbitrary shape. Noting that such a temperature field can be identified also in the case of an unpunched inhomogeneity when the inhomogeneity is line-shaped, we further prove that even a flake-shaped inhomogeneity can be made neutral if the thickness of the flake is much smaller than its length. In the case that the elastic body surrounding the unpunched inhomogeneity is subjected to remote hydrostatic loading, the temperature field within the inhomogeneity will remain uniform and independent of the shape of the inhomogeneity. In fact, in this case, the temperature field inside the inhomogeneity depends only on the elastic parameters of the composite and the direction of the remote loading and can be higher or lower than the operating temperature of the composite.

Neutral Inhomogeneity in Circular Cylinder Subjected to Axial Load on its Lateral Boundary

In this paper we consider the problem of single circular elastic inhomogeneity embedded within a circular cylinder whose curved boundary surface is subjected to surface traction acting on axial direction. We investigate the displacement neutrality of the coupled system of host body and inclusion. Neutral inhomogeneity (inclusion) does not disturb the displacement, strain and stress fields in the host body. The deformation of the considered inhomogenneous cylinder is antiplane shear deformation.

Neutral Inhomogeneity in Circular Cylinder Subjected to Axial Load on its Lateral Boundary

In this paper we consider the problem of single circular elastic inhomogeneity embedded within a circular cylinder whose curved boundary surface is subjected to surface traction acting on axial direction. We investigate the displacement neutrality of the coupled system of host body and inclusion. Neutral inhomogeneity (inclusion) does not disturb the displacement, strain and stress fields in the host body. The deformation of the considered inhomogenneous cylinder is antiplane shear deformation.

Thermal Expansion Induced Neutrality of a Circular and an Annular Elastic Inhomogeneity

Abstract An elastic inhomogeneity is termed neutral if its introduction does not disturb the original stress field in the initially uncut elastic body. Neutrality in this sense is often achieved by appropriate design criteria such as a careful choice of the shape of the inhomogeneity and the properties of the interfacial layer between the inhomogeneity and its surrounding matrix. Unfortunately, mismatched stress and strain fields in the resulting composite structure make it difficult to simultaneously control both the shape of the inhomogeneity and its interfacial properties to achieve the desired neutrality property. We assert that the associated temperature field can be used to adjust the stress and strain fields within the inhomogeneity via thermal expansion, thus allowing us to control the properties of the interfacial layer for a given shape of inhomogeneity. Our theoretical results show that the design of a neutral circular or annular elastic inhomogeneity requires an accompanying internal uniform temperature field when the elastic body is in equi-biaxial tension and an internal temperature field which is quadratic if the body is subjected to uniaxial tension or shear force. More importantly, in contrast to the well-established result in the literature for a purely elastic inhomogeneity, under certain conditions, a neutral elastic inhomogeneity can be designed via thermal expansion despite the assumption of a perfectly bonded interface between the inhomogeneity and the surrounding matrix.

Plasma formation and cross-field electron transport induced by azimuthal neutral inhomogeneity in an anode layer Hall thruster

The fluctuation of the azimuthal electric field caused by the electron drift instability or the rotating spokes in the E×B plasma is known to enhance the electron cross field transport. The increased electron current, observed during the operation of a Hall thruster with a nonuniform propellant supply in azimuthal direction, also appears to be related to the azimuthal electric field. In this paper, we experimentally investigate how neutral inhomogeneity in azimuth affects the plasma structure formation, and how this self-organized structure influences the electron cross field transport. We observed an axial-azimuthally varying space potential structure, which results in an alleviated effective axial potential profile and induces the azimuthal electric field. From the distributions of the light emission intensity and plasma density, we show that the azimuthal profile of plasma is skewed in the direction of Ez×Br drift of the magnetized electrons and that the spatial scale of the structure matches the spatial scale of the input neutral variation. The plasma structure reveals that the axial electron drift transport from the induced azimuthal electric field is the most dominant factor due to its equivalent mobility 1/B, which is two orders of magnitude greater than the classical collisional mobility perpendicular to the magnetic field. This indicates that neutrals contribute to the electron cross field transport not only directly through the elastic collisions but also indirectly through their influence on the formation of the plasma structure, which enhances the cross field transport. Lastly, we show that the effective electron mobility rides on 1/16Br line when deviating from the classical mobility line and that the effective Hall parameter is greatly reduced where Eθ develops.

Effect of a circular Eshelby inclusion on the non‐elliptical shape of a coated neutral inhomogeneity with internal uniform stresses

AbstractUsing conformal mapping techniques, we present the design of a coated non‐elliptical neutral inhomogeneity with internal uniform stresses which does not disturb a prescribed uniform anti‐plane stress field in the surrounding matrix when both a circular Eshelby inclusion present in the thick coating and the inhomogeneity itself undergo uniform eigenstrains. An appropriately chosen conformal mapping function maps the doubly connected domain of the thick coating onto an annulus in the image plane. All of the unknown complex constants appearing in the mapping function can be uniquely determined. Detailed numerical results are presented to demonstrate the proposed theory. We also consider a related problem concerning a neutral coated inhomogeneity with internal uniform stresses in the presence of a screw dislocation dipole in the thick coating.

Uniqueness of Neutral Elastic Circular Nano-Inhomogeneities in Antiplane Shear and Plane Deformations

In elasticity theory, a neutral inhomogeneity is defined as a foreign body which can be introduced into a host solid without disturbing the stress field in the solid. The existence of circular neutral elastic nano-inhomogeneities has been established for both antiplane shear and plane deformations when the interface effect is described by constant interface parameters, and the surrounding matrix is subjected to uniform external loading. It is of interest to determine whether noncircular neutral nano-inhomogeneities can be constructed under the same conditions. In fact, we prove that only the circular elastic nano-inhomogeneity can achieve neutrality under these conditions with the radius of the inhomogeneity determined by the corresponding (constant) interface parameters and bulk elastic constants. In particular, in the case of plane deformations, the (uniform) external loading imposed on the matrix must be hydrostatic in order for the corresponding circular nano-inhomogeneity to achieve neutrality. Moreover, we find that, even when we relax the interface condition to allow for a nonuniform interface effect (described by variable interface parameters), in the case of plane deformations, only the elliptical nano-inhomogeneity can achieve neutrality.

Neutral spherical inhomogeneities in a twisted circular cylindrical bar

We consider the torsion problem of a circular cylindrical bar which is filled up with composite spherical inclusions. The composite inclusions consist of a core and coating both of which are spherically orthotropic with the volume fractions of the core being the same in every composite inclusion. The center points of the spherical inhomogeneities are on the axis of revolution of the circular cylinder. The neutral inhomogeneity in the considered problem of elastic equilibrium is defined as a foreign body (inclusion) which can be introduced in a host body without disturbing the elastic field (displacements, stresses) in it. The conditions of the neutral inhomogeneity for the twisted circular cylindrical bar are derived, and some special cases of inhomogeneity are analyzed. The present paper gives a new example for neutral inhomogeneity in the field of elasticity.

Design of neutral elastic inhomogeneities in plane elasticity in the case of non-uniform loading

We use the concept of imperfect interface to design a (stress) neutral elastic inhomogeneity in the case when the inhomogeneity-matrix system is subjected to plane deformations. Of particular interest is the fact that the prescribed stress field inside the matrix is assumed to be non-uniform. Using complex variable techniques, we derive conditions on the functions describing the (imperfect) interface to ensure neutrality in several cases of practical interest.

Neutrality of the elliptic inhomogeneity in the case of non-uniform loading

In this paper, we consider the problem of a single elliptic elastic inhomogeneity embedded within an infinite elastic matrix in antiplane shear. In particular, we examine the (stress) neutrality of this inhomogeneity when a non-uniform stress field is prescribed in the surrounding matrix. Since it is known that neutral elastic inhomogeneities do not exist when the inhomogeneity is assumed to be perfectly bonded to the matrix, the method presented here is based on the assumption of imperfect interface and the appropriate choice of the (single) interface parameter (characterizing the imperfect interface) to achieve the desired neutrality. Specifically, neutrality is established for specific (polynomial) classes of prescribed states of stress in the surrounding matrix. The results in this paper affirm the feasibility of designing a neutral elastic inhomogeneity by controlling the (imperfect) interface parameter describing the inhomogeneity–matrix interface.

Neutral inhomogeneities in conduction phenomena

A neutral inhomogeneity in heat conduction is defined as a foreign body which can be introduced in a host solid without disturbing the temperature field in it. The existence of neutral inhomogeneities in conduction phenomena is studied in the present paper. Both the inhomogeneity and the host body are assumed to be isotropic, with the inhomogeneity being either less or more conducting than the surrounding body. The property of neutrality is defined in this work with respect to an applied constant temperature gradient in the host solid. It is achieved by introducing a non-ideal interface between the two media across which the continuity requirement of either the temperature field or the normal component of the heat flux is relaxed. These interfaces are called non-ideal interfaces and represent a thin interphase of low or high conductivity; they are characterized in terms of some scalar interface parameters which usually vary along the interface in order to ensure neutrality. The conditions to be satisfied by the field variables at a non-ideal interface with a variable interface parameter are first derived, and closed form solutions are presented for the interface parameters at neutral inhomogeneities of various shapes. In two-dimensional problems, duality relations are established for composite media with non-ideal interfaces and variable interface parameters. These are implemented in establishing general criteria for neutrality. The terminology of heat conduction is used throughout in the paper but all the results can be directly transferred to the domains of electrical conduction, dielectric behavior or magnetic permeability.