Interaction between a screw dislocation and an elastic elliptical inhomogeneity with interfacial cracks

The elastic interaction between a screw dislocation and an elliptical inhomogeneity with interfacial cracks is studied. The screw dislocation may be located outside or inside the inhomogeneity. An efficient complex variable method for the complex multiply connected region is developed, and the general solutions to the problem are derived. As illustrative examples, solutions in explicit series form for complex potentials are presented in the case of one or two interfacial cracks. Image forces on the dislocation are calculated by using the Peach-Koehler formula. The influence of crack geometries and material properties on the image forces is evaluated and discussed. It is shown that the interfacial crack has a significant effect on the equilibrium position of the dislocation near an elliptical-arc interface. The main results indicate, when the length of the crack goes up to a critical value, the presence of the interfacial crack can change the interaction mechanism between a screw dislocation and an elliptical inclusion. The present solutions can include a number of previously known results as special cases.

Analysis of a piezoelectric screw dislocation inside an elliptical inhomogeneity with confocal rigid line in piezoelectric material

This paper deals with the electro-elastic coupling interaction between a piezoelectric screw dislocation which is located inside the elliptical inhomogeneity and an electrically conductive confocal rigid line under remote anti-plane shear stresses and in-plane electrical loads in piezoelectric composite material. The analytical-functions of the complex potentials, stress fields and the image force acting on the piezoelectric screw dislocation are obtained based on the principle of conformal mapping, the method of series expansion, the technical of analytic continuation and the analysis of singularity of complex potentials. The rigid line and the piezoelectric material property combinations upon the image force and the equilibrium position of the dislocation are discussed in detail by the numerical computation.

ANALYSIS OF A PARTIALLY DEBONDED ELLIPTIC INHOMOGENEITY IN PIEZOELECTRIC MATERIALS

A generalized solution was obtained for the partially debonded elliptic inhomogeneity problem in piezoelectric materials under antiplane shear and inplane electric loading using the complex variable method. It was assumed that the interfacial debonding induced an electrically impermeable crack at the interface. The principle of conformal transformation and analytical continuation were employed to reduce the formulation into two Riemann-Hilbert problems. This enabled the determination of the complex potentials in the inhomogeneity and the matrix by means of series of expressions. The resulting solution was then used to obtain the electroelastic fields and the energy release rate involving the debonding at the inhomogeneity-matrix interface. The validity and versatility of the current general solution have been demonstrated through some specific examples such as the problems of perfectly bonded elliptic inhomogeneity, totally debonded elliptic inhomogeneity, partially debonded rigid and conducting elliptic inhomogeneity, and partially debonded circular inhomogeneity.

A RIGID LINE IN A CONFOCAL ELLIPTIC INHOMOGENEITY EMBEDDED IN AN INFINITE MEDIUM UNDER ANTIPLANE SHEAR

An effective method is developed and used to investigate the antiplane problem of a rigid line in a confocal elliptic inhomogeneity embedded in an infinite medium. The analytical solution is obtained. The proposed method is based upon the use of conformal mapping and the theorem of analytic continuation. Special solutions which are verified by comparison with existing ones are provided. Finally, the characteristics of stress singularity at the tip of the rigid line inhomogeneity are analyzed and the extension forces for the crack and the rigid line inhomogeneity are derived.

The Existence of a Weak Solution of Inhomogeneous Quasilinear Elliptic Equation with Critical Growth Conditions

In this paper, we get the existence of a weak solution of the following inhomogeneous quasilinear elliptic equation with critical growth conditions: where N≥2, f（x,u）～|u|m-1eb|u|γat +∞, with γ=N/N-1, m≥1, b】0.

Inhomogeneous lens antenna design with fan-beam radiation pattern

This Letter presents an original technique to design and synthesize an inhomogeneous asymmetrical lens resulting in a special fan-beam radiation pattern in a wide frequency bandwidth. The vertical and horizontal planes of the fan-beam radiation pattern can be determined separately. Wide angle search and detection are achievable by using this type of lens antenna because of its suitable radiation pattern. The proposed relative index profile is validated by the means of commercial CST software and an FDTD scheme.

Ellipticity of motion of particle in field of inhomogeneous plane wave

The elliptic motion of particle in the fields of the inhomogeneous plane wavs that are generated on a liquid thermoviscoelastic solid interface is studied.. Calculations show that the ellipticity of the motion of Particle is related to the incident angle that the homogeneous plane wave incidents upon the interface. The influeree of viscous properties of solid on the ellipticity of particle's motion is small and shows near the critical angles of longitudinal and transversal wavs. Under the incidence at Rayleigh angle, the change of the ellipticity of motion of the particle is periodic in the wake of its Rayleigh wavelength and its elliptic locus is couoter clockwise and clockwise rotation periodically.