Elliptical inclusion in an anisotropic plane:non-uniform interface effects

We study the plane deformation of an elastic composite system made up of an anisotropic elliptical inclusion and an anisotropic foreign matrix surrounding the inclusion.In order to capture the influence of interface energy on the local elastic field as the size of the inclusion approaches the nanoscale,we refer to the Gurtin-Murdoch model of interface elasticity to describe the inclusion-matrix interface as an imaginary and extremely stiff but zero-thickness layer of a finite stretching modulus.As opposed to isotropic cases in which the effects of interface elasticity are usually assumed to be uniform(described by a constant interface stretching modulus for the entire interface),the anisotropic case considered here necessitates non-uniform effects of interface elasticity(described by a non-constant interface stretching modulus),because the bulk surrounding the interface is anisotropic.To this end,we treat the interface stretching modulus of the anisotropic composite system as a variable on the interface curve depending on the specific tangential direction of the interface.We then devise a unified analytic procedure to determine the full stress field in the inclusion and matrix,which is applicable to the arbitrary orientation and aspect ratio of the inclusion,an arbitrarily variable interface modulus,and an arbitrary uniform external loading applied remotely.The non-uniform interface effects on the external loading-induced stress distribution near the interface are explored via a group of numerical examples.It is demonstrated that whether the nonuniformity of the interface effects has a significant effect on the stress field around the inclusion mainly depends on the direction of the external loading and the aspect ratio of the inclusion.

DECAGONAL QU ASICRYSTALLINE ELLIPTICAL INCLUSIONS UNDER THERMOMECHANICAL LOADING

In this work, an elegant method is proposed to derive the thermoelastic field in- duced by thermomechanical loadings in a decagonal quasicrystalline composite composed of an infinite matrix reinforced by an elliptical inclusion. The thermomechanical loadings include a uniform temperature change, remote uniform in-plane heat fluxes and remote uniform in-plane stresses. The corresponding boundary value problem is ultimately reduced to the solution of two independent sets of four coupled linear algebraic equations, each of which involves four complex constants characterizing the internal stress field. The solution demonstrates that a uniform tem- perature change and remote uniform stresses will induce an internal uniform stress field, and that uniform heat fluxes will result in a linearly distributed internal stress field within the elliptical inclusion. The induced uniform rigid body rotation within the inclusion is given explicitly.

PLANE STRAIN PROBLEM OF PIEZOELECTRIC SOLID WITH ELLIPTIC INCLUSION

By using the complex variables function theory, a plane strain electro-elastic analysis was performed on a transversely isotropic piezoelectric material containing an elliptic elastic inclusion, which is subjected to a uniform stress field and a uniform electric displacement loads at infinity. Based on the present finite element results and some related theoretical solutions, an acceptable conjecture was found that the stress field is constant inside the elastic inclusion. The stress field solutions in the piezoelectric matrix and the elastic inclusion were obtained in the form of complex potentials based on the impermeable electric boundary conditions.

Closed form solution and numerical analysis for Eshelby's elliptic inclusion in plane elasticity

This paper presents a closed form solution and numerical analysis for Es- helby＇s elliptic inclusion in an infinite plate. The complex variable method and the confor- real mapping technique are used. The continuity conditions for the traction and displace- ment along the interface in the physical plane are reduced to the similar conditions along the unit circle of the mapping plane. The properties of the complex potentials defined in the finite elliptic region are analyzed. From the continuity conditions, one can separate and obtain the relevant complex potentials defined in the inclusion and the matrix. From the obtained complex potentials, the dependence of the real strains and stresses in the inclusion from the assumed eigenstrains is evaluated. In addition, the stress distribution on the interface along the matrix side is evaluated. The results are obtained in the paper for the first time.