Oblate Spheroidal Inclusion Research Articles

Stress state of a piezoceramic body with a plane crack opened by a rigid inclusion

The paper establishes a relationship between the solutions for cracks located in the isotropy plane of a transversely isotropic piezoceramic medium and opened (without friction) by rigid inclusions and the solutions for cracks in a purely elastic medium. This makes it possible to calculate the stress intensity factor (SIF) for cracks in an electroelastic medium from the SIF for an elastic isotropic material, without the need to solve the electroelastic problem. The use of the approach is exemplified by a penny-shaped crack opened by either a disk-shaped rigid inclusion of constant thickness or a rigid oblate spheroidal inclusion in an electroelastic medium

Effective poroelastic properties of transversely isotropic rock-like composites with arbitrarily oriented ellipsoidal inclusions

The present work is devoted to the determination of the macroscopic poroelastic properties of transversely isotropic geomaterials or rock-like composites with arbitrarily oriented ellipsoïdal inhomogeneities. The key problem to solve is to separate respective effects of matrix anisotropy and of inhomogeneities’ orientation distribution and shape. Based on a numerical integration of the exact Green function provided by Pan and Chou [Pan, Y.C., Chou, T.W., 1976. Point force solution for an infinite transversely isotropic solid. Journal of Applied Mechanics 43, 608–612] for the transversely isotropic media, the Hill tensor P is obtained for an arbitrarily oriented oblate spheroidal inclusion. The integrate of the Hill tensor is performed in an intermediate system coordinate attached to the inhomogeneity and with one axis equal to the symmetry axis of the transversely isotropic matrix. This choice of system coordinate allows to simplify numerical calculations and to gain accuracy because partial integrate can be performed analytically. The obtained Hill tensor is next used to study the effect of matrix anisotropy, pores systems and microstructure-related parameters on the overall effective poroelastic properties in transversely isotropic rocks. As an example, a two step-homogenization scheme is presented to test the ability of the proposed model in the evaluation of effective Biot tensor and Biot modulus and stiffness tensor. With the help of an orientation distribution function (ODF) the anisotropy due to the pore systems is also accounted. Numerical applications are finally carried out for anisotropic porous rocks both composed of a matrix with solid minerals constituents and a pore space.

Thermal Stresses in a Thick Plate Containing an Oblate Spheroidal Inclusion with the Circle Regions of Both Plate Surfaces Being Heated and Cooled

Thermal Stresses in a Thick Plate Containing an Oblate Spheroidal Inclusion with the Circle Regions of Both Plate Surfaces Being Heated and Cooled

Stresses in a Thick Plate Containing an Oblate Spheroidal Inclusion under Transverse Bending

Stresses in a Thick Plate Containing an Oblate Spheroidal Inclusion under Transverse Bending

Stresses in a Thick Plate Containing an Oblate Spheroidal Inclusion under Eigenstrain with a Uniform Gradient

Stresses in a Thick Plate Containing an Oblate Spheroidal Inclusion under Eigenstrain with a Uniform Gradient

Stresses in a Thick Plate Containing an Oblate Spheroidal Inclusion Under Bending.

In the previous paper, we presented an axisymmetric solution for the stresses and displacements in an elastic thick plate containing an oblate spheroidal inclusion under axisymmetric bending around the z axis normal to the surface of the thick plate. In the present paper, we studied an asymmetric solution for an elastic thick plate containing an oblate spheroidal inclusion under transverse bending. Numerical results are given for different values of size, aspect ratio and stiffness ratio. The stress distributions around inclusion are shown graphically, and are compared with the axisymmetric results.

Stresses in a Thick Plate Containing an Oblate Spheroidal Inclusion Under Axisymmetric Bending.

Stresses in a Thick Plate Containing an Oblate Spheroidal Inclusion Under Axisymmetric Bending.

504 一定勾配を有する eigen 歪を受ける偏平楕円体状介在物を有する厚板

The paper presents an asymmetric solution for the stresses and displaements in an elastic thick plate containing an oblate spheroidal inclusion under shear eigenstrain with an uniform gragient. For related eigenstrain problems, Jasiuk et al. solved the axisymmetric problem of the half-space with a spheroidal inhomogeneity under uniform normal eigenstrain and Tsuchida et al. treated the asymmetric problem under uniform shear eigenstrain. The stress distributions around inclusion are shown graphically.

Stresses in a Thick Plate Containing an Oblate Spheroidal Inclusion under Axisymmetric Bending.

Stresses in a Thick Plate Containing an Oblate Spheroidal Inclusion under Axisymmetric Bending.

K-0847 偏平回転楕円体状介在物を有する厚板の曲げ(G03-15 複合材料)(G03 材料力学部門一般講演)

The paper presents an asymmetric solution for the stresses and displaements in an elastic thick plate containing an oblate spheroidal inclusion under transverse bending around the y axis. The related spherical cavity and inclusion problems were solved by Tsuchida et al. in 1975. by using Papcovich-Neuber displacement potentials. We extended the method to spheroidal inclusion problem.

839 偏平回転楕円体状介在物を有する厚板の軸対称曲げ

839 偏平回転楕円体状介在物を有する厚板の軸対称曲げ

Thermal stresses due to spheroidal inclusions

Thermal stresses due to a spheroidal inclusion were investigated using the equivalent inclusion approach proposed by Eshelby. The temperature inside the spheroid is maintained constant and different from that of the surrounding matrix of an infinite extent. A new relation between the Cartesian coordinates and spheroidal coordinates was established. Based on this relation, the solution for a prolate spheroidal inclusion was readily obtained from that for an oblate spheroidal inclusion. The principal stress inside the spheroid increases with decreasing m, the ratio of shear moduli of the spheroid and matrix. The value of σ I 11 inside the spheroid increases with increasing k, the aspect ratio, but the trend for σ I 33 is opposite. The stress components, σ 11, along the x 1 axis and, σ 33, along the x 3 axis in the matrix decrease with increasing distance away from the inclusion. For given combinations of m and k, the maximum stress components, σ 22 and σ 33, along the x 1 axis and σ 11 (= σ 22) along the x 3 axis in the matrix are located at certain distances away from the interface. Among all principal stresses, the maximum tensile stress is located at the interface between the inclusion and matrix. The numerical results are in agreement with those reported in the literature.

Elastic wave scattering by a fluid inclusion in an elastic half‐space

A fluid inclusion in an elastic half‐space is academically a challenging problem, and practically a very important one, especially in geophysics. The earth surface can be modeled as an elastic half‐space with vacuum above, and various fluid inclusions (oils, minerals, etc.) under it. We present here a T‐matrix solution to the problem of scattering of elastic waves from such a configuration. Numerical results are computed for the case of an oblate spheroidal fluid inclusion below an earthlike elastic half‐space. The multiple scattering effects between the half‐space and the fluid inclusion are studied by the different approximate expressions for the scattered field coefficients.

Theory of magnetic leakage fields from prolate and oblate spheroidal inclusions

Magnetic leakage fields from nonspherical inclusions in magnetic materials are discussed using classical electromagnetic theory. The model used is that of a prolate or oblate spheroidal inclusion embedded in an infinite medium. Deviations from the leakage field behavior of a spherical inclusion are discussed and procedures are suggested whereby one can test for inclusion shape.

Stress concentration due to an oblate spheroidal inclusion

The stress concentration of an oblate spheroidal inclusion parallel to the stress and deformation axis is obtained by using Eshelby's theory. This is complementary to our previous study, in which stress concentration is analyzed for an oblate spheroidal inclusion normal to the stress and deformation axis. Effects of the elastic stiffness and the aspect ratio of the inclusion on the stress concentration are examined in detail. The internal stresses inside the inclusion, and at the matrix-inclusion boundary, are calculated considering inhomogeneity and plastic deformation effects. Stress concentrations at graphite flakes and nodules in cast iron are discussed.

Internal stresses due to an oblate spheroidal inclusion: Misfit, inhomogeneity and plastic deformation effects

Internal stress in and around an oblate spheroidal inclusion is evaluated by using Eshelby theory. We consider three different sources of internal stress as a function of the aspect ratio and elastic moduli ratio; these are 1. (1) misfit effect, 2. (2) inhomogeneity effect 3. (3) plastic deformation effect. The misfit effect arises from the difference of thermal expansion coefficients of the matrix and inclusion. Normal stresses within the inclusion (or the principal stresses), maximum shear stress inside the inclusion, total strain energy and the normal stress at the matrix-inclusion boundary are determined. The inhomogeneity effect arises from the difference of the elastic moduli of the matrix and inclusion, which perturbs otherwise uniform applied stress. The direction of applied stress is parallel to the axis of revolution of the inclusion. Normal stresses within the inclusion and at the matrix-inclusion boundary are obtained. Plastic deformation of the matrix in the presence of a plastically non-deformable inclusion produces internal stresses, as shown by Ashby and by Tanaka and Mori. The approach developed by Tanaka and Mori is extended here to evaluate the internal stresses for the inclusion geometries appropriate to the analysis of technically important cases. The results of the present calculations in limiting cases agree with previously published calculations. Implications of the results are discussed in connection with several experimental studies.