Inhomogeneous Inclusion Research Articles

Analysis of equipotential lines as a basis for impedance imaging

A mathematical two-dimensional phantom model has been implemented. With this it has been possible to calculate the equipotential line patterns in a homogeneous medium with inhomogeneous inclusions. The results have been compared with measurements in a physical phantom with identical outline. The shape of the phantom can be adapted to varying outlines congruent with transections of the human body. The physical measurements verify closely the pattern of the equipotential lines. Three approaches are suggested in applying the mathematical phantom model as a useful tool in impedance imaging.

Fractographic investigation of tensile and fatigue fracture surfaces of rubber containing inhomogeneous inclusions

Fracture of rubber begins at flaws or inclusions where local stress exceeds a critical level. Recently, a study has been undertaken to investigate the effect of inclusions on the fracture property of rubber. The inclusions studied are dirt from guayule rubber of particle size between 18 and 6000/~m. A controlled amount of dirt of definite size has been incorporated in the rubber matrix. It is worth mentioning that these dirt particles remain present even after the extraction of rubber from shrub. Fracture of guayule rubber containing different sizes and amounts of "dirt", which are basically plant tissues in nature, has been reported elsewhere [1]. Thomas [2] and Gent [3] have treated the fracture of elastomers in detail and Greensmith [4] has reported tensile and fatigue failure of natural rubber containing sand and sawdust. He observed a reduction in strength properties with the incorporation of these foreign materials. Gent et al. have investigated the tensile failure of silicone rubber containing a glass bead [5]. In the above investigations, however, the surface morphology around a flaw has not been studied. Fractography of several elastomers under different modes of failure namely tensile, tear, fatigue and abrasion has been reported before by us [6-8]. In all these studies, it has been observed that different modes of failure generate typical fracture surfaces. In this letter, the results of my observations of tensile and fatigue fracture surfaces ofelastomers containing inhomogeneous inclusions are reported. Mix formulations are as follows: natural rubber 100%; zinc oxide 6%; stearic acid 0.5%; mercaptobenzothiazole 0.5%; sulphur 3.5%; dirt 0%, 3.0%. 3% dirt has been added to the sample. Mixing and compounding have been done on an open mill. Hence, there is some breakdown of the dirt, reducing the particle size ranges from 45 to 6000/~m to 45 to 1000/~m. The small amount of dirt does not have any effect on scorch time and optimum cure time. Curing was done at 150°C at the optimum cure time. Dumbbell specimens for tensile and fatigue testing were used. Tensile testing was carried out in an Instron machine (ASTM D 412-75 method) and the fatigue experiment in a Monsanto fatigue-to-failure tester (frequency, 100 cycles min ~ ). The samples were sputter-coated with gold immediately after fracture and the fracture surfaces were examined within 24 h of test. A JEOL SMU3 scanning electron microscope was used for the study. The tensile fracture surface of guayule rubber is shown in Fig. 1. Few tear lines running from one end Figure 1 Tensile fracture surface of guayule rubber containing no external dirt: general fracture surface.

Magnetotelluric response of a laterally inhomogeneous anisotropic inclusion

The field of H-polarisation is studied for an anisotropic two-dimensional conducting inclusion embedded in a less conducting isotropic surrounding, using a finite difference approximation technique. Contour lines for the Re( H X) have been plotted, laterally, across the inclusion. It is shown that: (1) for larger anisotropic factors in the inclusion, the contour lines converge in the embedded inclusion, and (2) the effects of changing lateral conductivity variations are reflected significantly in the apparent resistivity versus lateral distance variation patterns. Our results may provide an insight into the interpretation of magnetotelluric investigations over anisotropic inhomogeneities frequently encountered in mapping natural resources in sedimentary and fissured zones in geothermal fields.

Elastodynamic analysis of inhomogeneous anisotropic bodies

The integral equation method is presented for elastodynamic problems of inhomogeneous anisotropic bodies. Since fundamental solutions are not available for general inhomogeneous anisotropic media, we employ the fundamental solution for homogeneous elastostatics. The terms induced by material inhomogeneity and inertia force are regarded as body forces in elastostatics, and evaluated in the form of volume integrals. The scattering problems of elastic waves by inhomogeneous anisotropic inclusions are investigated for some test cases. Numerical results show the significant effects of inhomogeneity and anisotropy of materials on wave propagations.

Theory of Acoustic Emission From Phase Transformations.

A theoretical framework is developed within which it is possible to predict the dynamic elastic displacement field (acoustic emission) for a phase transformation in which there is a change of both crystal structure (elastic constants) and shape (density). An integral equation is presented for the acoustic emission displacement field due to formation of inhomogeneous inclusions. This integral equation is solved by expressing the source in multipolar form and using the Eshelby equivalent inclusion method to estimate the dynamic multipolar coefficients. Expressions for the source of elastic radiation are explicitly calculated for small isotropic spherical and ellipsoidal inclusions embedded in an isotropic matrix. These expressions are used for qualitative interpretation of recent experiments on martensitic transformations in steels and for identifying the information that may be deduced about transformation dynamics from quantitative measurements of acoustic emission.

Nonlinear scattering of laser radiation by absorbing microinhomogeneities in BK-8 glass

An experimental investigation was made of nonlinear scattering of laser radiation by absorbing microinhomogeneities in BK-8 glass. Curves giving the time evolution of the scattered radiation were obtained for the same inhomogeneous inclusion but different power densities of the incident radiation. It was observed that nonlinear scattering may be found even for power densities almost half the threshold value. Theoretical calculations showed that a model based on changes in the optical characteristics of the medium as a result of high-temperature heating of absorbing microinhomogeneities can give a good quantitative description of the experimental dependences.

Stress distribution around an inclusion in an Fe-N single crystal

Disturbance in elastic field due to an elastic inhomogeneous inclusion is examined around a spherical inclusion embedded in a dilute Fe-N single crystal. The stress disturbance around the inclusion is visualized through the morphology of the precipitate (Fe 16N 2) distribution which is strongly affected by the presence of internal or external stress. The experimental observation of the stress effect is compared with elasticity calculations, and excellent agreement is found between the experiments and the calculations, particularly when elastic anisotropy is taken into account.

Interpretation of the Rice integral in continuum mechanics

The author starts by defining, thanks to the virtual work principle, the notion of “succion force” which represents in an continuous mediums the influence of the medium itself on each of its molecules. Mathematically this quantity appears as dual to the displacement of the molecule with regard to the medium; in Lagrange variables, it is analogue to a mass force expressing the influence of the extorior. This force is shown to act only on the points where the medium is elastically inhomogeneous (inclusion, crack, plastified zone…). The study is made for any particular position, eventually a very deformed one. The vectorial sum of these forces in a given volume is calculated with the help of an integral stretched to the surface which limits this volume. This integral generalises the Rice integral which had only been written in the case of the approximation of small deformations.

Effect of permeability and form of inhomoge ne ous inclusions on the maximum water-free oil yield

Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 156–159, January–February, 1978. Полный текст статьи можно найти по адресу: http://www.springerlink.com/content/g077g480hq88v887/fulltext.pdf

The determination of the elastic field of an ellipsoidal inclusion in an anisotropic medium

1. Introduction. In studying the elastic behaviour of inhomogeneous systems certain inclusion and inhomogeneity problems are fundamental. In the ‘transformation problem’, a region (the ‘inclusion’) of an unbounded homogeneous anisotropic elastic medium would undergo some prescribed infinitesimal uniform strain (because of some spontaneous change in its shape) if it were not for the constraint imposed by the surrounding matrix. When the inclusion has an ellipsoidal shape, Eshelby (3, 4) was able to show that the stress and strain fields within the constrained inclusion are uniform and that calculations could be completed when the medium was isotropic. A generally anisotropic medium seemed to raise forbidding analyses, but Eshelby (3) did point the way to an evaluation of the uniform strain which several authors (referred to later) developed into an expression amenable to numerical computation. Here we offer an elementary and immediate route to this expression of the uniform strain, which has been accessible hitherto only by the circuitous procedures of Fourier transforms. It is available as soon as the uniform state of strain in the inclusion is perceived and before an alternative evaluation is commenced. First, we appeal to a theorem (not it seems previously known) which reveals (in particular) the vanishing of the mean strain in the infinitesimally thin ellipsoidal homoeoid lying just outside the inclusion. Secondly, we need only reflect that at each point of the interface there is an immediate algebraic expression of the strain just outside the inclusion in terms of the uniform strain just inside.

On the problem of the ferroelectric inclusion in a matrix subjected to pressure

The energy of formation of a ferroelectric phase in an inhomogeneous inclusion, forming part of a composite system, is shown to be determined by the energy balance within, and, in reference to, the composite system as a whole. Eshelby's theory of the elastic inhomogeneity is applied to obtain the elastic strain energy as a result of temperature variations, phase change, and externally applied pressure. The dependence of the dielectric properties on temperature and pressure is related to the permittivity variations and to changes in screening of the local field intensity through changes in the depolarization factors.

Stress concentration around a small spherical inhomogeneous inclusion on the axis of a circular cylinder in torsion

Stresses are calculated for a small elastic inclusion bonded (in a way to ensure continuous displacements and tractions across the surface of the inclusion) to a large circular cylindrical shaft. The inclusion considered is inhomogeneous and of spherical shape. The shear modulus of the inclusion is assumed to be μ0 exp(−1/2β2r2). Some special cases are also discussed.

Radial deformation of an annular piezoelectric disk with a concentric inhomogeneous annular rigid inclusion

The equations of elasticity, the equations of electricity supplemented by the constitutive equations of a piezoelectric quartz have been employed to investigate the deformation of an annular piezoelectric disk containing a concentric inhomogeneous rigid inclusion. The effects on the deformations have also been discussed in the paper.