On the Eshelby’s Inclusion Problem for Ellipsoids With Nonuniform Dilatational Gaussian and Exponential Eigenstrains

2003 ◽  
Vol 70 (3) ◽  
pp. 418-425 ◽  
Author(s):  
P. Sharma ◽  
R. Sharma
Keyword(s):  
Point Source ◽  
Material Science ◽  
Elastic Strain ◽  
Three Dimensional ◽  
Spherical Shape ◽  
Inclusion Problem ◽  
Elastic State ◽  
One Dimensional ◽  
Source Type ◽  
Limited Degree

This work investigates the three-dimensional elastic state of inclusions in which the prescribed stress-free transformation strains or eigenstrains are spatially nonuniform and distributed either in a Gaussian, or an exponential manner. The prescribed eigenstrain distributions are taken to be dilatational. Typical research in the micromechanics of inclusions and inhomogeneities has dealt, by and large, with spatially uniform eigenstrains and, to some limited degree, with polynomial distributions. Solutions to Eshelby’s inclusion problem, where eigenstrains are Gaussian and exponential in nature, do not exist. Such eigenstrain distributions arise naturally due to highly localized point-source type heating (typical in electronic chips), due to compositional differences, and those due to diffusion related mechanisms among others. The current paper provides such a solution for ellipsoidal shaped inclusions located in an infinite isotropic elastic matrix. It is shown, similar to the much-discussed uniform eigenstrain problem, that the elastic state is completely determined in closed form save for some simple one-dimensional integrals that are evaluated trivially using numerical quadrature. For the specialized case of a spherical shape, solutions in terms of known functions are derived and numerical results are presented. The elastic state both within and outside the inclusion is investigated. For the specific case of a sphere, the elastic strain energies are given in terms of simple formulas. Some applications of the current work in various areas such as electronics, micromechanics of composites, and material science are also discussed.

scholarly journals Modeling of three-dimensional elastic strain fields by point-source method

2015 ◽  
Vol 15 (4) ◽  
pp. 13-23 ◽  
Author(s):  
Sergey Knyazev ◽  
Elena Shcherbakova ◽  
Viktor Pustovoyt ◽  
Anton- Shcherbakov-
Keyword(s):  
Point Source ◽  
Elastic Strain ◽  
Three Dimensional ◽  
Strain Fields ◽  
Source Method

On the Use of Point Source Solutions for Forced Air Cooling of Electronic Components—Part I: Thermal Wake Models for Rectangular Heat Sources

2003 ◽  
Vol 125 (2) ◽  
pp. 226-234 ◽  
Author(s):  
Alfonso Ortega ◽  
Shankar Ramanathan
Keyword(s):  
Temperature Field ◽  
Point Source ◽  
Three Dimensional ◽  
Air Cooling ◽  
Heat Sources ◽  
Multiple Sources ◽  
One Dimensional ◽  
Forced Air ◽  
The Individual ◽  
Thermal Wake

Analytical solutions are presented for the temperature field that arises from the application of a source of heat on an adiabatic plate or board when the fluid is represented as a uniform flow with an effective turbulent diffusivity, i.e., the so-called UFED flow model. Solutions are summarized for a point source, a one-dimensional strip source, and a rectangular source of heat. The ability to superpose the individual kernel solutions to obtain the temperature field due to multiple sources is demonstrated. The point source solution reveals that the N−1 law commonly observed for the centerline thermal wake decay for three-dimensional arrays is predicted by the point source solution for the UFED model. Examination of the solution for rectangular sources shows that the thermal wake approaches the point source behavior downstream from the source, suggesting a new scaling for the far thermal wake based on the total component power and a length scale given by ε/U. The new scaling successfully collapses the thermal wake for several sizes of components and provides a fundamental basis for experimental observations previously made for arrays of three-dimensional components.

Multidimensional Water Flow in Variably Saturated Soils

2003 ◽  
Author(s):  
Arthur W. Warrick
Keyword(s):  
Point Source ◽  
Three Dimensional ◽  
Practical Interest ◽  
Two Dimensions ◽  
Point Sources ◽  
Radial Coordinate ◽  
Dimensional Problem ◽  
One Dimensional ◽  
Divergent Flow ◽  
Suction Sampler

Chapters 4 and 5 dealt with one-dimensional rectilinear flow, with and without the effect of gravity. Now the focus is on multidimensional flow. We will refer to two- and three-dimensional flow based on the number of Cartesian coordinates necessary to describe the problem. For this convention, a point source emitting a volume of water per unit time results in a three-dimensional problem even if it can be described with a single spherical coordinate. Similarly, a line source would be two-dimensional even if it could be described with a single radial coordinate. A problem with axial symmetry will be termed a three-dimensional problem even when only a depth and radius are needed to describe the geometry. The pressure at a point source is undefined. But more generally, three-dimensional point sources refer to flow from finite-sized sources into a larger soil domain, such as infiltration from a small surface pond into the soil. Often, the soil domain can be taken as infinite in one or more directions. Also, a point sink can occur with flow to a sump or to a suction sampler. In two dimensions, the same types of example can be given, but we will refer to them as line sources or sinks. Practical interest in point sources includes analyses of surface or subsurface leaks and of trickle (drip) irrigation. The desirability of determining soil properties in situ has provided the impetus for a rigorous analysis of disctension and borehole infiltrometers. Also, environmental monitoring with suction cups or candles, pan lysimeters, and wicking devices all include convergent or divergent flow in multidimensions. There are some conceptual differences between line and point sources and one-dimensional sources. For discussion, consider water supplied at a constant matric potential into drier surroundings. For a one-dimensional source, the corresponding physical problem includes a planar source over an area large enough for “edge” effects to be negligible. For two dimensions, the source might be a long horizontal cylinder or a furrow of finite depth from which water flows. For three dimensions, the source could be a small orifice providing water at a finite rate or a small, shallow pond on the soil surface.

Elastic strain energy and forces on point defects in a two-phase medium

1986 ◽  
Vol 1 (1) ◽  
pp. 193-201 ◽  
Author(s):  
K. Jagannadham ◽  
J. Narayan
Keyword(s):  
Point Source ◽  
Point Defects ◽  
Elastic Strain ◽  
Strain Energy ◽  
Three Dimensional ◽  
Elastic Strain Energy ◽  
Second Phase ◽  
Two Phase ◽  
Phase Medium ◽  
Important Field

Elastic strain energy and forces on point defects in a two-phase medium with a planar interface are analyzed employing the surface dislocation analysis developed earlier for three-dimensional distortions. The important field components, namely, the tractions and the displacements arising due to the point source at the interface, are determined. Furthermore, the field components at the interface are used to determine the elastic strain energy associated with the point source in the two-phase medium and the elastic force exerted by the second phase on the point defect. The significance of these results to the force acting on a vacancy or an interstitial at the interface is emphasized.

Structure and function of neural networks in the retina

1988 ◽  
Vol 46 ◽  
pp. 26-27
Author(s):  
Peter Sterling
Keyword(s):  
Ganglion Cells ◽  
Three Dimensional ◽  
Structure And Function ◽  
Synaptic Connections ◽  
Visual Axis ◽  
One Dimensional ◽  
Cat Retina ◽  
Ultrathin Sections ◽  
And Function ◽  
Insight Into

The synaptic connections in cat retina that link photoreceptors to ganglion cells have been analyzed quantitatively. Our approach has been to prepare serial, ultrathin sections and photograph en montage at low magnification (˜2000X) in the electron microscope. Six series, 100-300 sections long, have been prepared over the last decade. They derive from different cats but always from the same region of retina, about one degree from the center of the visual axis. The material has been analyzed by reconstructing adjacent neurons in each array and then identifying systematically the synaptic connections between arrays. Most reconstructions were done manually by tracing the outlines of processes in successive sections onto acetate sheets aligned on a cartoonist's jig. The tracings were then digitized, stacked by computer, and printed with the hidden lines removed. The results have provided rather than the usual one-dimensional account of pathways, a three-dimensional account of circuits. From this has emerged insight into the functional architecture.

Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

2008 ◽  
Vol 67 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Stefano Passini
Keyword(s):  
Social Dominance ◽  
Factor Model ◽  
Three Dimensional ◽  
Social Dominance Orientation ◽  
Model Fit ◽  
Regression Analyses ◽  
One Dimensional ◽  
Confirmatory Factor ◽  
The One ◽  
Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

Incorporation of spatial variability in modeling non-point source groundwater nitrate pollution

1996 ◽  
Vol 33 (4-5) ◽  
pp. 233-240 ◽  
Author(s):  
F. S. Goderya ◽  
M. F. Dahab ◽  
W. E. Woldt ◽  
I. Bogardi
Keyword(s):  
Spatial Variability ◽  
Point Source ◽  
Three Dimensional ◽  
Nitrate Contamination ◽  
Geostatistical Simulation ◽  
Chemical Measurements ◽  
Spatially Distributed ◽  
Potential Benefits ◽  
Zone Modeling ◽  
Physical And Chemical

A methodology for incorporation of spatial variability in modeling non-point source groundwater nitrate contamination is presented. The methodology combines geostatistical simulation and unsaturated zone modeling for estimating the amount of nitrate loading to groundwater. Three dimensional soil nitrogen variability and 2-dimensional crop yield variability are used in quantifying potential benefits of spatially distributed nitrogen input. This technique, in combination with physical and chemical measurements, is utilized as a means of illustrating how the spatial statistical properties of nitrate leaching can be obtained for different scenarios of fixed and variable rate nitrogen applications.

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