On the Eigenstrain Problem of a Spherical Inclusion With an Imperfectly Bonded Interface

1996 ◽  
Vol 63 (4) ◽  
pp. 877-883 ◽  
Author(s):  
Z. Zhong ◽  
S. A. Meguid
Keyword(s):  
Spherical Inclusion ◽  
Normal Displacement ◽  
Theoretical Treatment ◽  
Interfacial Condition ◽  
Isotropic Materials ◽  
Interfacial Sliding ◽  
Bonded Interface ◽  
Special Cases ◽  
Normal Separation ◽  
Displacement Jumps

This article provides a comprehensive theoretical treatment of the eigenstrain problem of a spherical inclusion with an imperfectly bonded interface. Both tangential and normal discontinuities at the interface are considered and a linear interfacial condition, which assumes that the tangential and the normal displacement jumps are proportional to the associated tractions, is adopted. The solution to the corresponding eigenstrain problem is obtained by combining Eshelby’s solution for a perfectly bonded inclusion with Volterra’s solution for an equivalent Somigliana dislocation field which models the interfacial sliding and normal separation. For isotropic materials, the Burger’s vector of the equivalent Somigliana dislocation is exactly determined; the solution is explicitly presented and its uniqueness demonstrated. It is found that the stresses inside the inclusion are not uniform, except for some special cases.

On the Imperfectly Bonded Spherical Inclusion Problem

1999 ◽  
Vol 66 (4) ◽  
pp. 839-846 ◽  
Author(s):  
Z. Zhong ◽  
S. A. Meguid
Keyword(s):  
Superposition Principle ◽  
Spherical Inclusion ◽  
Elastic Strain Energy ◽  
Elastic Field ◽  
Displacement Discontinuity ◽  
Inclusion Problem ◽  
Interfacial Condition ◽  
Interfacial Sliding ◽  
Equivalent Inclusion Method ◽  
The Matrix

An exact solution is developed for the problem of a spherical inclusion with an imperfectly bonded interface. The inclusion is assumed to have a uniform eigenstrain and a different elastic modulus tensor from that of the matrix. The displacement discontinuity at the interface is considered and a linear interfacial condition, which assumes that the displacement jump is proportional to the interfacial traction, is adopted. The elastic field induced by the uniform eigenstrain given in the imperfectly bonded inclusion is decomposed into three parts. The first part is prescribed by a uniform eigenstrain in a perfectly bonded spherical inclusion. The second part is formulated in terms of an equivalent nonuniform eigenstrain distributed over a perfectly bonded spherical inclusion which models the material mismatch between the inclusion and the matrix, while the third part is obtained in terms of an imaginary Somigliana dislocation field which models the interfacial sliding and normal separation. The exact form of the equivalent nonuniform eigenstrain and the imaginary Somigliana dislocation are fully determined using the equivalent inclusion method and the associated interfacial condition. The elastic fields are then obtained explicitly by means of the superposition principle. The resulting solution is then used to evaluate the average Eshelby tensor and the elastic strain energy.

Boussinesq's problem for a flat-ended cylinder

1946 ◽  
Vol 42 (1) ◽  
pp. 29-39 ◽  
Author(s):  
Ian N. Sneddon
Keyword(s):  
Free Surface ◽  
Rigid Body ◽  
Elastic Medium ◽  
Normal Displacement ◽  
Full Account ◽  
Elastic Stresses ◽  
Special Cases ◽  
Cylindrical Punch ◽  
Distribution Of Stress ◽  
Boussinesq’S Problem

1. In a recent paper(1) expressions were found for the elastic stresses produced in a semi-infinite elastic medium when its boundary is deformed by the pressure against it of a perfectly rigid body. In deriving the solution of this problem—the ‘Boussinesq’ problem—it was assumed that the normal displacement of a point within the area of contact between the elastic medium and the rigid body is prescribed and that the distribution of pressure over that area is determined subsequently. The solutions for the special cases in which the free surface was indented by a cone, a sphere and a flat-ended cylindrical punch were derived, but no attempt was made to give a full account of the distribution of stress in the interior of the medium in any of these cases.

Proof of the Splitting Mode of Compressive Brittle Failure and Integration With General Failure Theory

2019 ◽  
Vol 86 (9) ◽  
Author(s):  
Richard M. Christensen
Keyword(s):  
Uniaxial Compression ◽  
Special Interest ◽  
Brittle Failure ◽  
Difficult Problem ◽  
Theoretical Treatment ◽  
Isotropic Materials ◽  
Failure Theory ◽  
Mode Of Failure ◽  
Technical Capability

The problem of special interest is the nature of the mode of failure in uniaxial compression at the brittle limit. This problem is known by observation to undergo a splitting mode of failure. The present work gives a full theoretical treatment and proof for this mode of failure. The general failure theory of Christensen for isotropic materials provides the basis for the derivation. The solution demonstrates the depth of technical capability that is required from the failure theory to treat such a classically difficult problem.

scholarly journals Stress systems in isotropic and aeolotropic plates. V

1945 ◽  
Vol 184 (998) ◽  
pp. 231-252 ◽  
Keyword(s):  
Isotropic Plate ◽  
Elliptical Hole ◽  
Numerical Results ◽  
Theoretical Solution ◽  
Stress Distributions ◽  
Isotropic Materials ◽  
Tension Member ◽  
Special Cases ◽  
Distribution Of Stress ◽  
Square Hole

A general theoretical solution is obtained for certain stress distributions in isotropic and aeolotropic plates containing holes of various types. The solution includes as special cases some well-known results for isotropic materials, and it is used here to obtain new results for both isotropic and aeolotropic plates. Numerical results are given for the distribution of stress round the edges of an elliptical hole in a spruce plank under tension, a square hole with rounded corners in an isotropic tension member and in an isotropic plate under shear, and a triangular hole with rounded comers in an isotropic tension member.

On the parametric model of loose bonding between poroelastic half-spaces

2011 ◽  
Vol 18 (9) ◽  
pp. 1261-1274 ◽  
Author(s):  
C Nageswara Nath ◽  
M Tajuddin ◽  
JM Kumar
Keyword(s):  
Wave Propagation ◽  
Viscous Liquid ◽  
Liquid Layer ◽  
Shear Viscosity ◽  
Secular Equation ◽  
Parametric Model ◽  
Interfacial Waves ◽  
Bonded Interface ◽  
Special Cases ◽  
Loose Bonding

Wave propagation in a Newtonian viscous liquid layer of thickness ‘ h’ and of shear viscosity ‘ η’ bounded by two poroelastic half-spaces is studied. Possible bonding between the poroelastic half-spaces is discussed by considering the limiting forms of the secular equation, when h→0: (1) η is finite or η→0 such that η/h → ∞, (2) η→0 such that η/h → 0, (3) η → 0 such that η/h is a finite nonzero quantity, for each permeable and impermeable surface. It is shown that these three forms respectively represent welded, smooth and loosely bonded interface of poroelastic half-spaces. The secular equation for the interfacial waves for each of the above three types of bonding for infinite wavelength is derived as a particular case. It is observed that this secular equation is the same for all three types of bonding for each permeable and impermeable surface. Several other special cases are obtained.

Electron Beam Damage of Biomolecules Assessed by Energy Loss Spectroscopy

1978 ◽  
Vol 36 (3) ◽  
pp. 61-69
Author(s):  
M. Isaacson ◽  
M.L. Collins ◽  
M. Listvan
Keyword(s):  
Electron Microscopy ◽  
Radiation Damage ◽  
Structural Integrity ◽  
Analytical Electron Microscopy ◽  
High Dose ◽  
Dose Rates ◽  
Special Cases ◽  
Analytical Electron ◽  
Atom Migration ◽  
Beam Damage

Over the past five years it has become evident that radiation damage provides the fundamental limit to the study of blomolecular structure by electron microscopy. In some special cases structural determinations at very low doses can be achieved through superposition techniques to study periodic (Unwin & Henderson, 1975) and nonperiodic (Saxton & Frank, 1977) specimens. In addition, protection methods such as glucose embedding (Unwin & Henderson, 1975) and maintenance of specimen hydration at low temperatures (Taylor & Glaeser, 1976) have also shown promise. Despite these successes, the basic nature of radiation damage in the electron microscope is far from clear. In general we cannot predict exactly how different structures will behave during electron Irradiation at high dose rates. Moreover, with the rapid rise of analytical electron microscopy over the last few years, nvicroscopists are becoming concerned with questions of compositional as well as structural integrity. It is important to measure changes in elemental composition arising from atom migration in or loss from the specimen as a result of electron bombardment.

Decoration technique and surface physics

1978 ◽  
Vol 36 (1) ◽  
pp. 436-437 ◽  
Author(s):  
H. Bethge
Keyword(s):  
Diffusion Path ◽  
Special Importance ◽  
Surface Physics ◽  
Step Structure ◽  
Initial Stage ◽  
Special Cases ◽  
Atomic Surface ◽  
The Mean ◽  
Bulk Structure ◽  
Decoration Technique

Besides the atomic surface structure, diverging in special cases with respect to the bulk structure, the real structure of a surface Is determined by the step structure. Using the decoration technique /1/ it is possible to image step structures having step heights down to a single lattice plane distance electron-microscopically. For a number of problems the knowledge of the monatomic step structures is important, because numerous problems of surface physics are directly connected with processes taking place at these steps, e.g. crystal growth or evaporation, sorption and nucleatlon as initial stage of overgrowth of thin films.To demonstrate the decoration technique by means of evaporation of heavy metals Fig. 1 from our former investigations shows the monatomic step structure of an evaporated NaCI crystal. of special Importance Is the detection of the movement of steps during the growth or evaporation of a crystal. From the velocity of a step fundamental quantities for the molecular processes can be determined, e.g. the mean free diffusion path of molecules.

Contrasts of planar defects in reflection electron microscopy

1993 ◽  
Vol 51 ◽  
pp. 1004-1005
Author(s):  
Feng Tsai ◽  
J. M. Cowley
Keyword(s):  
Electron Microscopy ◽  
Surface Defects ◽  
Practical Importance ◽  
Theoretical Treatment ◽  
Crystal Surfaces ◽  
Planar Defects ◽  
Surface Steps ◽  
Surface Reconstructions ◽  
Domain Boundaries ◽  
Reflection Electron Microscopy

Reflection electron microscopy (REM) has been used to study surface defects such as surface steps, dislocations emerging on crystal surfaces, and surface reconstructions. However, only a few REM studies have been reported about the planar defects emerging on surfaces. The interaction of planar defects with surfaces may be of considerable practical importance but so far there seems to be only one relatively simple theoretical treatment of the REM contrast and very little experimental evidence to support its predications. Recently, intersections of both 90° and 180° ferroelectric domain boundaries with BaTiO3 crystal surfaces have been investigated by Tsai and Cowley with REM.The REM observations of several planar defects, such as stacking faults and domain boundaries have been continued by the present authors. All REM observations are performed on a JEM-2000FX transmission electron microscope. The sample preparations may be seen somewhere else. In REM, the incident electron beam strikes the surface of a crystal with a small glancing angle.

One Size Fits All?

Methodology ◽  
2012 ◽  
Vol 8 (1) ◽  
pp. 23-38 ◽  
Author(s):  
Manuel C. Voelkle ◽  
Patrick E. McKnight
Keyword(s):  
Repeated Measures ◽  
Structural Equation ◽  
Type I Error ◽  
Equation Modeling ◽  
Type I ◽  
Finite Sample ◽  
Traditional Methods ◽  
Repeated Measures Anova ◽  
Special Cases ◽  
Latent Curve

The use of latent curve models (LCMs) has increased almost exponentially during the last decade. Oftentimes, researchers regard LCM as a “new” method to analyze change with little attention paid to the fact that the technique was originally introduced as an “alternative to standard repeated measures ANOVA and first-order auto-regressive methods” (Meredith & Tisak, 1990, p. 107). In the first part of the paper, this close relationship is reviewed, and it is demonstrated how “traditional” methods, such as the repeated measures ANOVA, and MANOVA, can be formulated as LCMs. Given that latent curve modeling is essentially a large-sample technique, compared to “traditional” finite-sample approaches, the second part of the paper addresses the question to what degree the more flexible LCMs can actually replace some of the older tests by means of a Monte-Carlo simulation. In addition, a structural equation modeling alternative to Mauchly’s (1940) test of sphericity is explored. Although “traditional” methods may be expressed as special cases of more general LCMs, we found the equivalence holds only asymptotically. For practical purposes, however, no approach always outperformed the other alternatives in terms of power and type I error, so the best method to be used depends on the situation. We provide detailed recommendations of when to use which method.

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