Elastic field of a surface step: Atomistic simulations and anisotropic elastic theory

1996 ◽  
Vol 53 (16) ◽  
pp. 11120-11127 ◽  
Author(s):  
L. E. Shilkrot ◽  
D. J. Srolovitz
Keyword(s):  
Elastic Field ◽  
Elastic Theory ◽  
Atomistic Simulations ◽  
Surface Step ◽  
Anisotropic Elastic

Anisotropic Elastic Field of a Thin Bicrystal Deformed by a Biperiodic Network of Misfit Dislocations

2001 ◽  
Vol 188 (3) ◽  
pp. 1041-1045 ◽  
Author(s):  
T. Outtas ◽  
L. Adami ◽  
A. Derardja ◽  
S. Madani ◽  
R. Bonnet
Keyword(s):  
Elastic Field ◽  
Misfit Dislocations ◽  
Anisotropic Elastic

scholarly journals The elastic field of a surface step: The Marchenko–Parshin formula in the linear case

2006 ◽  
Vol 196 (2) ◽  
pp. 368-386 ◽  
Author(s):  
Cameron R. Connell ◽  
Russel E. Caflisch ◽  
Erding Luo ◽  
Geoff Simms
Keyword(s):  
Elastic Field ◽  
Linear Case ◽  
Surface Step

scholarly journals Anisotropic elastic theory of preloaded granular media

2004 ◽  
Vol 68 (1) ◽  
pp. 51-57 ◽  
Author(s):  
C Gay ◽  
R. A. da Silveira
Keyword(s):  
Granular Media ◽  
Elastic Theory ◽  
Anisotropic Elastic

Atomistic Simulation and Elastic Theory of Surface Steps

1995 ◽  
Vol 399 ◽  
Author(s):  
L. E. Shilkrot ◽  
D. J. Srolovitz
Keyword(s):  
Interaction Energy ◽  
Elastic Field ◽  
Elastic Half Space ◽  
Elastic Theory ◽  
Elastic Model ◽  
Displacement Fields ◽  
Surface Steps ◽  
Line Force ◽  
Step Step ◽  
Force Dipole

ABSTRACTAtomistic computer simulations and anisotropic elastic theory are employed to determine the elastic fields of surface steps and vicinal surfaces. The displacement field of and interaction energies between <100> steps on an {001} Ni surface are determined using atomistic simulations and EAM potentials. The step-step interaction energy found from the simulations is consistent with a surface line force dipole elastic model of a step. We derive an anisotropic form for the elastic field associated with a surface line force dipole using a two dimensional surface Green tensor for a cubic elastic half-space. Both the displacement fields and step-step interaction energy predicted by the theory are shown to be in excellent agreement with the simulations.

A translated rigid ellipsoidal inclusion in an elastic medium

1991 ◽  
Vol 434 (1892) ◽  
pp. 571-585 ◽  
Keyword(s):  
Elastic Medium ◽  
Elastic Field ◽  
Transversely Isotropic ◽  
Ellipsoidal Inclusion ◽  
Arbitrary Orientation ◽  
Isotropic Matrix ◽  
The Matrix ◽  
Ellipsoidal Surface ◽  
Axis Of Symmetry ◽  
Anisotropic Elastic

A rigid ellipsoidal inclusion is embedded at arbitrary orientation in a homogeneous, arbitrarily anisotropic, elastic matrix and is translated infinitesimally by an externally imposed force. We find directly the relation between the force and translation vectors, and the stress, strain and rotation concentrations over the ellipsoidal surface, without having to solve the equations of equilibrium in the matrix, or the fundamental ones of a point force. We refer particularly then to a spheroid aligned along the axis of symmetry of a transversely isotropic matrix, and subsequently to the full elastic field of a general ellipsoid in an isotropic matrix.

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

1977 ◽  
Vol 81 (2) ◽  
pp. 283-289 ◽  
Author(s):  
L. J. Walpole
Keyword(s):  
Anisotropic Medium ◽  
Fourier Transforms ◽  
Elastic Field ◽  
Uniform Strain ◽  
Elastic Behaviour ◽  
Algebraic Expression ◽  
Alternative Evaluation ◽  
Surrounding Matrix ◽  
Anisotropic Elastic

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.

A rotated rigid ellipsoidal inclusion in an elastic medium

1991 ◽  
Vol 433 (1887) ◽  
pp. 179-207 ◽  
Keyword(s):  
Elastic Field ◽  
Ellipsoidal Inclusion ◽  
Arbitrary Orientation ◽  
Governing Equations ◽  
Simple Singularity ◽  
The Matrix ◽  
Ellipsoidal Surface ◽  
Rotation Vectors ◽  
Anisotropic Elastic ◽  
Full Solution

A rigid ellipsoidal inclusion is embedded at arbitrary orientation in a homogeneous, arbitrarily anisotropic, elastic matrix and is rotated infinitesimally by means of an imposed couple. Far away the matrix remains either unstrained or at a prescribed uniform strain. A simple ‘singularity’ representation of the elastic field is proposed. It yields directly the relation between the couple and rotation vectors, and the stress, strain and rotation concentrations over the ellipsoidal surface, without having to solve either the governing equations of equilibrium in the matrix, or the fundamental ones of a point force. A full solution is given for an isotropic matrix.

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