XVII. <i>Notes on electric and magnetic field constants and their expression in terms of Bessel functions and elliptic integrals</i>

Gray, Andrew

doi:10.1080/14786440808635943

Cited by 20 publications

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“…By substituting (B 2) and (B 4) into (5.17a) and (5.17 6), respectively, the results are The functions J m and J are Bessel functions of the respectively. The integrals in (5.19) are the L ip sch itz-H an k el ty p e involving products of Bessel functions (Gary 1919), and th eir properties have been considered in detail by E ason et al (1955), Salam on & D undurs (1971), and Salam on & W alter (1979. F or isotropic solids, the result (5.18a) and (5.186) are the same as those obtained by Yu & Sanday 1991 d).…”

Section: (D) Circular 'Prismatic Dislocation Loops With Burgers Vector Perpendicular To the Interfacementioning

confidence: 99%

Elastic fields due to defects in transversely isotropic bimaterials

Sanday

Rath

et al. 1995

Proc. R. Soc. Lond. A

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A method for obtaining the analytic solution of the elastic fields due to defects such as inclusions, dislocations, disclinations, and point defects in transversely isotropic bimaterials is presented. The bimaterial consists of two semi-infinite transversely isotropic solids either perfectly bonded together or in frictionless contact with each other at a planar interface which is parallel to the plane of isotropy of both solids. The elastic solution is expressed in terms of the hexagonal stress vectors for the double force and the double force with moment. Closed form solutions for inclusions with pure dilatational eigenstrain, straight dislocation and disclination lines, circular, dislocation loops, and point defects are presented.

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Section: (D) Circular 'Prismatic Dislocation Loops With Burgers Vector Perpendicular To the Interfacementioning

confidence: 99%

Elastic fields due to defects in transversely isotropic bimaterials

Sanday

Rath

et al. 1995

Proc. R. Soc. Lond. A

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Elastic fields of a dislocation loop in a two-phase material

Salamon

Dundurs

1971

J Elasticity

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The purpose of this study is to set forth the mathematical framework for an efficient treatment of a plane dislocation loop in a two-phase material, and to carry the elastostatic part of the analysis far enough, so that the resolts are immediately tractable for applications to solid state. The two-phase material is idealized as two isotropic elastic half-space~ with perfect adhesion, while the loop is placed in a plane parallel to the interface. It is shown that the elastic fields can be obtained by differentiating two types of integrals and, thus, are readily evaluated for any shape of the loop for which the integrals are available from potential theory. Explicit results are given for circular prismatic and glide loops. ZUSAMMENFASSUNGMit der vorliegenden Arbeit wird die Absicht verfolgt, den mathematischen Rahmen zu einer leistungsf/ihigen Behandlung von ebenen Versetzungsschleifen in einem Zweiphasenmaterial zu erweitern und den elastostatischen Teil der Berechnung so weit fortzufiihren ,dab die Resultate fiir die Anwendung in der Festk6rperphysik unmittelbar zur Verfiigung stehen. Das Zweiphasen-Material wird idealisiert durch zwei isotrope elastische Halbr~ume mit perfekter Adh~ision, w~hrend die Versetzungsschleife in einer Ebene parallel zur Trennfl/iche angenommen wird. Es wird gezeigt, dab die elastischen Felder durch Differentiation zweier Integraltypen und damit fiir jede beliebige Form der Versetzungsschleife erhalten werden k6nnen, fi]r die die Integrale sich aus der Potentialtheorie ergeben. Explizite Resultate werden flit kreisf6rmige prismatische und gleitende Schleifen angegeben.

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Elastic fields due to centers of dilatation and thermal inhomogeneities in plane-layered solids

Sanday

1993

Journal of the Mechanics and Physics of Solids

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XVII. Notes on electric and magnetic field constants and their expression in terms of Bessel functions and elliptic integrals

Cited by 20 publications

References 0 publications

Elastic fields due to defects in transversely isotropic bimaterials

Elastic fields due to defects in transversely isotropic bimaterials

Elastic fields of a dislocation loop in a two-phase material

Elastic fields due to centers of dilatation and thermal inhomogeneities in plane-layered solids

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