DOI: 10.1098/rspa.1957.0133. The determination of the elastic field of an ellipsoidal inclusion, and related problems

The determination of the elastic field of an ellipsoidal inclusion, and related problems

10.1098/rspa.1957.0133

Crossref journal-article

The Royal Society

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences (175)

Abstract

It is supposed that a region within an isotropic elastic solid undergoes a spontaneous change of form which, if the surrounding material were absent, would be some prescribed homogeneous deformation. Because of the presence of the surrounding material stresses will be present both inside and outside the region. The resulting elastic field may be found very simply with the help of a sequence of imaginary cutting, straining and welding operations. In particular, if the region is an ellipsoid the strain inside it is uniform and may be expressed in terms of tabulated elliptic integrals. In this case a further problem may be solved. An ellipsoidal region in an infinite medium has elastic constants different from those of the rest of the material; how does the presence of this inhomogeneity disturb an applied stress-field uniform at large distances? It is shown that to answer several questions of physical or engineering interest it is necessary to know only the relatively simple elastic field inside the ellipsoid.

Bibliography

The determination of the elastic field of an ellipsoidal inclusion, and related problems. (1957). Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 241(1226), 376â396.

Authors 0

None

References 16 Referenced 8,436

Bruggemann D. A. G. 1937 Ann.Phys. Lpz. 160. (10.1002/andp.19374210205)
Byrd P. F. & Friedman M. D. 1954 Handbook of elliptic integrals p. 4. Berlin: Springer# Verlag. (10.1007/978-3-642-52803-3_10)
Cochardt A. W. Schoek G. & Wiedersich H. 1955 Acta Met. 3 533. (10.1016/0001-6160(55)90111-5)
Dirichlet G. L. 1839 Verh. K .
{'key': 'p_5', 'first-page': '133', 'article-title': 'Z. phys', 'volume': '163', 'author': 'Eisenschitz R.', 'year': '1933', 'journal-title': 'Chem. A'} / Chem. A / Z. phys by Eisenschitz R. (1933)
10.1098/rsta.1951.0016
Eshelby J. D. 1955 Acta Met. 3 487. Preuss. Akad.p. 18 (Werke 1 383). (10.1016/0001-6160(55)90140-1)
Eshelby J. D. 1956 In Progress in solid state physics (ed. Seitz & Turnbull) 3 79. New York and London: Academic Press. (10.1016/S0081-1947(08)60132-0)
10.1080/14786443608561718
{'key': 'p_10', 'first-page': '46', 'volume': '5', 'author': 'Hashin Z.', 'year': '1955', 'journal-title': 'Bull. Res. Coun. Israel. C'} / Bull. Res. Coun. Israel. C by Hashin Z. (1955)
{'key': 'p_11', 'first-page': '161', 'article-title': 'Proc. Roy', 'volume': '102', 'author': 'Jeffery G. B.', 'year': '1922', 'journal-title': 'Soc. A'} / Soc. A / Proc. Roy by Jeffery G. B. (1922)
Kellogg O. D. 1929 Potential theory. Berlin: Springer-Verlag. (10.1007/978-3-642-90850-7_3)
Kroner E. 1954 Acta Met. 2 301. (10.1016/0001-6160(54)90171-6)
{'key': 'p_14', 'first-page': '90', 'article-title': 'Proc. Roy', 'volume': '237', 'author': 'Kynch G. J.', 'year': '1956', 'journal-title': 'Soc. A'} / Soc. A / Proc. Roy by Kynch G. J. (1956)
Landau L. D. & Lifshitz E. M. Gostekhizdat.
Leibffied G. 1954 1954 Mekhanika Sploshnykh Sred p. 666. Moscow;

Dates

Type	When
Created	18 years, 8 months ago (Dec. 15, 2006, 4:38 p.m.)
Deposited	2 years, 3 months ago (May 9, 2023, 8:47 p.m.)
Indexed	12 hours, 36 minutes ago (Aug. 21, 2025, 2:02 p.m.)
Issued	68 years ago (Aug. 20, 1957)
Published	68 years ago (Aug. 20, 1957)
Published Online	28 years, 7 months ago (Jan. 1, 1997)
Published Print	68 years ago (Aug. 20, 1957)

Funders 0

None

BibTeX

@article{1957, and related problems_1957, volume={241}, ISSN={2053-9169}, url={http://dx.doi.org/10.1098/rspa.1957.0133}, DOI={10.1098/rspa.1957.0133}, number={1226}, journal={Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences}, publisher={The Royal Society}, year={1957}, month=aug, pages={376–396} }

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