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Field of Stresses in an Isotropic Plane with Circular Inclusion under Tensile Stress
Institute for Strength Physics and Materials Science (ISPMS SB RAS), Tomsk, Russia
Staatliche Materialprufungsanstalt (МPА), University of Stuttgart, Stuttgart, Germany
- 1 Institute for Strength Physics and Materials Science (ISPMS SB RAS), Tomsk, Russia
- 2 Staatliche Materialprufungsanstalt (МPА), University of Stuttgart, Stuttgart, Germany
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Abstract
Within the framework of the linear theory of elasticity, the analytical equations for the components of the stress tensor for а plane with а circular inclusion under tensile loading have been derived using the method of superposition. The given approach allows one to describe the plane-stress state of the plane both for the case of rigid and “soft” inclusions.
KeywordsLinear Theory of ElasticityMethod of SuperpositionBoundary ConditionsStress Field ComponentsInclusionCircular Hole
- I. A. Ovid’ko and A. G. Sheinerman, “Elastic Fields of Nanoscopic Inclusions in Nanocomposites,” Reviews on Advanced Materials Science, Vol. 9, 2005, pp. 17-33.
- N. A. Bert, A. L. Kolesnicova, A. E. Romanov and V. V. Tshaldushev, “Elastic Behavior of a Spherical Inclusion with a Given Uniaxial Dilatation,” Physics of the Solid State, Vol. 44, No. 12, 2002, pp. 2139-2148. doi:10.1134/1.1529918
- M. Lai, E. Krempl and D. Ruben, “Introduction in Continuum Mechanics,” 4th Edition, Elsevier, Oxford, 2010.
- S. P. Timoshenko and J. N. Goodier, “Theory of Elasticity,” 3rd Edition, McGraw Hill, New York, 1970.
- V. А. Levin, “Many-Folded Superposition of Great Deformations in Elastic and Viscous-Elastic Bodies,” Fizmatgiz, Moscow, 1999.
- S. L. Crouch and А. М. Starfield, “Boundary Element Methods in Solid Mechanics,” George Allen & Unwin, London, 1983.
- А. V. Mal and S. J. Singh, “Deformation of Elastic Solids,” Prentice Hall, New York, 1992.
- D. E. Eshelby, “Definition of the Stress Field, Which Was Creating bу Elliptical Inclusion,” Proceedings of the Royal Society А, Vol. 241, No. 1226, 1957, p. 376. doi:10.1098/rspa.1957.0133
- D. E. Eshelby, “Elastic Field outside the Elliptical Inclusion,” Proceedings of the Royal Society А, Vol. 252, No. 1271, 1959, p. 561. doi:10.1098/rspa.1959.0173
- G. Kirsch, “Die Theorie der Elastizitat und die Bedurfnisse der Festigkeitslehre,” Zantralblatt Verlin Deutscher Ingenieure, Vol. 42, 1898, pp. 797-807.
- “Physical Values: Handbook,” Energoatomizdat, Moscow, 1991.