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Warianty tytułu
Języki publikacji
Abstrakty
Using conformal mapping techniques, analytic continuation and the theory of Cauchy singular integral equations, we prove that a non-parabolic open inhomogeneity embedded in an elastic matrix subjected to a uniform remote anti-plane stress nevertheless admits an internal uniform stress field despite the presence of a finite mode III crack in its vicinity. Our analysis indicates that: (i) the internal uniform stress field is independent of the specific shape of the inhomogeneity and the presence of the finite crack; (ii) the existence of the finite crack plays a key role in the non-parabolic open shape of the inhomogeneity and in the non-uniform stresses in the surrounding matrix; (iii) the two-term asymptotic expansion at infinity of the stress field in the matrix is independent of the presence of the finite crack. Detailed numerical results are presented to demonstrate the proposed theory.
Czasopismo
Rocznik
Tom
Strony
67--81
Opis fizyczny
Bibliogr. 23 poz., rys. kolor.
Twórcy
autor
- School of Mechanical and Power Engineering, East China University of Science and Technology, 130 Meilong Road, Shanghai 200237, China
autor
- Department of Mechanical Engineering, University of Alberta, 10-203 Donadeo Innovation Centre for Engineering Edmonton, Alberta Canada T6G 1H9
Bibliografia
- 1. J.D. Eshelby, Elastic inclusions and inhomogeneities, Progress in Solid Mechanics, vol. II, 89–140, 1961.
- 2. G.P Sendeckyj, Elastic inclusion problem in plane elastostatics, International Journal of Solids and Structures, 6, 1535–1543, 1970.
- 3. C.Q. Ru, P. Schiavone, On the elliptic inclusion in anti-plane shear, Mathematics and Mechanics of Solids, 1, 327–333, 1996.
- 4. V.A. Lubarda, X. Markenscoff, On the absence of Eshelby property for non-ellipsoidal inclusions, International Journal of Solids and Structures, 35, 3405–3411, 1998.
- 5. X. Markenscoff, Inclusions with constant eigenstress, Journal of the Mechanics and Physics of Solids, 46, 2297–2301, 1998.
- 6. X. Markenscoff, On the shape of the Eshelby inclusion, Journal of Elasticity, 49, 163–166, 1998.
- 7. Y.A. Antipov, P. Schiavone, On the uniformity of stresses inside an inhomogeneity of arbitrary shape, IMA Journal of Applied Mathematics, 68, 299–311, 2003.
- 8. L.P. Liu, Solution to the Eshelby conjectures, Proceedings of the Royal Society of London A, 464, 573–594, 2008.
- 9. H. Kang, E. Kim, G.W. Milton, Inclusion pairs satisfying Eshelby’s uniformity property, SIAM Journal of Applied Mathematics, 69, 577–595, 2008.
- 10. H. Kang, G.W. Milton, Solutions to the Pólya–Szegö conjecture and the weak Eshelby conjecture, Archive for Rational Mechanics and Analysis, 188, 93–116, 2008.
- 11. H. Ammari, Y. Capdeboscq, H. Kang, H. Lee, G.W. Milton, H. Zribi, Progress on the strong Eshelby’s conjecture and extremal structures for the elastic moment tensor, Journal de Mathématiques Pures et Appliquées, 94, 93–106, 2010.
- 12. X. Wang, Uniform fields inside two non-elliptical inclusions, Mathematics and Mechanics of Solids, 17, 736–761, 2012.
- 13. K. Zhou, H.J. Hoh, X. Wang, L.M. Keer, J.H.L. Pang, B. Song, Q.J. Wang, A review of recent works on inclusions, Mechanics of Materials, 60, 144–158, 2013.
- 14. X. Wang, L. Chen, P. Schiavone, Uniformity of stresses inside a non-elliptical inhomogeneity interacting with a mode III crack, Proceedings of the Royal Society of London A, 474, 2218, 20180304, 2018.
- 15. X. Wang, P. Schiavone, Uniformity of stresses inside a parabolic inhomogeneity, Journal of Applied Mathematics and Physics, 71, 2, 48, 2020.
- 16. J.R. Philip, Seepage shedding by parabolic capillary barriers and cavities, Water Resources Research, 34, 2827–2835, 1998.
- 17. A.R. Kacimov, Yu.V. Obnosov, Steady water flow around parabolic cavities and through parabolic inclusions in unsaturated and saturated soils, Journal of Hydrology, 238, 65–77, 2000.
- 18. Z.G. Suo, Singularities interacting with interfaces and cracks, International Journal of Solids and Structures, 25, 1133–1142, 1989.
- 19. C.Q. Ru, Analytic solution for Eshelby’s problem of an inclusion of arbitrary shape in a plane or half-plane, ASME Journal of Applied Mechanics, 66, 315–322, 1999.
- 20. N.I. Muskhelishvili, Singular Integral Equations, P. Noordhoff Ltd., Groningen, Holland, 1953.
- 21. F. Erdogan, G.D. Gupta, On the numerical solution of singular integral equations, Quarterly of Applied Mathematics, 29, 525–534, 1972.
- 22. T.C.T. Ting, Anisotropic Elasticity-Theory and Applications, Oxford University Press, New York, 1996.
- 23. Z.G. Suo, Complex Variable Method, [in:] Advanced Elasticity, Lecture Notes, Harvard University, 2007.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-b513cc57-7b99-4fdc-94c4-40d3ac27f0e6