A circular inclusion with inhomogeneous sliding imperfect interface in harmonic materials

• Autorzy: McArthur D. R. , Sudak L. J.
• Języki publikacji: EN

Abstrakty

EN

In the following study we rigorously analyze the problem of a circular inclusion with inhomogeneous imperfect sliding interface in finite deformation of harmonic materials. The work begins by defining the inhomogeneous sliding boundary conditions characterized by two interface parameters corresponding to the normal and tangential coordinate directions (with respect to the interface boundary curve), respectively. Then, through the process of analytic continuation the problem is eventually reduced to the determination of a single analytic function given by an ordinary differential equation with variable coefficients. A specific example is selected to illustrate the method. The effects of the circumferential variation of the interface parameter on the mean stress at the interface and the average mean stress in the inclusion are discussed.

Słowa kluczowe

EN

inclusion; harmonic material; imperfect interface

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2018
• Tom: Vol. 70, nr 4
• Strony: 365--386
• Opis fizyczny: Bibliogr. 26 poz.

Twórcy

autor

McArthur D. R.

• University of Calgary 2500 University Drive NW Calgary, Alberta, Canada T2N-1N4

autor

Sudak L. J.

• University of Calgary 2500 University Drive NW Calgary, Alberta, Canada T2N-1N4

Bibliografia

• 1. J. Eshelby, The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proceedings of the Royal Society. A, Mathematical, Physical and Engineering Sciences, 241, 1226, 376–396, 1957.
• 2. N.I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity, P. Noordhoff, Groningen, The Netherlands, 1953.
• 3. C.Q. Ru, Analytic solution for Eshelby’s problem of an inclusion of arbitrary shape in a plane or half-plane, Journal of Applied Mechanics, 68, 315–322, 1999.
• 4. C.Q. Ru, P. Schiavone, A. Mioduchowski, Elastic fields in two jointed half-planes with an inclusion of arbitrary shape, Journal of Applied Mathematics and Phisics (ZAMP), 52, 18–32, 2001.
• 5. X. Wang, L.J. Sudak, Interaction of screw dislocation with an arbitrary shaped elastic inhomogeneity, Journal of Applied Mechanics, 73, 206–211, 2006.
• 6. Z. Hashin, The spherical inclusion with imperfect interface, Journal of AppliedMechanics, 58, 444–449, 1991.
• 7. Z. Gao, A circular inclusion with imperfect interface: Eshelby’s tensor and related problems, Journal of Applied Mechanics, 62, 860–866, 1995.
• 8. L.J. Sudak, X.Wang, An irregular-shaped inclusion with imperfect interface in antiplane elasticity, Acta Mechanica, 224, 9, 2009–2023, 2013.
• 9. S. Lurie, P. Belov, D. Volkov-Bogorodsky, N. Tuchkova, Interphase layer theory and applications in the mechanics of composite materials, Journal of Materials Science, 41, 20, 6693–6707, 2006.
• 10. F. John, Plane strain problems for a perfectly elastic material of harmonic type, Communications on Pure and Applied Mathematics, 13, 239–296, 1960.
• 11. R.W. Ogden, D.A. Isherwood, Solutions of some finite plane-strain problems for compressible elastic solids, Quarterly Journal of Mechanics and Applied Mathematics, 31, 3, 219–249, 1977.
• 12. E. Varley, E. Cumberbatch, Finite deformations of elastic materials surrounding cylindrical holes, Journal of Elasticity, 10, 4, 341–405, 1980.
• 13. E. Knowles, J.K. Sternberg, On the singularity induced by certain mixed boundary conditions in linearized and nonlinear elastostatics, International Journal of Solids and Structures, 11, 11, 1173–1201, 1975.
• 14. C.Q, Ru, On complex-variable forumulations for finite plane elastostatics of harmonic materials, Acta Mechanica, 234, 156, 219–234, 2002.
• 15. C.Q. Ru, P. Schiavone, L.J. Sudak, A. Mioduchowski, Uniformity of stresses inside and elliptic inclusion in finite plane elaststatics, International Journal of Non-Linear Mechanics, 40, 281–287, 2005.
• 16. C.I. Kim, P. Schiavone, Designing an inhomogeneity with uniform interior stress in finite plane elastostatics, Acta Mechanica, 197, 285–299, 2008.
• 17. X. Wang, E. Pan, On partially debonded circular inclusion in finite plane elastostatics of harmonic materials, Journal of Applied Mechanics, 76, 1–5, 2008.
• 18. X. Wang, A circular inclusion with imperfect interface in finite plane elastostatics, Acta Mechanica, 491, 481–491, 2012.
• 19. D.R. McArthur, L.J. Sudak, A circular inclusion with circumferentially inhomogeneous imperfect interface in harmonic materials, Continuum Mechanics and Thermodynamics, 28, 317–329, 2016.
• 20. D.R. McArthur, L.J. Sudak, A circular inclusion with inhomogeneous non-slip imperfect interface in harmonic materials, Proceedings of the Royal Society. A, Mathematical, Physical and Engineering Sciences, 472, 2190, 2016.
• 21. S. Mijailovich, D. Stamenovic, J. Fredberg, Toward a kinetic theory of connective tissue micromechanics, Journal of Applied Physiology, 74, 2, 665–681, 1993.
• 22. H. Van Swygenhoven, Plastic deformation in metals with nanosized grains: atomistic simulations and experiments, Materials Science Forum, 447-448, 3–10, 2004.
• 23. L. Wei, Y.J. Anand, Grain-boundary sliding and separation in polycrystalline metals: applications to nanocrystalline fcc metals, Journal of the Mechanics and Physics of Solids, 52, 2587–2616, 2004.
• 24. D. Barton, P. Drikakis, An Eulerian method for multi-component problems in non-linear elasticity with sliding interfaces, Journal of Computational Physics, 229, 5518–5540, 2010. 386 D. R. McArthur, L. J. Sudak
• 25. C.Q. Ru, A circular inclusion with circumferentially inhomogeneous sliding interface in plane elastostatics, Journal of Applied Mechanics, 65, 1, 30–38, 1998.
• 26. C. Constanda, A Mathematical Analysis of Bending of Plates with Transverse Shear Deformation, Longman Scientific and Technical, Harlow, 1990.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).