Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
We rigorously prove that a non-elliptical inhomogeneity continues to permit an internal uniform stress field despite the presence of a nearby non-circular Eshelby inclusion undergoing uniform anti-plane eigenstrains when the surrounding matrix is subjected to uniform remote anti-plane stresses. Here, we adopt a specific representation of the non-circular Eshelby inclusion as a Booth’s lemniscate inclusion. Our analysis indicates that the internal uniform stress field inside the non-elliptical inhomogeneity is independent of the existence of the Booth’s lemniscate inclusion whereas the non-elliptical shape of the inhomogeneity is attributed entirely to its presence. Representative numerical examples are presented to demonstrate the feasibility of the proposed method of general solution.
Czasopismo
Rocznik
Tom
Strony
541--555
Opis fizyczny
Bibliogr. 17 poz., rys., wykr.
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. 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.
- 2. M. Dai, C.F. Gao, C.Q. Ru, Uniform stress fields inside multiple inclusions in an elasticinfinite plane under plane deformation, Proceedings of the Royal Society of London A,471, 2177, 20140933, 2015.
- 3. M. Dai, C.Q. Ru, C.F. Gao, Uniform strain fields inside multiple inclusions in anelastic infinite plane under anti-plane shear, Mathematics and Mechanics of Solids, 22,114–128, 2017.
- 4. X. Wang, L. Chen, P. Schiavone, Uniformity of stresses inside a non-elliptical inhomogeneity interacting with a circular Eshelby inclusion in anti-plane shear, Archive of Applied Mechanics, 88, 1759–1766, 2018.
- 5. X. Wang, P. Schiavone, A circular Eshelby inclusion interacting with a coated nonelliptical inhomogeneity with internal uniform stresses in anti-plane shear, Mechanics of Materials, 128, 59–63, 2019.
- 6. X. Wang, P. Yang, P. Schiavone, A circular Eshelby inclusion interacting with a nonparabolic open inhomogeneity with internal uniform anti-plane stresses, Mathematics and Mechanics of Solids, 25, 3, 573–581, 2020.
- 7. X. Wang, P. Yang, P. Schiavone, Uniform fields inside two interacting non-parabolicand non-elliptical inhomogeneities, Journal of Applied Mathematics and Physics, 71, 1,25, 2020.
- 8. Y.A. Antipov, Method of automorphic functions for an inverse problem of antiplaneelasticity, Quarterly Journal of Mechanics and Applied Mathematics, 72, 2, 213–234,2019.
- 9. Y.A. Antipov, Method of Riemann surfaces for an inverse antiplane problem in an nconnected domain, Complex Variables and Elliptic Equations, 65, 455–480, 2020.
- 10. J.S. Marshall, On sets of multiple equally strong holes in an infinite elastic plate: parameterization and existence, SIAM Journal on Applied Mathematics, 79, 2288–2312,2019.
- 11. M. Lim, G.W. Milton, Inclusions of general shapes having constant field inside the coreand nonelliptical neutral coated inclusions with anisotropic conductivity, SIAM Journal on Applied Mathematics, 80, 3, 1420–1440, 2020.
- 12. C.Q. Ru, Analytic solution for Eshelby’s problem of an inclusion of arbitrary shape ina plane or half-plane, ASME Journal of Applied Mechanics, 66, 315–322, 1999.
- 13. H. Nozaki, M. Taya, Elastic fields in a polygon-shaped inclusion with uniform eigenstrains, ASME Journal of Applied Mechanics, 64, 495–502, 1997.
- 14. H. Nozaki, M. Taya, Elastic fields in a polyhedral inclusion with uniform eigenstrains and related problems, ASME Journal of Applied Mechanics, 68, 3, 441–452, 2001.
- 15. T.C.T. Ting, Anisotropic Elasticity: Theory and Applications, Oxford University Press,New York, 1996.
- 16. Z.M. Xiao, H.X. Zhang, B.J. Chen, Micro-crack initiation at the tip of a semi-infiniterigid line inhomogeneity in piezoelectric solids, International Journal of Engineering Science, 43, 1223–1233, 2005.
- 17. Z.M. Xiao, K.D. Pae, The interaction between a penny-shaped crack and a spherical inhomogeneity in an infinite solid under uniaxial tension, Acta Mechanica, 90, 91–104,1991.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-c462b294-6833-4b83-ab6d-2671a4f2d3ff