RESEARCH PAPER
AN ANTICRACK IN A TRANSVERSELY ISOTROPIC SPACE
1
Faculty of Mathematics and Information Science, Warsaw University of Technology, ul. Koszykowa 75, 00-662 Warszawa, Poland
Online publication date: 2014-01-22
Publication date: 2013-09-01
Acta Mechanica et Automatica 2013;7(3):140-147
KEYWORDS
Three-Dimensional ElasticityTransversely Isotropic MaterialPlane AnticrackSingular Integral EquationsStress Singularity
ABSTRACT
An absolutely rigid inclusion (anticrack) embedded in an unbound transversely isotropic elastic solid with the axis of elastic symmetry normal to the inclusion plane is considered. A general method of solving the anticrack problem is presented. Effective results have been achieved by constructing the appropriate harmonic potentials. With the use of the Fourier transform technique, the governing system of two-dimensional equations of Newtonian potential type for the stress jump functions on the opposite surfaces of the inclusion is obtained. For illustration, a complete solution to the problem of a penny-shaped anticrack under perpendicular tension at infinity is given and discussed from the point of view of material failure.
REFERENCES (27)
1.
Berezhnitskii L.T., Panasyuk V.V. , Stashchuk N.G. (1983), The Interaction of Rigid Linear Inclusions and Cracks in a Deformable Body (in Russian), Naukova Dumka, Kiev.
2.
Chaudhuri R.A. (2003), Three-dimensional asymptotic stress field in the vicinity of the circumference of a penny-shaped discontinuity, International Journal of Solids and Structures, Vol. 40, 3787-3805.
3.
Chaudhuri R.A. (2012), On three-dimensional singular stress field at the front of a planar rigid inclusion (anticrack) in an orthorhombic mono-crystalline plate, International Journal of Fracture, Vol. 174, 103-126.
4.
Ding H., Chen W., Zhang L. (2006), Elasticity of Transversely Isotropic Materials, Solid Mechanics and its Applications, Vol. 126, Springer, The Netherlands.
6.
Fabrikant V.I. (1989), Applications of Potential Theory in Mechanics: A Selection of New Results, Kluwer Academic Publishers, Dordrecht.
7.
Fabrikant V.I. (1991), Mixed Boundary Value Problems of Potential Theory and their Applications, Kluwer Academic Publishers, Dordrecht.
8.
Kaczyński A. (1993),On the three-dimensional interface crack problems in periodic two-layered composites, International Journal of Fracture, Vol. 62, 283-306.
9.
Kaczyński A. (1999), Rigid sheet-like interface inclusion in an infinite bimaterial periodically layered composite, Journal of Theoretical and Applied Mechanics, Vol. 37, 81-94.
10.
Kanaun S.K., Levin V.M. (2008), Self-Consistent Methods for Composites. Vol. 1: Static Problems, Solid Mechanics and its Applications, Vol. 148, Springer,The Netherlands, Dordrecht.
11.
Kassir M.K., Sih G.C. (1968), Some three-dimensional inclusion problems in elasticity, International Journal of Solids and Structures, Vol. 4, 225-241.
12.
Kassir M.K., Sih G.C. (1975), Three-Dimensional Crack Problems, Mechanics of Fracture 2, Noordhoof Int. Publ., Leyden.
13.
Khai M.V. (1993), Two-Dimensional Integral Equations of the Newton-Potential Type and their Applications (in Russian), Naukova Dumka, Kiev.
14.
Kit G.S., Khai M.V. (1989), Method of Potentials in Three- Dimensional Problems of Thermoelasticity of Bodies with Cracks (in Russian), Naukova Dumka, Kiev.
15.
Mura T. (1982), Micromechanics of Defects in Solids, Martinus Nijhoff, The Hague.
16.
Panasyuk V.V., Stadnik M.M., Silovanyuk V.P. (1986), Stress Concentrations in Three-Dimensional Bodies with Thin Inclusions (in Russian), Naukova Dumka, Kiev.
17.
Podil’chuk Y.N. (1997), Stress state of a transversely-isotropic body with elliptical inclusion, International Applied Mechanics, Vol. 33, 881-887.
18.
Rahman M. (1999), Some problems of a rigid elliptical disc-inclusion bonded inside a transversely isotropic space, Transactions of the ASME Journal of Applied Mechanics, Vol. 66, 612-630.
19.
Rahman M. (2002), A rigid elliptical disc-inclusion, in an elastic solid, subjected to a polynomial normal shift, Journal of Elasticity, Vol. 66, 207-235.
20.
Rogowski B. (2006), Inclusion Problems for Anisotropic Media, Technical University of Lodz, Lodz.
21.
Selvadurai A.P.S. (1982),On the interaction between an elastically embedded rigid inhomogeneity and a laterally placed concentrated force, Journal of Applied Mathematics and Physics (ZAMP), Vol. 33, 241-250.
22.
Shodja H.M., Ojaghnezhad F. (2007), A general unified treatment of lamellar inhomogeneities, Engineering Fracture Mechanics, Vol. 74, 1499-1510.
23.
Silovanyuk V.P. (1984), A rigid lamellar inclusion in elastic space, Materials Science, Vol. 20, 482-485.
24.
Silovanyuk V.P. (2000), Fracture of Prestressed and Transversely Isotropic Bodies with Defects, National Academy of Science of Ukraine, Physico-Mechanical Institute named G.V. Karpenko, Lviv.
26.
Ting T.C.T. (1996), Anisotropic Elasticity: Theory and Applications, Oxford University Press, New York.
27.
Vorovich I.I., Alexandrov V. V., Babeshko V. A. (1974), Nonclassical Mixed Boundary Problems of Theory of Elasticity (in Russian), Nauka, Moscow.
| eISSN: | 2300-5319 |
| ISSN: | 1898-4088 |
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