A mathematical analogy and a unified asymptotic formulation for singular elastic and electromagnetic fields at multimaterial wedges

Journal of Elasticity

Volumn 99, Issue 2, 2010, Pages 131-146

  Paggi, Marco ^a   Carpinteri, Alberto ^a   Orta, Renato ^a  

^a POLITECNICO DI TORINO   (Italy)

Author keywords

Antiplane loading; Electromagnetic fields; Linear Elasticity; Re entrant corners; Singularities

Indexed keywords

ANTIPLANE LOADING; ASYMPTOTIC FORMULATION; ELASTIC SOLUTIONS; ELECTROMAGNETIC PROBLEMS; ELECTROMAGNETIC STRUCTURE; LINEAR ELASTICITY; MULTI MATERIALS; SINGULAR STRESS FIELD;

COMPOSITE MICROMECHANICS; DISSIMILAR MATERIALS; ELASTICITY; ELECTROMAGNETIC FIELD MEASUREMENT; ELECTROMAGNETIC FIELDS; STRESS ANALYSIS;

MAGNETIC MATERIALS;

EID: 77951024276     PISSN: 03743535     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10659-009-9236-y     Document Type: Article

References (33)

1. A.H. England 1971 On stress singularities in linear elasticity Int. J. Eng. Sci. 9 571 585 0219.73005 10.1016/0020-7225(71)90039-5
2. G.B. Sinclair 2004 Stress singularities in classical elasticity-I: removal, interpretation, and analysis Appl. Mech. Rev. 57 251 297 10.1115/1.1762503 (Pubitemid 40748669)
3. G.B. Sinclair 2004 Stress singularities in classical elasticity-II: asymptotic identification Appl. Mech. Rev. 57 385 439 10.1115/1.1767846 (Pubitemid 40748671)
4. M. Paggi A. Carpinteri 2008 On the stress singularities at multimaterial interfaces and related analogies with fluid dynamics and diffusion Appl. Mech. Rev. 61 1 22 10.1115/1.2885134 2421216
5. D.B. Bogy 1971 Two edge-bonded elastic wedges of different materials and wedge angles under surface tractions ASME J. Appl. Mech. 38 377 386
6. V.L. Hein F. Erdogan 1971 Stress singularities in a two-material wedge Int. J. Fract. Mech. 7 317 330
7. D.B. Bogy K.C. Wang 1971 Stress singularities at interface corners in bonded dissimilar isotropic elastic materials Int. J. Solids Struct. 7 993 1005 0236.73020 10.1016/0020-7683(71)90077-1
8. P.S. Theocaris 1974 The order of singularity at a multi-wedge corner of a composite plate Int. J. Eng. Sci. 12 107 120 0272.73038 10.1016/0020-7225(74) 90011-1
9. S.S. Pageau P.F. Joseph S.B. Biggers Jr. 1994 The order of stress singularities for bonded and disbonded three-material junctions ASME J. Appl. Mech. 31 2979 2997 0943.74504
10. A. Carpinteri M. Paggi 2007 Analytical study of the singularities arising at multi-material interfaces in 2D linear elastic problems Eng. Fract. Mech. 74 59 74 10.1016/j.engfracmech.2006.01.030 (Pubitemid 44391181)
11. T. Inoue H. Koguchi 1996 Influence of the intermediate material on the order of stress singularity in three-phase bonded structure Int. J. Solids Struct. 33 399 417 0900.73454 10.1016/0020-7683(95)00040-H (Pubitemid 126400117)
12. A.K. Rao 1971 Stress concentrations and singularities at interface corners Z. Angew. Math. Mech. (ZAMM) 51 395 406 0228.73092 10.1002/zamm. 19710510509
13. D.N. Fenner 1976 Stress singularities in composite materials with an arbitrarily oriented crack meeting an interface Int. J. Fract. 12 705 712
14. M.L. Williams 1952 Stress singularities resulting from various boundary conditions in angular corners of plates in extension ASME J. Appl. Mech. 74 526 528
15. C.C. Ma B.L. Hour 1989 Analysis of dissimilar anisotropic wedges subjected to antiplane shear deformation Int. J. Solids Struct. 25 1295 1308 0703.73008 10.1016/0020-7683(89)90093-0 (Pubitemid 20622673)
16. C.C. Ma B.L. Hour 1990 Antiplane problems in composite materials with an inclined crack terminating at a bi-material interface Int. J. Solids Struct. 26 1387 1400 10.1016/0020-7683(90)90085-A
17. S.S. Pageau P.F. Joseph S.B. Biggers Jr. 1995 Finite element evaluation of free-edge singular stress fields in anisotropic materials Int. J. Numer. Methods Eng. 38 2225 2239 0847.73066 10.1002/nme.1620381306
18. G.B. Sinclair 1980 On the singular eigenfunctions for plane harmonic problems in composite regions ASME J. Appl. Mech. 47 87 92 0445.73009
19. C. Bouwkamp 1946 A note on singularities occurring at sharp edges in electromagnetic diffraction theory Physica 12 467 0063.00574 10.1016/S0031-8914(46)80061-2 19064 1946Phy....12..467B
20. J. Meixner 1949 Die Kentenbedingung in der Theorie der beugung electromagnetischer Wellen an vollkommen leitenden ebenen Schirmen Ann. Phys. 6 1 9 34238
21. J. Meixner 1972 The behavior of electromagnetic fields at edges IEEE Trans. Antennas Propag. AP-20 442 446 10.1109/TAP.1972.1140243 1972ITAP...20..442M
22. D.S. Jones 1952 Diffraction by an edge and by a corner Q. J. Mech. Appl. Math. 5 363 378 0048.21102 10.1093/qjmam/5.3.363
23. Poincelot, P.: Précis d'Électromagnétisme Théorique. Dunod, Paris (1963), pp. 84-90
24. van Bladel, J.: Singular Electromagnetic Fields and Sources. Clarendon Press, Oxford (1991)
25. K.C. Lang 1973 Edge condition of a perfectly conducting wedge with its exterior region divided by a resistive sheet IEEE Trans. Antennas Propag. AP-21 237 238 10.1109/TAP.1973.1140446 1973ITAP...21..237L
26. R.A. Hurd 1976 The edge condition in electromagnetics IEEE Trans. Antennas Propag. AP-24 70 73 10.1109/TAP.1976.1141290 1976ITAP...24...70H
27. G.H. Brooke M.M.Z. Kharadly 1977 Field behavior near anisotropic and multidielectric edges IEEE Trans. Antennas Propag. AP-25 571 575 10.1109/TAP.1977.1141646 1977ITAP...25..571B
28. J. Back Andersen 1978 Field behavior near a dielectric wedge IEEE Trans. Antennas Propag. AP-26 598 602 10.1109/TAP.1978.1141899 (Pubitemid 8610470)
29. A. Carpinteri M. Paggi N. Pugno 2006 Numerical evaluation of generalized stress-intensity factors in multi-layered composites Int. J. Solids Struct. 43 627 641 1119.74388 10.1016/j.ijsolstr.2005.06.009 (Pubitemid 41705844)
30. R.D. Graglia G. Lombardi 2004 Singular higher order complete vector bases for finite methods IEEE Trans. Antennas Propag. 52 1672 1685 10.1109/TAP.2004.831292 2069137 2004ITAP...52.1672G
31. F. Olyslager 1994 The behavior of electromagnetic fields at edges in bi-isotropic and bi-anisotropic materials IEEE Trans. Antennas Propag. 42 1392 1397 10.1109/8.320745 1994ITAP...42.1392O
32. Harrington, R.F.: Time-Harmonic Electromagnetic Fields. McGraw-Hill, New York (1961)
33. B.D.H. Tellegen 1948 The gyrator, a new electric network element Philips Res. Rep. 3 81 101 24825