Green's Functions - Reading List

References to reading material related to Green's functions have been selected and compiled by Professor Thomas C. T. Ting, Professor of Applied Mechanics, Department of Civil & Materials Engineering, University of Illinois at Chicago.

REFERENCES

Alshits, V.I., Kirchner, H. O. K., and Ting, T. C. T. (1995) "Angularly inhomogeneous piezoelectric, piezomagnetic, magnetoelectric, anisotropic media," Phil Mag. Letters 71, 285-288.

Asaro, R. J., Hirth, J. P., Barnett, D. M., and Lothe, J. (1973) "A further synthesis of sextic and integral theories for dislocations and line forces in anisotropic media," Physica Status Solidi B 60, 261–271.

Barnett, D. M. (1972) "The precise evaluation of derivatives of the anisotropic elastic Green's functions," Physica Status Solidi B 49, 741-748.

Barnett, D. M., and Lothe, J. (1973) "Synthesis of the sextic and the integral formalism for dislocations, Greens function and surface waves in anisotropic elastic solids," Phys. Norv. 7, 13–19.

Barnett, D. M., and Lothe, J. (1974) "An image force theorem for dislocations in bicrystals," J. Phys. F. 4, 1618–1635.

Barnett, D. M., and Lothe, J. (1975a) "Line force loadings on anisotropic half-spaces and wedges," Phys. Norv. 8, 13–22.

Barnett, D. M., and Lothe, J. (1975b) "Dislocations and line charges in anisotropic piezoelectric insulators," Physica Status Solidi B 67, 105–111.

Barnett, D. M., and Lothe, J. (1995) "Mutual attraction of a dislocation to a bi-metallic interface and a theorem on proportional anisotropic bimaterials," Int. J. Solids Structures 32, 291-301.

Barnett, D. M., and Swanger, L. A. (1971) "The elastic energy of a straight dislocation in an infinite anisotropic elastic medium," Physica Status Solidi B 48, 419–428.

Boussinesq, J. (1885) Applications des Potentiels, Gauthier-Villars, Paris.

Chadwick, P., and Smith, G. D. (1977) "Foundations of the theory of surface waves in anisotropic elastic materials," Adv. Appl. Mech. 17, 303–376.

Chiu, Y. T. and Wu, K. C. (1998) Analysis for elastic strips under concentrated loads. J. Appl. Mech. 65, 626-634.

Chung, M. Y., and Ting, T. C. T. (1995a) "Line force, charge, and dislocation in anisotropic piezoelectric composite wedges and spaces," J. Appl. Mech. 62, 423-428.

Chung, M. Y., and Ting, T. C. T. (1995b) "Line force, charge, and dislocation in angularly inhomogeneous anisotropic piezoelectric wedges and spaces," Phil. Mag. A71, 1335-1343.

Dederichs, P. H. and Leibfried G. (1969), Physical Review, 188, 1175-1183.

Dikici, Mustafa, (1986) "Green's tensor for a cubic material," Acta Crystallographica, A 42, 202-203.

Dundurs, J. (1967) "On the interaction of a screw dislocation with inhomogeneities," in Recent Advances in Engineering Science, Vol. 2, 223–233.

Dundurs, J. (1969) "Elastic interaction of dislocations with inhomogeneities," in Mathematical Theory of Dislocations, T. Mura, ed., ASME, New York, 70–115.

Dundurs, J., and Hetényi, M. (1965) "Transmission of force between two semi-infinite solids," J. Appl. Mech. 32, 671–674.

Dundurs, J., and Mura, T. (1964) "Interaction between an edge dislocation and a circular inclusion," J. Mech. Phys. Solids 12, 177–189.

Dundurs, J., and Sendeckyj, G. P. (1965a) "Behavior of an edge dislocation near a bimetallic interface," J. Appl. Phys. 36, 3353–3354.

Dundurs, J., and Sendeckyj, G. P. (1965b) "Edge dislocation inside a circular inclusion," J. Mech. Phys. Solids 13, 141–147.

Dunn, Martin L. and Wienecke, H. A. (1996). Green's functions for transversely isotropic piezoelectric solids. Int. J. Solids Structures 33, 4571-4581.

Dunn, Martin L. and Wienecke, H. A. (1999). Half-space Green's functions for transversely isotropic piezoelectric solids. J. Appl. Mech. In press.

Elliott, H. A. (1948) "Three-dimensional stress distributions in hexagonal aeolotropic crystals," Proc. Camb. Phil. Soc. 44, 522–533.

Eshelby, J. D., Read, W. T., and Shockley, W. (1953) "Anisotropic elasticity with applications to dislocation theory," Acta Metall. 1, 251–259.

Fredholm, I. (1900) "Sur les equations de l'equilibre d'un corps solide elastique," Act. Math. 23, 1–42.

Hanson, M. T. and Wong, Yang (1997). Concentrated ring loadings in a full space or half-space: Solutions for transverse isotropy and isotropy. Int. J. Solids Structures 34, 1379-1418.

Head, A. K. (1953) "Interaction of dislocations and boundaries," Phil. Mag. 44, 92–94.

Head, A. K. (1965) "The dislocation image force in cubic polycrystals," Physica Status Solidi 10, 481–484.

Hwu, Chyanbin, and Yen, Wen J. (1991) "Green's functions of two-dimensional anisotropic plates containing an elliptic hole," Int. J. Solids Structures 27, 1705–1719.

Hwu, Chyanbin, and Yen, Wen J. (1993) "On anisotropic elastic inclusions in plane elastostatics," J. Appl. Mech. 60, 626–632.

Indenbom, V. L., and Orlov, S. S. (1968) "Construction of Green's function in terms of Green's function of lower dimension," J. Appl. Mech. 32, 414–420.

Kirchner, H. O. K. (1987) "Line defects along the axis of rotationally inhomogeneous media," Phil. Mag. A 55, 537–542.

Kirchner, H.O.K. and Alshits, V. I. (1996). Elastically anisotropic angularly inhomogeneous media II, The Green's function for piezoelectric, piezomagnetic and magnetoelectric media. Phil Mag. 74, 861-885.

Kröner, E. (1953) "Das Fundamentalintegral der anisotropen elastischen Differentialgleichungen," Zeit. Phys. 136, 402–410.

Lee, N. G. (1979) "Elastic Green's function for an infinite half-space of a hexagonal continuum with its basal plane as surface," Int. J. Eng. Sci. 17, 681–689.

Lejcek, L. (1969) "The Green function of the theory of elasticity in an anisotropic hexagonal medium," Czech. J. Phys. B 19, 799-803.

Lekhnitskii, S. G. (1950) Theory of Elasticity of an Anisotropic Body, Gostekhizdat, Moscow (in Russian). Theory of Elasticity of an Anisotropic Elastic Body, Holden-Day, San Francisco (in English, 1963), and Mir Pub. Moscow (in English, 1981).

Lekhnitskii, S. G. (1957) Anisotropic Plates, 2nd ed., Gostekhizdat, Moscow (in Russian); transl. by S. W. Tsai and T. Cheron, Gordon and Breach, New York (1968, 1984, 1987).

Lie, Kyoon-Haeng Choh and Koehler, J. S. (1968) "The elastic stress field produced by a point force in a cubic crystal," Advances in Physics, 17 421-478.

Lifshitz, I. M., and Rozenzweig, L. N. (1947) "On the construction of the Green's tensor for the basic equation of the theory of elasticity of an anisotropic infinite medium," Zh. Eksp. Teor. Fiz. 17, 783–791.

Malen, K. (1971) "A unified six-dimensional treatment of elastic Green's functions and dislocations," Physica Status Solidi B 44, 661–672.

Mindlin, R. D. (1953) "Force at a point in the interior of a semi-infinite solid," Proc. Midwest. Conf. Solid Mech. 56–59.

Mura, T., and Kinoshita, N. (1971) "Green's functions for anisotropic elasticity," Physica Status Solidi B 47, 607–618.

Nakamura, G. and Tanuma, K. (1996) " " Q. J. Mech. Appl. Math. .

Pan, Y. C., and Chou, T. W. (1976) "Point force solution for an infinite transversely isotropic solid," J. Appl. Mech. 43, 608–612.

Pan, Y. C., and Chou, T. W. (1979a) "Green's function solutions for semi-infinite transversely isotropic materials," Int. J. Eng. Sci. 17, 545–551.

Pan, Y. C., and Chou, T. W. (1979b) "Green's functions for two-phase transversely isotropic materials," J. Appl. Mech. 46, 551–556.

Qu, Jianmin (1991) "Green's functions in anisotropic bimaterials," in Modern Theory of Anisotropic Elasticity and Applications, J. J. Wu, T. C. T. Ting and D. M. Barnett, eds., SIAM Proceedings Series, SIAM, Philadelphia, 62–73.

Rongved, R. (1955a) "Point force in the interior of a semi-infinite solid with fixed boundary," J. Appl. Mech. 22, 545–546.

Rongved, R. (1955b) "Force interior to one of two joined semi-infinite solids," Proc. 2nd Midwest. Conf. Appl. Mech. 1–13.

Santare, M. H., and Keer, L. M. (1986) "Interaction between an edge dislocation and a rigid elliptical inclusion," J. Appl. Mech. 53, 382–385.

Sih, G. C. (1971) "A review of the three dimensional stress problem for a cracked plate," Int. J. Frac. Mech. 9, 39–61.

Stagni, L., and Lizzio, R. (1983) "Shape effects in the interaction between an edge dislocation and an elliptic inhomogeneity," Appl. Phys. A 30, 217–221.

Steeds, J. W. (1973) Anisotropic Elasticity theory of Dislocations, Oxford, Clarendon Press.

Stroh, A. N. (1958) "Dislocations and cracks in anisotropic elasticity," Phil. Mag. 3, 625–646.

Synge, J. L. (1957) The Hypercircle in Mathematical Physics. Cambridge Univ. Press, Cambridge, 411–413.

Tewary, V. K. (1995) "Computationally efficient representation for elastostatic and elastodynamic Green's functions," Physical Review B 51, 15695-15702.

Tewary, V. K., Wagoner, R. H., and Hirth, J. P. (1989a) "Elastic Green's function for a composite solids with a planar interface," J. Mater. Res. 4, 113–123.

Tewary, V. K., Wagoner, R. H., and Hirth, J. P. (1989b) "Elastic Green's function for a composite solids with a planar crack in the interface," J. Mater. Res. 4, 124–136.

Ting, T. C. T. (1988) "Line forces and dislocations in anisotropic elastic composite wedges and spaces," Physica Status Solidi B 146, 81–90.

Ting, T. C. T. (1989) "Line forces and dislocations in angularly inhomogeneous anisotropic elastic wedges and spaces," Q. Appl. Math. 47, 123–128.

Ting, T. C. T. (1992a) "Image singularities of Green's functions for anisotropic elastic half-spaces and bimaterials," Q. J. Mech. Appl. Math. 45, 119–139.

Ting, T. C. T. (1992b) "Anatomy of Green's functions for line forces and dislocations in anisotropic media and degenerate materials," in The Jens Lothe Symposium Volume, Physica Scripta T 44, 137–144.

Ting, T. C. T. (1995) "Green's functions for an anisotropic elliptic inclusion under antiplane deformations," in Anisotropy, Inhomogeneity, & Nonlinearity in Solid Mechanics, D. F. Parker and A. H. England, eds., Kluwer Acad. Pub., 321-326.

Ting, T. C. T. (1996) "Green's functions for an anisotropic elliptic inclusion under generalized plane strain deformations," Q. J. Mech. Appl. Math. 49, No.1.

Ting, T. C. T., and Barnett, D. M. (1993) "Image force on line dislocations in anisotropic elastic half-spaces with a fixed boundary," Int. J. Solids Structures 30, 313–323.

Ting, T. C. T. and Lee, Ven-Gen (1997). The three-dimensional elastostatic Green's function for general anisotropic linear elastic solids. Q. J. Mech. Appl. Math. 50, 407-426.

Tucker, M. O. (1969) "Plane boundaries and straight dislocations in elastically anisotropic materials," Phil. Mag. 19, 1141–1159.

Vitek, V. and Hirth, J. P. (1977) "Line singularity fields in the presence of a crack of elliptic cross section," Scripta Metall. 11, 339–340.

Wang, C. -Y. and Achenbach, J. D. (1992) "A new look at 2-D time-domain elastodynamic Green's functions for general anisotropic solids," Wave Motion 16, 389-405.

Wang, C.-Y., and Achenbach, J. D. (1993) "A new method to obtain 3-D Green's functions for anisotropic solids," Wave Motion 18, 273-289.

Wang, C. -Y. and Achenbach, J. D. (1994) " " Geophys. J. Int. 118, 384-392.

Wang, Y. M., and Tarn, J. Q. (1993) "Green's functions for generalized plane problems of anisotropic bodies with a hole or rigid inclusion," J. Appl. Mech. 60, 583–588.

Warren, W. E. (1983) "The edge dislocation inside an elliptical inclusion," Mech. Materials 2, 319–330.

Willis, J. R. (1964) "Anisotropic elastic inclusion problems," Q. J. Mech. Appl. Math. 17, 157–174.

Willis, J. R. (1966) "Hertzian contact of anisotropic bodies," J. Mech. Phys. Solids 14, 163–176.

Willis, J. R. (1970) "Stress field produced by dislocations in anisotropic media," Phil Mag. 21, 931–949.

Wu, K. C. (1998). The elastic fields of a line force or dislocation in an anisotropic wedge. Int. J. Solids Structures 35, 3483-3495.

Wu, K. C. (1999). Generalization of the Stroh formalism to three-dimensional anisotropic elasticity. J. Elasticity 51, 213-225.

Yen, Wen J., and Hwu, Chyanbin (1994) "Interactions between dislocations and anisotropic elastic elliptical inclusions," J. Appl. Mech. 61, 548-554.

Yen, Wen J., Hwu, Chyanbin, and Liang, Y. K. (1995) "Dislocation inside, outside, or on the interface of an anisotropic elliptical inclusion," J. Appl. Mech. 62, 306-311.

Yu, H. Y., and Sanday, S. C. (1994) "Dislocations and disclinations in transversely isotropic elastic solids," Phil. Mag. A 70, 725-738.

Yu, H. Y., Sanday, S. C., and Chang, C. I. (1994) "Elastic inclusions and inhomogeneities in transversely isotropic solids," Proc. Roy. Soc. London A 444, 239-252.

Yu, H. Y., Sanday, S. C., and Chang, C. I. (1995) "Elastic fields due to defects in transversely isotropic bimaterials," Proc. Roy. Soc. London, A 449, 1-30.