Green’s Functions for Two-Phase Transversely Isotropic Materials

[+] Author and Article Information
Y.-C. Pan

Engineering Division, Argonne National Laboratory, Argonne, Ill. 60439

T.-W. Chou

Department of Mechanical and Aerospace Engineering, University of Delaware, Newark, Del. 19711

J. Appl. Mech 46(3), 551-556 (Sep 01, 1979) (6 pages) doi:10.1115/1.3424604 History: Received February 01, 1979; Revised April 01, 1979; Online July 12, 2010


Closed-form solutions are obtained for the Green’s function problems of point forces applied in the interior of a two-phase material consisting of two semi-infinite transversely isotropic elastic media bonded along a plane interface. The interface is parallel to the plane of isotropy of both media. The solutions are applicable to all combinations of elastic constants. The present solution reduces to Sueklo’s expression when the point force is normal to the plane of isotropy and (C11 C33 )1/2 ≠ C13 + 2C44 for both phases. When the elastic constants of one of the phases are set to zero, the solution can be reduced to the Green’s function for semi-infinite media obtained by Michell, Lekhnitzki, Hu, Shield, and Pan and Chou. The Green’s function solution of Pan and Chou for an infinite transversely isotropic solid can be reproduced from the present expression by setting the elastic constants of both phases to be equal. Finally, the Green’s function for isotropic materials can also be obtained from the present solution by suitable substitution of elastic constants.

Copyright © 1979 by ASME
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