Explicit Determination of Piezoelectric Eshelby Tensors for a Spheroidal Inclusion

Technical Report · Thu Jun 21 04:00:00 EDT 2001

DOI:https://doi.org/10.2172/821311· OSTI ID:821311

Mikata, Yozo

In this paper, by systematically treating the integrals involved in the piezoelectric inclusion problem, explicit results were obtained for the piezoelectric Eshelby tensors for a spheroidal inclusion aligned along the axis of the anisotropy in a transversely isotropic piezoelectric material. This problem was first treated by Dunn and Wienecke (1996) using a Green's function approach, which closely follows Withers' approach (1989) for an ellipsoidal inclusion problem in a transversely isotropic elastic medium. The same problem was recently treated by Michelitsch and Levin (2000) also using a Green's function approach. In this paper, a different method was used to obtain the explicit results for the piezoelectric Eshelby tensors for a spheroidal inclusion. The method is a direct extension of a more unified approach, which has been recently developed by Mikata (2000), which is based on Deeg's results (1980) on a piezoelectric inclusion problem. The main advantage of this method is that it is more straightforward and simpler than Dunn and Wienecke (1996), or Michelitsch and Levin (2000), and the results are a little bit more explicit than their solutions. The key step of this paper is an analytical closed form evaluation of several integrals, which was made possible after a careful treatment of a certain bi-cubic equation.

• Research Organization: Lockheed Martin Corporation, Schenectady, NY 12301 (US)
• Sponsoring Organization: US Department of Energy (US)
• DOE Contract Number: AC12-00SN39357
• OSTI ID: 821311
• Report Number(s): LM-01K058
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
ANISOTROPY
EVALUATION
PIEZOELECTRICITY