Summary
This paper presents an analysis of the scattering of anti-plane shear waves by a single piezo-electric cylindrical inclusion partially bonded to an unbounded matrix. The anti-plane governing equations for piezoelectric materials are reduced to Helmholtz and Laplacian equations. The fields of scattered waves are obtained by means of the wave function expansion method when the bonded interface is perfect. When the interface is partially debonded, the region of the debonding is modeled as an interface crack with non-contacting faces. The electric permeable boundary conditions are adopted, i.e. the normal electric displacement and electric potential are continuous across the crack faces. The crack opening displacement is represented by Chebyshev polynomials and a system of equations is derived and solved for the unknown coefficients.
Similar content being viewed by others
References
Shindo, Y., Nozaki, H., Datta, S. K.: Effects of interface layers on elastic wave propagation in a metal matrix composite reinforced by particles. ASME J. Appl. Mech.62 (1), 178–185 (1995).
Huang, W., Wang, Y. J., Rokhilin, S. I.: Oblique scattering of an elastic wave from a mutilayered cylinder in a solid: Transfer-matrix approach. J. Acoust. Soc. Amer.99 (5), 2742–2751 (1996).
Lu, Y.: Guided antiplane shear wave propagation in layers reinforced by periodically spaced cylinders. J. Acoust. Soc. Am.99 (4), 1937–1946 (1996).
Sato, H., Shindo, Y.: Multiple scattering of plane elastic waves in a fiber-reinforced composite medium with graded interfacial layers. Int. J. Solids Struct.38, 2549–2571 (2001).
Narita, F., Shindo, Y.: Scattering of antiplane shear waves by a finite crack in piezoelectric laminates. Acta Mech.134, 27–43 (1999).
Zhou, Z. G., Li, H. C., Wang, B.: Investigation of the scattering of anti-plane shear waves by two collinear cracks in a piezoelectric material using a new method. Acta Mech.147, 87–97 (2001).
Li, S., Mataga, P. A.: Dynamic crack propagation in piezoelectric materials-Part I: Electrode solution. J. Mech. Phys. Solids44, 1799–1830 (1996).
Li, S., Mataga, P. A.: Dynamic crack propagation in piezoelectric materials-Part II: Vacuum solution. J. Mech. Phys. Solids44, 1831–1866 (1996).
Sosa, H., Khutoryansky, N.: New developments concerning piezoelectric materials with defects. Int. J. Solids Struct.33, 3399–3414 (1996).
Shengping Shen, Kuang, Z.-B. and Toshihisa Nishioka: Wave scattering from an interface crack in multilayered piezoelectric plate. Eur. J. Mech. A/Solids19, 547–559 (2000).
Yang, Y., Norris, A. N.: Shear wave scattering from a debonded fibre. J. Mech. Phys. Solids39 (2), 273–294 (1991).
Xiaoming, W., Chongfu, Y.: Scattering of guided SH-wave by a partly debonded circular cylinder in a traction free plate. Science in China (Series A)44 (3), 378–388 (2001).
Parton, V. Z.: Fracture mechanics of piezoelectric materials. Acta Astron3, 671–683 (1976).
Zhang, T. Y., Hack, J. E.: Mode III cracks in piezoelectric materials. J. Appl. Phys.71, 5865–5870 (1992).
Dunn, M. L.: The effects of cracks face boundary conditions on the fracture mechanics. Eng. Fract. Mech.48, 25–39 (1994).
Wang, T. C., Han, X. L.: Fracture mechanics of piezoelectric materials. Int. J. Fract.98, 15–35 (1999).
Rubinstein, I., Rubinstein, L.: Partial differential equations in classical mathematical physics. Cambridge: Cambridge University Press 1998.
Graff, K. F.: Wave motion in elastic solids. Oxford: Clarendon Press 1975.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Du, J.K., Shen, Y.P. & Wang, X. Scattering of anti-plane shear waves by a partially debonded piezoelectric circular cylindrical inclusion. Acta Mechanica 158, 169–183 (2002). https://doi.org/10.1007/BF01176907
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01176907