Antiplane problem of periodic cracks in piezoelectric medium

Abstract

In this article, the generalized two-dimensional problem of periodic interfacial cracks, which under antiplane deformation and in-plane electric field in piezoelectric materials, is studied by means of the complex variable method of Muskhelishvili and Riemann–Schwarz theorem. In terms of the electrically impermeable boundary condition, the problem is reduced to a Riemann–Hilbert problem and then explicit closed-form solutions are obtained. Moreover, it can be found that the solution procedure in this article is very direct and concise.

Keywords:

• Antiplane problem
• Periodic interfacial cracks
• Piezoelectric materials
• Mathematics Subject Classifications: 30E25
• 35Q72
• 74B10

Acknowledgements

The authors are grateful for the support through the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE, and NNSF(10161009) of P.R. China.