Published by AMSS Press, Wuhan, China Acta Mechanica Solida Sinica, Vol. 23, No. 4, August, 2010 ISSN 0894-9166 MULTIPLE PARALLEL SYMMETRIC PERMEABLE MODEL-III CRACKS IN A PIEZOELECTRIC/PIEZOMAGNETIC COMPOSITE MATERIAL PLANE ⋆⋆ Zhengong Zhou ⋆ Peiwei Zhang Linzhi Wu (P. O. Box 3010, No.2, Yikuang Street, Center for Composite Materials and Structures, Harbin Institute of Technology, Harbin, 150080, China) Received 2 March 2009; revision received 29 June 2010 ABSTRACT In this paper, the interactions of multiple parallel symmetric and permeable finite length cracks in a piezoelectric/piezomagnetic material plane subjected to anti-plane shear stress loading are studied by the Schmidt method. The problem is formulated through Fourier transform into dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. To solve the dual integral equations, the displacement jumps across the crack surfaces are directly expanded as a series of Jacobi polynomials. Finally, the relation between the electric field, the magnetic flux field and the stress field near the crack tips is obtained. The results show that the stress, the electric displacement and the magnetic flux intensity factors at the crack tips depend on the length and spacing of the cracks. It is also revealed that the crack shielding effect presents in piezoelectric/piezomagnetic materials. KEY WORDS piezoelectric/piezomagnetic composites, multiple parallel symmetric cracks, crack shielding effect, mechanics of solids I. INTRODUCTION The piezoelectric/piezomagnetic composites possess piezoelectric, piezomagnetic and magneto- electric effects. In some cases, the coupling effect of piezoelectric/piezomagnetic composites can be a hundred times larger than that in a single-phase magnetoelectric material, thereby resulting in sensitivity of the composite to elastic, electric and magnetic fields. Consequently, they are extensively used in electric packaging, sensors and actuators, e.g., magnetic field probes, acoustic/ultrasonic devices, hydrophones, and transducers for the electro-magneto-mechanical energy conversion [1] . When subjected to mechanical, magnetic and electrical loads in service, these magneto-electro-elastic composites can fail prematurely due to some defects, e.g. cracks, holes, etc. from their manufacturing processes. Therefore, it is of great importance to study the magneto-electro-elastic interaction and fracture behaviors of magneto- electro-elastic materials [2–8] . The development of piezoelectric/piezomagnetic composites has its roots in the early work of Van Suchtelen [9] who proposed that the combination of piezoelectric/piezomagnetic phases may exhibit a new material property—the magnetoelectric coupling effect. Since then, many ⋆ Corresponding author. Tel: +86-451-86402396, Email: zhouzhg@hit.edu.cn ⋆⋆ Project supported by the National Natural Science Foundation of China (Nos. 10572043 and 10872057), the Research Fund for the Doctoral Program of Higher Education of China (No. 20092302110006) and the Natural Science Foundation of Hei Long Jiang Province (No. A2007-05).