Non-local theory solution to two collinear limited-permeable mode-I cracks in a piezoelectric/piezomagnetic material plane  

作　　者：ZHOU ZhenGong TANG YuLing WU LinZhi 

机构地区：[1]Center for Composite Materials and Structures Harbin Institute of Technology,Harbin 150080,China

出　　处：《Science China(Physics,Mechanics & Astronomy)》2012年第7期1272-1290,共19页中国科学：物理学、力学、天文学（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant No. 10872057);the Research Fund for the Doctoral Program of Higher Education of China (Grant No.20092302110006);the Natural Science Foundation of Heilongjiang Province (Grant No. A2007-05)

摘　　要：The non-local theory solution to two collinear limited-permeable mode-1 cracks in a piezoelectric/piezomagnetic medium was investigated by using the generalized Almansi＇s theorem and the Schmidt method in the present paper. The problem was for- mulated through Fourier transformation into two pairs of dual integral equations, in which the unknown variables are the dis- placement jumps across the crack surfaces. For solving the dual integral equations, the displacement jumps across the crack surfaces were directly expanded as a series of Jacobi polynomials. Numerical examples were provided to show the effects of the crack length, the distance between the two collinear cracks, the lattice parameter, the electric permittivity and the magnetic permeability of the air inside the crack on the stress fields, the electric displacement fields and the magnetic flux fields near the crack tips in a piezoeleetric/piezomaguetic medium. Different from the classical solutions, the present solution exhibits no stress, electric displacement and magnetic flux singularities at the crack tips in a piezoelectric/piezomagnetic medium.The non-local theory solution to two collinear limited-permeable mode-I cracks in a piezoelectric/piezomagnetic medium was investigated by using the generalized Almansi's theorem and the Schmidt method in the present paper. The problem was formulated through Fourier transformation into two pairs of dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. For solving the dual integral equations, the displacement jumps across the crack surfaces were directly expanded as a series of Jacobi polynomials. Numerical examples were provided to show the effects of the crack length, the distance between the two collinear cracks, the lattice parameter, the electric permittivity and the magnetic permeability of the air inside the crack on the stress fields, the electric displacement fields and the magnetic flux fields near the crack tips in a piezoelectric/piezomagnetic medium. Different from the classical solutions, the present solution exhibits no stress, electric displacement and magnetic flux singularities at the crack tips in a piezoelectric/piezomagnetic medium.

关 键 词：piezoelectric/piezomagnetic medium fracture mechanics the non-local theory integral transforms 

分 类 号：O346.1[理学—固体力学] TV134.1[理学—力学]