A crack in a confocal elliptic piezoelectric inhomogeneity embedded in an infinite piezoelectric medium

An effective method is developed and used to investigate the elastic field and the electric field of a crack in a confocal elliptic piezoelectric inhomogeneity embedded in an infinite piezoelectric medium. The matrix is subjected to the remote antiplane shear and inplane electric field. The analytical solution is obtained using the conformal mapping and the theorem of analytic continuation. Specific solutions which are compared with existing ones are provided. The characteristics of the elastic field and electric field singularities at the crack tip are analyzed and the corresponding crack extension forces are derived.

[1]  T. C. T. Ting,et al.  Piezoelectric solid with an elliptic inclusion or hole , 1996 .

[2]  Y. Eugene Pak,et al.  Circular inclusion problem in antiplane piezoelectricity , 1992 .

[3]  C. Hui,et al.  Stress and induction field of a spheroidal inclusion or a penny-shaped crack in a transversely isotropic piezo-electric material , 1996 .

[4]  Tong-Yi Zhang,et al.  Fracture mechanics for a mode III crack in a piezoelectric material , 1996 .

[5]  Chao-Hsun Chen,et al.  A Crack in a Confocal Elliptic Inhomogeneity Embedded in an Infinite Medium , 1990 .

[6]  T. C. T. Ting,et al.  Modern Theory of Anisotropic Elasticity and Applications , 1992 .

[7]  Vladimir Z. Parton,et al.  Fracture mechanics of piezoelectric materials , 1976 .

[8]  H. Sosa,et al.  Three-dimensional eigenfunction analysis of a crack in a piezoelectric material , 1990 .

[9]  Horacio Sosa,et al.  New developments concerning piezoelectric materials with defects , 1996 .

[10]  J. Lothe,et al.  Integral formalism for surface waves in piezoelectric crystals. Existence considerations , 1976 .

[11]  Zhigang Suo,et al.  Fracture mechanics for piezoelectric ceramics , 1992 .

[12]  J. Rice.  A path-independent integral and the approximate analysis of strain , 1968 .

[13]  Jong S. Lee,et al.  Exact electroelastic analysis of piezoelectric laminae via state space approach , 1996 .

[14]  W. Deeg,et al.  The analysis of dislocation, crack, and inclusion problems in piezoelectric solids , 1980 .