Numerical distributed dislocation modeling of multiple cracks in piezoelectric media considering different crack-face boundary conditions and finite size effects
Piezoelectric materials primarily consist in smart composite materials have been extensively used as sensors/actuators in smart adaptive structures due to their excellent electromechanical properties. In this paper, the generalized fracture parameters of multiple semi-permeable and impermeable cracks in two-dimensional (2-D) piezoelectric materials related to multilayered/multiferroic composite materials are numerically investigated based on distributed dislocation method (DDM), emphasizing on the finite-specimen-size effects. The Lobatto–Chebychev quadrature method is used to solve the simultaneous singular integral equations, which are obtained after distributed dislocation modeling of the problem. Different configurations of multiple cracks under impermeable and semi-permeable crack-face boundary conditions are performed. The numerical results of generalized intensity factors obtained by the DDM are validated against reference solutions derived from the extended finite element method. The present results show great effects of finite size of a specimen, mutual influence of multiple cracks and crack-face boundary conditions on the generalized fracture parameters. In addition, numerical results also reveal the accuracy and efficacy of the DDM in studying the crack problems in 2-D finite piezoelectric media. The method of distributed dislocation which employed here to analyze the fracture parameters in finite piezoelectric media can be extended to finite multiferroic composites or multilayered piezoelectric/piezomagnetic media under various electrical boundary conditions.
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