A slit-like inclusion in an orthorhombic piezoelectric solid

A slit-like inclusion in an unbounded orthorhombic piezoelectric solid is considered. We demonstrate that the associated polarization tensor correct to the first order of the aspect ratio of the inclusion can be obtained in an analytical form. As an application, the results are exploited to estimate the effective moduli of a cracked piezoelectric solid. Micromechanical models of the self-consistent and Mori-Tanaka methods are implemented in the present case. The methods offer simple approaches to estimate the stiffness changes due to the presence of aligned longitudinal slit-like cracks.