A generalized and mathematically rigorous model is developed to treat the partially-debonded circular inhomogeneity problem in piezoelectric materials under antiplane shear and in plane electric field using the complex variable method. The principle of analytical continuation and the complex series expansion method were employed to reduce the formulations into Riemann Hilbert problems. This enabled the explicit determination of the complex potentials inside the inhomogeneity and the matrix. The resulting closed form expressions were then used to obtain the energy release rate for several interesting cases involving partial-debonding at the inhomogeneity-matrix interface.

This paper is concerned with the development of a model for the treatment of a circular arc-crack in piezoelectric materials under antiplane shear and inplane electric field using the complex variable method. The problem is formulated in terms of the analytical continuation principle and complex series expansion, and as a result is reduced to two Riemann-Hilbert problems. The resulting closed form solution was then used to obtain the electroelastic field intensity factor and the energy release rate. Unlike the electric enthalpy release rate, the internal energy release rate is always positive and can thus be used as a more reliable fracture parameter in piezoelectric materials. It is also observed that the crack configuration has a significant influence upon the energy release rate.

This study is devoted to the development of a unified and explicit elastic solution to the problem of a spherical inhomogeneity with an imperfectly bonded interface. Both tangential and normal displacement discontinuities at the interface are considered and a linear interfacial condition, which assumes that the tangential and the normal displacement jumps are proportional to the associated tractions, is adopted. The elastic disturbance due to the presence of an imperfectly bonded inhomogeneity is decomposed into two parts: the first is formulated in terms of an equivalent nonuniform eigenstrain distributed over a perfectly bonded spherical inclusion, while the second is formulated in terms of an imaginary Somigliana dislocation field which models the interfacial sliding and normal separation. The exact form of the equivalent nonuniform eigenstrain and the imaginary Somigliana dislocation are fully determined in this paper.

In this paper, the problem of a cracklocated in a functionally gradient piezoelectric interlayer between two dissimilar homogeneous piezoelectric half-planes being subjected to an anti-plane mechanical loading and an in-plane electric loading is considered. The material properties of the interlayer, such as the elastic stiffness, piezoelectric constant and dielectric constant, are assumed to vary continuously along the thickness of the interlayer, and the crack surface condition is assumed to be impermeable or permeable. By using the Fourier transform, the problem is first reduced to two pairs of dual integral equations and then into a Fredholm integral equation of the second kind. Numerical calculations are carried out, and the effects of crackgeomet ric parameters on the stress intensity factor and the energy release rate are shown graphically.

In this paper, theoretical analysis of longitudinal free vibration was carried out for Tb-Dy-Fe series magnetostrictive actuator and transducer. The formulations considered two constitutive laws; in one we employ the standard square nonlinear constitutive equation of magnetostriction and in the other we employ the linear piezomagnetic equation. The results obtained from the nonlinear equation can be reduced to the linear piezomagnetic equation when the amplitude of the excitation magnetic field provided by the coil is very small compared to the bias magnetic field and its frequency does not induce resonance of the system. For the case of a relatively large excitation magnetic field, which usually exists for an actuator, the nonlinear constitutive equation should be adopted in order to provide an accurate prediction for the design and analysis of actuator and transducer. Another important aspect is the resonance of the Tb-Dy-Fe series transducers that was revealed in the analysis using the nonlinear constitutive equation. The resonance not only appears at the natural frequencies of the system, but also arises when the frequency of excitation current in the coil happens to be half of one of the natural frequencies of the system. This conclusion cannot be reached using the linear piezomagnetic formulation.