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.

A model is presented in this article to investigate the dependence of effective magnetostriction of the magnetostrictive composites on the parameters of components including the elastic modulus, permeability, and volume fraction, etc. Concentrating on the two-component magnetostrictive composites and choosing the two components to be general magnetostrictive materials, this model yields, analytically, the effective magnetostriction of composites by means of the method of complex potential. In terms of the analysis of this model, the magnetostrictive composites can be roughly divided into two kinds. One kind is that the matrix material is nonmagnetic or a material with very low magnetostriction, in which the effective magnetostriction is independent of the permeability of components. Another kind is the case in which the two components have close magnetostriction, and the effective magnetostriction of the composites generally depends on the elastic and the magnetic parameters of both components and the volume fraction. Unlike the first kind of composite, in a certain range, effective magnetostriction of this kind of composite can be improved by increasing the permeability of matrix. In addition, dependence of the effective magnetostriction on the other parameters of the components has also been discussed systematically. To evaluate the accuracy of this model, comparisons are made between the theoretical values and the experimental results published in the literature, which indicate that predictions of this model agree qualitatively with the experimental data.

In this article, we study the effective elastic and plastic properties of particle-reinforced composite mterials with imperfect interface. The imperfect interface is described by a spring-type model assuming that the traction conitnuity remains intact, while the displacement experiences a jump proportional to the interfactial traction. Both the tangential and normal displacement discontinuities at the interfaces are considered and the effective elastic moduli are obtained using a generalized version of dilute model, self-consitent model, Mori-Tanaka model, and efferential model. A comparison between the effective elastic moduli obtained by these different models is made and the determination of an effective plastic behavior of particulate composite materials, by means of the Mori-Tanaka model and secant moduli method, is also discussed. Finally, we examine the influence of interfacial compliance on the macrossopic averaged mechanical properties of composite materials.

In this paper, we give the elastic solution for a special type of microstructure-a circular cylindrical rod containing periodically distributed inclusions along its axial direction. Each inclusion has the same uniform axisymmetric transformation strain (eigenstrain). Analytical elastic solutions are obtained for the displacements, stresses and elastic strain energy of the rod. The effects of microstructure and its evolution (growth of inclusions) on the elastic stress and strain fields as well as the strain energy of the rod are quantitatively demonstrated. As a result of such microstructure evolution nominal stress-strain relation with strain softening is derived for a rod under uniaxial tension.