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.

An exact three-dimensional analysis is presented for a functionally gradient piezoelectric material rectangular plate that is simply supported and grounded along its four edges. The state equations of the functionally gradient piezoelectric material are developed based on the state space approach. Assuming that the mechanical and electric properties of the material have the same exponent-law dependence on the thickness-coordinate, we obtain an exact threedimensional solution of the coupling electroelastic fields in the plate under mechanical, and electric loading on the upper and lower surfaces of the plate. The influences of the different functionally gradient material properties on the structural response of the plate to the mechanical and electric stimuli are then studied through examples.

The problem of a finitely long circular cylindrical shell of cylindrically orthotropic piezoelectric/piezomagnetic composite under pressuring loading and a uniform temperature change is analytically investigated in detail. The analytical solution is obtained through the power series expansion method and the Fourier series expansion method. Numerical results are presented and compared for two-layered piezoelectric/piezomagnetic composite circular cylindrical shells with different stacking sequences under inner pressuring loading.

A cylindrically anisotropic magnetoelectroelastic material is a special inhomogeneous anisotropic magnetoelectroelastic material. The constitutive law for any material point is the same when it is referred to a cylindrical coordinate system. An example of cylindrically anisotropic magnetoelectroelastic material is composite made of cylindrically anisotropic piezoelectric/piezomagnetic materials. In this paper an exact solution is derived for the two-dimensional problem of a circular tube or bar of cylindrically anisotropic magnetoelectroelastic material under pressuring loading by applying the Stroh formalism for a cylindrical coordinate system. The explicit expressions for the extended displacement vector and the extended traction vectors are presented. As encountered in the cases of elastic material and piezoelectric material, the stresses, electric fields, and magnetic fields at the axis of a circular rod may be infinite when the rod is subjected to a radial pressure. The existence of the singular stresses is also verified by our calculations for some magnetoelectroelastic materials.

This paper presents an exact solution for a simply-supported and laminated anisotropic cylindrical shell strip with imperfect bonding at the off-axis elastic layer interfaces and with attached anisotropic piezoelectric actuator and sensor subjected to transverse loading. In this research, the imperfect interface conditions are described in terms of linear relations between the interface tractions in the normal and tangential directions, and the respective discontinuities in displacements. The solution for an elastic (or piezoelectric) layer of the smart laminated cylindrical shell strip is obtained in terms of the six-dimensional (or eight-dimensional) pseudo-Stroh formalism, solution for multilayered system is then derived based on the transfer matrix method. Finally, a numerical example is presented to demonstrate the effect of imperfect interface on the static response of the smart laminated cylindrical shell. The derived solutions can serve as benchmark results to assess various approximate shell theories and numerical methods.

In this paper we studied a finite crack in an infinite medium made of a functionally gradient piezoelectric material subjected to antiplane shear and inplane electric field. The material properties, including the elastic shear modulus, the piezoelectric modulus and the dielectric modulus are assumed to vary exponentially with spatial position. By means of Fourier transformation, the governing equations of the problem are firstly reduced to two pairs of dual integral equations and then to a Fredholm integral equation of second kind. The electroelastic fields are completely determined and the field intensity factors can be defined. It is found that the stress and the electric displacement have the inverse square-root singularity at the crack tip as that of homogeneous piezoelectric materials, and the stress intensity factor and the electric displacement intensity factor increase with the increase of the material gradient constant of functionally gradient piezoelectric materials.