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.

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.

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.

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.