This paper presents a novel efficient procedure to analyze the two-phase confocally elliptical inclusion embedded in an unbounded matrix under antiplane loadings. The antiplane loadings considered in this paper include a point force and a screw dislocation or a far-field antiplane shear. The analytical continuation method together with an alternating technique is used to derive the general forms of the elastic fields in terms of the corresponding problem subjected to the same loadings in a homogeneous body. This approach could lead to some interesting simplifications in solution procedures, and the derived analytical solution for singularity problems could be employed as a Green's function to investigate matrix cracking in the corresponding crack problems. Several specific solutions are provided in closed form, which are verified by comparison with existing ones. Numerical results are provided to show the effect of the material mismatch, the aspect ratio, and the loading condition on the elastic field due to the presence of inhomogeneities.
In this work, the singularity problem of a three-phase anisotropic piezoelectric media is studied using the extended Stroh formalism. Based on the method of analytical continuation in conjunction with alternating technique, the general expressions for the complex potentials are derived in each medium of a three-phase anisotropic piezoelectric media. This approach has a clear advantage in deriving the solution to the heterogeneous problem in terms of the solution for the corresponding homogeneous problem. The presented series solutions have rapid convergence which is guaranteed numerically. Stress and electric fields which are dependent on the mismatch in the material constants, the location of singularities and the magnitude of electromechanical loadings are studied in detail. Numerical results demonstrate that the continuity conditions at the interfaces are indeed satisfied and show the effects of material mismatch on the stress and electric displacement fields. The image forces exerted on a dislocation due to the interfaces are also calculated by means of the generalized Peach-Koehler formula.
In this paper, an analytical solution in series form for the problem of a circularly cylindrical layered piezoelectric composite consisting of N dissimilar layers is presented within the framework of linear piezoelectricity. Each layer of the composite is assumed to be transversely isotropic with respect to the longitudinal direction (x 3 direction), and the composite is subject to arbitrary electromechanical singularities infinitely extended in a direction perpendicular to the x 1 -x 2 plane such that only in-plane electric fields and out-of-plane displacement are produced. The alternating technique in conjunction with the method of analytical continuation is applied to derive the general multilayered media solution in an explicit series form, whose convergence is guaranteed numerically. The distributions of the shear stress and electric field are found to be dependent on the material combinations and the magnitude and position of the electromechanical singularities. An exactly closed form solution is obtained and discussed graphically for a practical example.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.