Axisymmetric deformation of piezoelectric multilayers

Multilayers are of technological importance. From the mechanical point of view they represent inhomogeneity in the elasticity. The material properties in one layer may be different from those in another although each layer may still be homogeneous. Mechanically, multilayers can be characterized by a variation in thermophysical constants with the direction normal to the layer interfaces. Few solutions of the basic equations of piezoelasticity have been found for such systems. In this paper we develop the foundations of the theory of piezoelasticity under axisymmetric deformation for heterogeneity. Integral transform techniques are used to reduce the problem to the solution of singular integral equations. The fundamental solutions for multilayered piezoelectric materials and structure are established. The model is general enough to account for any number of layers, and for any number of penny-shaped cracks. An additional advantage of the present model is that it can treat some certain inhomogeneous materials such as functionally graded materials.