11. Piezoelectric and Magneto-Electro-Elastic Materials

It is well known that piezoelectric and piezomagnetic materials have the ability of converting energy from one form (between electric/magnetic and mechanical energies) to the other. In other words, these materials can produce an electric or a magnetic field when deformed and undergo deformation when subjected to an electric or a magnetic field. If a multilayered composite is made up of different layers such as a fiber-reinforced composite layer and a composite layer consisting of the piezoelectric materials and/or piezomagnetic materials, it may exhibit magnetoelectric effects that are more complicated than those of single-phase piezoelectric or piezomagnetic materials. Because of this intrinsic coupling phenomenon, piezoelectric, piezomagnetic and magneto-electro-elastic (MEE) materials are widely used as sensors and actuators in intelligent advanced structure design. To study the electromechanical behaviors of piezoelectric materials, magnetomechanical behaviors of piezomagnetic materials, and the magneto-electro-mechanical behaviors of MEE materials, suitable mathematical modeling becomes important. As stated in Chap. 2 the expanded Stroh formalism for piezoelectric materials preserves most essential features of Stroh formalism, it becomes a popular tool for the study of piezoelectric anisotropic elasticity. By proper replacement of piezoelectric properties with piezomagnetic properties, the expanded Stroh formalism for piezoelectric materials can be applied to the cases with piezomagnetic materials. Moreover, further expansion can also be applied to the problems with MEE materials. Most of the matlab functions designed previously for the anisotropic elastic materials can be applied directly to the piezoelectric, piezomagnetic, and MEE materials. Actually, this function was originally designed for anisotropic elastic materials, due to the equivalent mathematical form it can now be applied to piezoelectric materials. Same situation is applicable for the piezomagnetic/MEE materials and other functions coded in AEPH. Since all the formulations for the piezomagnetic materials are exactly the same as those of piezoelectric materials, no further discussions will be provided in this chapter for the piezomagnetic materials. Because the related formulations for the piezoelectric materials have been stated in Chaps. 1 and 2, the first two sections of this chapter will focus on the constitutive laws and expanded Stroh formalism of the MEE materials. The functions presented in the following sections of this chapter are just collections of some particular problems such as holes, multi-material wedges, and cracks. For the problems that are not collected in this chapter such as half-plane, bi-material, inclusion, contact, and thermoelastic problems, functions of AEPH can still be implemented by simply choosing the associated Ltype with Ptype \(\ne\) 0.