Waves in Strained/Polarized Media

The problems related to electroelastic materials subject to incremental fields superposed on initial mechanical and electric fields have attracted considerable attention recently, due their complexity and to multiple applications (see [3, 5, 10, 31–33]). The basic equations of the theory of piezoelectric bodies subject to infinitesimal deformations and fields superposed on large initial mechanical and electric fields were described by Eringen and Maugin in their well-known monograph [6]. An useful development of the equations of electromagnetism in material continua may be found in [30]. As regards the description of mechanics of a continuum medium we refer to the classical textbook of Malvern [12]. The chapter is divided into four parts. The first one presents the fundamental equations of incremental fields superposed on large static deformation and electric fields. Following the paper [2], we derive the balance equations, constitutive equations, and boundary conditions for this problem, using the updated Lagrangean description. We analyse the important special case of homogeneous initial state and nonpolarisable environment. In this framework we obtain the dynamic and static energy balance, we present the static and dynamic local stability criteria, we derive the conditions of plane harmonic wave propagation, and we define the characteristic surfaces.