On the bending of piezoelectric plates with microstructure D. Ies ¸an Department of Applied Mathematics, Alexandru Ioan Cuza University, Ias ¸i, Romania Received 2 July 2007; Accepted 11 October 2007; Published online 28 January 2008 Ó Springer-Verlag 2008 Summary. This paper is concerned with the linear theory of piezoelectricity for homogeneous and isotropic bodies with microstructure. First, we present the basic equations which govern the bending of thin plates. Then, we establish a uniqueness result with no definiteness assumption on constitutive coefficients. A variational characterization of solution to the boundary-initial-value problem is presented. Finally, the effects of a concentrated body force in an unbounded plate are investigated. 1 Introduction The interaction of electromagnetic fields with elastic continua has been the subject of many investigations (see, e.g., [1]–[6] and the literature cited therein). It is well known that the material response to external stimuli depends on the motion of its inner structure. The origin of the modern theories of continua with microstructure goes back to papers of Mindlin [7], Eringen and Suhubi [8], and Green and Rivlin [9]. The theory of elastic solids with microstructure, including electromagnetic and thermal interactions, has been introduced by Eringen [10], [11]. In [10], special cases of the field equations, the micropolar piezoelectricity and magnetoelasticity are investigated. The theory of microstretch elastic bodies subjected to electromagnetic fields was established in [12]. The material particles of the microstretch bodies can stretch and contract independently of their translations and rotations. The intended applications of the theory are to porous elastic bodies, animal bones and solids with deformable microstructures. In recent years, there has been much interest in the study of piezoelectric plates (see, e.g., [13]– [23] and the literature cited therein). In this paper we use the results of Mindlin [24], Eringen [10], [25] and Naghdi [26] in order to derive a theory of bending of microstretch piezoelectric thin plates. We assume that on the upper and lower faces of the plate there are prescribed the surface traction, the surface moment, the surface microforce and the normal component of the electrical displacement. In Sect. 2 we present the basic equations of the linear theory of homogeneous and isotropic microstretch piezoelectric solids. Section 3 is devoted to the deriving of the bending theory Correspondence: Dorin Ies ¸an, Department of Applied Mathematics, Alexandru Ioan Cuza University, Bd. Carol I, No. 11, 700506 Ias ¸i, Romania e-mail: iesan@uaic.ro Acta Mech 198, 191–208 (2008) DOI 10.1007/s00707-007-0527-8 Printed in The Netherlands Acta Mechanica