UN THE NONLOCAL THEORY OF QUASI-STATIC ELASTIC DIELECTRICS HiLMl DEMtRAYt Princeton University, Department of Aerospace and Mechanical Sciences, Princeton, NJ. 08540. U.S.A. AWraet-The nonfocal theory of polar elastic dielectrics that is in interaction with quasi-static efectric field is developed, and various special cases are discussed. For the illustration of the theory, the solution of a sample problem is given. I. INTRODUCTION IN RECENT years there has been considerable interest and activity in generalized con- tinuum mechanics. Among them are: The director theories of Ericksentl], Toupinl21, Mindlin[3], the multipolar theory of Green and Rivlin[41, the micromorphic theory of Eringen and Suhubi [5], and higher gradient theories of Toupin [61 and others. These theories, as far as the constitutive equations are concerned, have certain restricted nonlocdities. The second group of theory introduced by Kunin171, Kroner@], Krum- hansl[9], and Edelen f I O] differs from the first group in a way that there are no general- ized forces, and no additional balance laws while the nonlocality is a direct consequence of the constitutive assumptions. As is well known from experimental studies, the energy of a wave incident on the surface of a dielectric is partially absorbed by the dielectric. Many researchers are, therefore, forced to seek the theoretical explanation of this phenomena. Among those etIorts it is worthy to cite the quadrupole theory of IDixon and Eringen[I I], the polar- ization gradient theory of Mindlin [ 123,and Suhubi 1131, and the polarization rate theory of Voigt[14]. However, in many of these theories one must introduce additional bal- ance equations and state variables of which the physical meanings are not so clear, for instance, certain tensors associated with paiarization gradients, In this work we study the same problem within the spirit ofreference[fOJ, without introducing the additional state variables and/or balance equations. To this end, we first report the balance equations of [lo] with different interpretation, including a quasi-static electric field. In the later parts of the study, making use of the nonlocal variational principle we develop a set of canstitutive equations. Finally, the solution of some illustrative problems is presented. 2. BALANCE EQUATIONS Let 5!Jbe a simply connected open subset of three dimensional Euclidean point space E3 that is occupied by a body at an initial time t = 0. We take a fixed coordinate cover of Es and identify the points of the body with their coordinates XK(K = I, 2,3) at the initid time. The subsequent deformation of the body at time f is specified by xk = “@(XX, t) (2.1) TPresentIy, Research Associate at McMaster University. Department of Engineering Mechanics, Hamilton, Qntario, Canada. 285