Journal of Engineering Mathematics, Vol. 14, No. 2, April 1980 © 1980 Sijthoff & Noordhoff International Publishers - Alphen aan den Rijn Printed in the Netherlands 81 A continuum theory of thermoelastic solids with diatomic structure H. DEMIRAY Faculty of Science, Technical University of lstanbul, Teknik Universite Istanbul, Turkey (Received March 6, 1979 and in final form October 15, 1979) SUMMARY Generalizing the idea of the deformable elastic shell model by Dick and Overhauser 111,a continuum model for thermoelastic diatomic elastic solids is presented. The model used is based on the assumption that a diatomic solid may be considered to consist of two simple and initially overlapping elastic media interacting with each other. Based on this assumption, the kinematics, balance laws and the appropriate constitutive relations for heat conducting diatomic elastic solids with multiple temperature are presented. For the illustra- tion of the theory, the propagation of time-harmonic thermal waves in elastically rigid heat-conducting diatomic solids is studied and some particular cases axe discussed. 1. Introduction It is a well-known fact that most of the elastic materials are made of complex molecules rather than simple atoms. From the viewpoint of lattice dynamics it is, therefore, apparent that the internal structure of such solids is multi-atomic. The classical continuum theory of elastic solids ignores the relative motions of particles in the same cell, and comes up with the result that the wave propagation in such an elastic medium is not dispersive. However, the results of phonon dispersion experiments (c.f. Brockhause [2], Harrison [3] and Wallis [4]) show that the phase velocity changes with wave number. These facts have forced the researchers to introduce generalized continuum theories that take the relative motion of particles into account. Among these studies it is worthy to mention the director theory of T0upin [5], the micromorphic theory of Eringen and Suhubi [6], and the multipolar theory of Green and Rivlin [7]. These theories are mathematically complete, yet they have found little applications in physical prob- lems concerning elastic solids. The continuum theory of elastic solids with diatomic structure was first laid down by Demiray [8, 10], in which the body is assumed to consist of two simple and initially overlap- ping elastic media interacting with each other. The balance laws and thermodynamically admis- sible constitutive equations, and related kernel functions characterizing the elastic properties of constituents are also reported in the same work. In the present work, a continuum formulation of heat-conducting elastic diatomic solids with multiple temperature is presented. The balance laws are formulated for each species in the medium whereas the entropy inequality is formu- lated for the whole of the body. A set of nonlinear and linear constitutive equations is derived 0022-0833/80/02/081-11 $00.20/0 Journal o f Engineering Math., Vol. 14 (1980) 81-91