A nonlocal continuum theory for diatomic elastic solids

In this study, taking the effects of long range intermolecular forces into account, a mechanical model for diatomic solids is presented. The model we use is based upon the assumption that a diatomic solid may be considered to consist of two simple elastically interacting media which are initially overlapping but may have relative motions at a later time $\text{t}$. Based on this assumption, the kinematics and balance laws, i.e. conservation of mass, balance of momenta, conservation of energy and equation of entropy production are presented. The nonlinear and linear constitutive equations and the discussion of some special cases are introduced in Sections 3 and 4, respectively. To illustrate the theory, in the final part, the propagation of time harmonic waves in such a medium is studied, and by comparing present result with those of lattice dynamics, the explicit form of influence functions is obtained.