A multiscale approximation method to describe diatomic crystalline systems: constitutive equations

We model the mechanical behavior of diatomic crystals in the light of mixture theory. Use is made of an approximation method similar to one proposed by Signorini within the theory of elasticity, by supposing that the relative motion between phases is infinitesimal. The constitutive equations for a mixture of elastic bodies in the absence of diffusion are adapted to the partially linearized case considered here, and the representation theorems for constitutive fields are applied to obtain the final expression of dynamical equations in the form which appears in theories of continua with vectorial microstructure. Comparisons are made with results of lattice theories.