  A method for homogenization of a heterogeneous (finite or periodic) elastic
composite is presented. It allows direct, consistent, and accurate evaluation
of the averaged overall frequency-dependent dynamic material constitutive
relations. It is shown that when the spatial variation of the field variables
is restricted by a Bloch-form (Floquet-form) periodicity, then these relations
together with the overall conservation and kinematical equations accurately
yield the displacement or stress modeshapes and, necessarily, the dispersion
relations. It also gives as a matter of course point-wise solution of the
elasto-dynamic field equations, to any desired degree of accuracy. The
resulting overall dynamic constitutive relations however, are general and need
not be restricted by the Bloch-form periodicity. The formulation is based on
micro-mechanical modeling of a representative unit cell of the composite
proposed by Nemat-Nasser and coworkers; see, e.g., [1] and [2].
