  The vibrational properties of a face-centered cubic granular crystal of
monodisperse particles are predicted using a discrete model as well as two
micropolar models, first the classical Cosserat and second an enhanced
Cosserat-type model, that properly takes into account all degrees of freedom at
the contacts between the particles. The continuum models are derived from the
discrete model via a micro-macro transition of the discrete relative
displacements and particle rotations to the respective continuum field
variables. Next, only the long wavelength approximations of the models are
compared and, considering the discrete model as reference, the Cosserat model
shows inconsistent predictions of the bulk wave dispersion relations. This can
be explained by an insufficient modeling of sliding mode of particle
interactions in the Cosserat model. An enhanced micropolar model is proposed
including only one new elastic tensor from the more complete second order
gradient micropolar theory. This enhanced micropolar model then involves the
minimum number of elastic constants to consistently predict the dispersion
relations in the long wavelength limit.
