  Beginning with Cosserat theory in the early 20th century, there have been
several different formulations for size-dependent elastic response. In this
paper, we concentrate on the application of classical Cauchy theory and the
recent parsimonious consistent couple stress theory to model a homogeneous
linear elastic solid, exemplified by a pure single crystal with cubic
structure. The focus is on an examination of elastodynamic response based upon
wave velocities from ultrasonic excitation and phonon dispersion curves, along
with adiabatic bulk moduli measurements. In particular, we consider in detail
elastic parameter estimation within classical elasticity and consistent couple
stress theory for four different cubic single crystals (NaCl, KCl, Cu, CuZn).
The classical theory requires the estimation of three independent material
parameters, while only one additional parameter relating skew-symmetric mean
curvature to skew-symmetric couple-stress is needed for the size-dependent
consistent couple stress theory. This additional parameter can be defined for
cubic crystals in terms of a material length scale, which is found to be on the
order of tens of microns for the four materials studied here. Furthermore, a
detailed statistical investigation provides strong to very strong evidence that
couple stress theory is superior to classical Cauchy elasticity for
representing the wave velocities and adiabatic bulk moduli for all four single
crystals.
