  Several different versions of couple stress theory have appeared in the
literature, including the indeterminate Mindlin-Tiersten-Koiter couple stress
theory (MTK-CST), indeterminate symmetric modified couple stress theory (M-CST)
and determinate skew-symmetric consistent couple stress theory (C-CST). First,
the solutions within each of these theories for pure torsion of cylindrical
bars composed of isotropic elastic material are presented and found to provide
a remarkable basis for comparison with observed physical response. In
particular, recent novel physical experiments to characterize torsion of
micro-diameter copper wires in quasi-static tests show no significant size
effect in the elastic range. This result agrees with the prediction of the
skew-symmetric C-CST that there is no size effect for torsion of an elastic
circular bar in quasi-static loading, because the mean curvature tensor
vanishes in a pure twist deformation. On the other hand, solutions within the
other two theories exhibit size-dependent torsional response, which depends
upon either one or two additional material parameters, respectively, for the
indeterminate symmetric M-CST or indeterminate MTK-CST. Results are presented
to illustrate the magnitude of the expected size-dependence within these two
theories in torsion. Interestingly, if the material length scales for copper in
these two theories with size-dependent torsion is on the order of microns or
larger, then the recent physical experiments in torsion would align only with
the self-consistent skew-symmetric couple stress theory, which inherently shows
no size effect.
