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Several different versions of couple stress theory have appeared in theliterature, including the indeterminate Mindlin-Tiersten-Koiter couple stresstheory (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 cylindricalbars composed of isotropic elastic material are presented and found to providea remarkable basis for comparison with observed physical response. Inparticular, recent novel physical experiments to characterize torsion ofmicro-diameter copper wires in quasi-static tests show no significant sizeeffect in the elastic range. This result agrees with the prediction of theskew-symmetric C-CST that there is no size effect for torsion of an elasticcircular bar in quasi-static loading, because the mean curvature tensorvanishes in a pure twist deformation. On the other hand, solutions within theother two theories exhibit size-dependent torsional response, which dependsupon either one or two additional material parameters, respectively, for theindeterminate symmetric M-CST or indeterminate MTK-CST. Results are presentedto illustrate the magnitude of the expected size-dependence within these twotheories in torsion. Interestingly, if the material length scales for copper inthese two theories with size-dependent torsion is on the order of microns orlarger, then the recent physical experiments in torsion would align only withthe self-consistent skew-symmetric couple stress theory, which inherently showsno size effect.

Comparison of theoretical elastic couple stress predictions with physical experiments for pure torsion