2016/04/24 by Ali R. Hadjesfandiari, Hadjesfandiari, Ali R., Gary F. Dargush +1 · 1 citation
Materials Science · Engineering · #Nonlocal and gradient elasticity in micro/nano structures #Metal Forming Simulation Techniques #Microstructure and mechanical properties
paper · pdf · doi:10.48550/arxiv.1605.02556
Several different versions of couple stress theory have appeared in the\nliterature, including the indeterminate Mindlin-Tiersten-Koiter couple stress\ntheory (MTK-CST), indeterminate symmetric modified couple stress theory (M-CST)\nand determinate skew-symmetric consistent couple stress theory (C-CST). First,\nthe solutions within each of these theories for pure torsion of cylindrical\nbars composed of isotropic elastic material are presented and found to provide\na remarkable basis for comparison with observed physical response. In\nparticular, recent novel physical experiments to characterize torsion of\nmicro-diameter copper wires in quasi-static tests show no significant size\neffect in the elastic range. This result agrees with the prediction of the\nskew-symmetric C-CST that there is no size effect for torsion of an elastic\ncircular bar in quasi-static loading, because the mean curvature tensor\nvanishes in a pure twist deformation. On the other hand, solutions within the\nother two theories exhibit size-dependent torsional response, which depends\nupon either one or two additional material parameters, respectively, for the\nindeterminate symmetric M-CST or indeterminate MTK-CST. Results are presented\nto illustrate the magnitude of the expected size-dependence within these two\ntheories in torsion. Interestingly, if the material length scales for copper in\nthese two theories with size-dependent torsion is on the order of microns or\nlarger, then the recent physical experiments in torsion would align only with\nthe self-consistent skew-symmetric couple stress theory, which inherently shows\nno size effect.\n