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Wavelike ripping morphologies and strain energy distributions of a 10-walled MWCNT (5,5)@…@(50,50) under torsion (Top: longitudinal view, bottom: cross-sectional view). From (a) to (e), the twisting angle per unit length , 0.0087, 0.0128, 0.0154, and , respectively. Regions are colored according to the magnitude of the strain energy density (red for the higher energy state and blue for lower).
Mechanical responses of a 10-walled MWCNT under torsion. For comparisons, an idealized case is considered, where the deformation of the MWCNT is constrained to the cylindrical shape without rippling throughout the entire loading process. (a) Beyond the bifurcation point, the rippling deformation mode (actual) corresponds to a lower (higher) in-plane strain energy (interlayer nonbonding energy) than the idealized deformation mode; (b) Applied torque as a function of the torsional deformation (torsional angle per unit length). The rippling deformation mode leads to a lower torsional rigidity than the idealized deformation mode.
Size effect of rippling morphology and the bifurcation torsion of MWCNTs. (a) The wave number of the rippling morphology in the circumferential direction tends to increase with increasing tube radius. (b) The bifurcation torsion scales with .
Geometric and mechanical parameters for different MWCNTs. In the table, is the number of layers in a MWCNT, and are tube radius and length, respectively, is the bifurcation torsion, and and are torsional rigidities of pre- and postbuckling, respectively. Note that is nearly a constant.
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