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It accounts for the orientation distribution and volume fraction of CNTs in the assembly, the bending rigidity of a CNT and its decrease after onset of buckling and for friction and slippage between CNTs.
As important examples with direct application to the development and characterization of single-walled carbon nanotubes and the design of nanotube-based structural devices, the modeling technique has been applied to two independent examples: the determination of the effective-continuum geometry and bending rigidity of a graphene sheet.
Previous studies treated the displacement at the intersection of the tooth-form central line and the line of action of the normal vector load as the deflection when evaluating the bending rigidity of a tooth (Deng et al. 2003).
A coarse-grained computational model is used to investigate how the bending rigidity of a polymer under tension affects the formation of a trefoil knot.
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In this work, we give an analytical solution of the bending rigidity of bilayered structures as a function of the interfacial shear strength.
The left femur received a high-rigidity titanium nail (Ti-6Al-4V; elastic modulus 110 GPa with a bending rigidity of 272 (SD7.1) N/mm; maximum load: 172 (SD 5.2) N) whereas the right femur received a low-rigidity titanium nail (Ti-24Nb-4Zr-7.9Sn; elastic modulus 33 GPa with a bending rigidity of 81 (SD 5.2) N/mm; maximum load: 265 (SD 8.2) N).
The effective bending rigidity of the equivalent-continuum model of a graphene sheet was determined by equating the molecular potential energy of the molecular model of a graphene sheet subjected to cylindrical bending (to form a nanotube) with the strain energy of an equivalent-continuum plate subjected to cylindrical bending.
For n = 72 at 200 K (for a bending rigidity of D200K = 10.4 nN-nm2 by Equation 5), this results in local curvature increase in approximately 7.4 to 27.5 Å of the loop.
Similarly, considering n = 144 at 725 K (for a bending rigidity of D725K = 24.0 nN-nm2), with curvature increases from 0.11 Å-1 to local peaks of 0.3 Å-1, results in local curvature increasing in approximately 7.2 Å to 27.2 Å to develop the determined energy barrier, again in good agreement with Figure 8, which indicated multiple (but short spanning) peaks across the molecular length.
The bending rigidity of two-dimensional (2D) materials is a key parameter for understanding the mechanics of 2D NEMS devices.
The research in the paper proposes the effective in-plane stiffness and bending rigidity of armchair and zigzag carbon nanotubes (CNTs) through the analysis of a representative volume element (RVE) of the graphene layer via continuous elastic models.
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