ElsevierMerli Gisbert, R.; Lazaro, C.; Monleón Cremades, S.; Domingo Cabo, A. (2013). A molecular structural mechanics model applied to the static behavior of single-walled carbon nanotubes: New general formulation. Computers and Structures. 127:68-87. doi:10.1016/j.compstruc.2012.11.023 AbstractA new general formulation for the mechanical behavior of Single-Walled Carbon Nanotubes is presented. Carbon atoms are located at the nodes of an hexagonal honeycomb lattice wrapped into a cylinder. They are linked by covalent C − C bonds represented by a truss or spring element, and the three-body interaction among two neighboring covalent bonds is reproduced by a rotational spring. The main advantage of our approach is to allow general load conditions (and any chirality) with no need of specific formulation for each load case, in contrast with previous works [26], [27], [31]. Four load configurations are adopted: tension, compression, bending and torsion of cantivelered SWCNTs. Calculations with our own codes for both AMBER and Morse potential functions have been carried out, aimed to compare their final results. Initial positions of the atoms (nodes) into nanotube cylindrical geometry has been reproduced in great detail by means of a conformal mapping from the planar graphene sheet. Therefore, the effect of initial SWCNTs curvature has been introduced explicitly through a system of initial stresses (prestressed state) which contribute to maintain their circular cross-section. Numerical results and deformed shapes for nanotubes with several diameters and chiralities under each load case are used to obtain their mechanical parameters with the only objective of checking the present formulation with previous works [28], [30], [20], [24]. Also, the significance of the atomistic discrete simulations at the nano-scale size against other continuum models is underlined.

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This article reviews the different aspects involved in computational form finding of bending-active structures based on the dynamic relaxation technique. Dynamic relaxation has been applied to form-finding problems of bending-active structures in a number of references. Due to the complex nature of large spatial deformations of flexible beams, the implementation of suitable mechanical beam models in the dynamic relaxation algorithm is a non-trivial task. Type of discretization and underlying beam theory have been identified as key aspects for numerical implementations. References can be classified into two groups depending on the selected discretization: finite-difference-like and finite-element-like. The first group includes 3-and 4-degree-of-freedom implementations based on increasingly complex beam models. The second gathers 6-degree-of-freedom discretizations based on co-rotational three-dimensional Kirchhoff-Love beam elements and geometrically exact Reissner-Simo beam elements. After reviewing and comparing implementation details, the advantages and drawbacks of each group have been discussed, and open aspects for future work have been pointed out.

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