The effect of nanotube radius on the constitutive model for carbon nanotubes

Jiang, Hanqing; Zhang, P.; Liu, B.; Huang, Yingsong; Geubelle, Philippe H.; Gao, Huajian; Hwang, Keh Chih

doi:10.1016/j.commatsci.2003.08.004

Cited by 158 publications

(109 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In fact, equations (32) and (33) are tangent stiffnesses to the equilibrium path of each element and they depend on the SWCNT deformed shape at each point of these trajectories. This variable nature of stiffness can be called constitutive nonlinearity and leads to the iterative procedure outlined in figure 6, based in the so-called Newton-like methods for solving nonlinear problems numerically.…”

Section: Morse Potentialmentioning

confidence: 99%

“…A special issue not explicitly included in MSM models (although the wall-curvature was included in the equations) is the preenergy, defined as the excess of strain energy from an infinite planar graphene sheet to the nanotube [17,32]. As has been shown [5,33,34,35], this preenergy is proportional to the curvature of the wall 1/R 2 (where R is the tube radius) leading to an stabilization effect into its cross-sectional area. In this paper, we introduce the preenergy as a system of initial strains which produces a 'prestressed state' previous to the action of any external loading.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A molecular structural mechanics model applied to the static behavior of single-walled carbon nanotubes: New general formulation

Merli

Lázaro

Monleón

et al. 2013

Computers & Structures

View full text Add to dashboard Cite

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.

show abstract

Section: Morse Potentialmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A molecular structural mechanics model applied to the static behavior of single-walled carbon nanotubes: New general formulation

Merli

Lázaro

Monleón

et al. 2013

Computers & Structures

View full text Add to dashboard Cite

show abstract

“…., (x N , y N ) respectively, which need to be determined by the energy method. It should be noted that to calculate the energy of the CAC bonds, the coordinates of the atoms in the cylindrical configuration should be determined first by the transformation relation from the Cartesian coordinate system to the cylindrical coordinate system, as described by Jiang et al (2003). The energy stored in the region A can be written as the summation of all the CAC bonds: …”

Section: Combined Atomistic/continuum Methods For Defect Nucleationmentioning

confidence: 99%

“…At lower tensile strains, the CNT will undergo uniform elastic deformation, and no Stone-Wales defect occurs. A non-centrosymmetric, hexagonal lattice structure can be decomposed into two triangular sub-lattices, marked respectively by solid and open circles in Figure 2 (Jiang et al, 2003). Each sub-lattice has a centrosymmetry and therefore follows the Cauchy-Born rule.…”

Section: Uniform Deformation Before Defect Nucleationmentioning

confidence: 99%

Multiscale Analysis of Fracture of Carbon Nanotubes Embedded in Composites

et al. 2005

View full text Add to dashboard Cite

Abstract. Due to the enormous difference in the scales involved in correlating the macroscopic properties with the micro-and nano-physical mechanisms of carbon nanotube-reinforced composites, multiscale mechanics analysis is of considerable interest. A hybrid atomistic/continuum mechanics method is established in the present paper to study the deformation and fracture behaviors of carbon nanotubes (CNTs) in composites. The unit cell containing a CNT embedded in a matrix is divided in three regions, which are simulated by the atomic-potential method, the continuum method based on the modified Cauchy-Born rule, and the classical continuum mechanics, respectively. The effect of CNT interaction is taken into account via the Mori-Tanaka effective field method of micromechanics. This method not only can predict the formation of Stone-Wales (5-7-7-5) defects, but also simulate the subsequent deformation and fracture process of CNTs. It is found that the critical strain of defect nucleation in a CNT is sensitive to its chiral angle but not to its diameter. The critical strain of Stone-Wales defect formation of zigzag CNTs is nearly twice that of armchair CNTs. Due to the constraint effect of matrix, the CNTs embedded in a composite are easier to fracture in comparison with those not embedded. With the increase in the Young's modulus of the matrix, the critical breaking strain of CNTs decreases.

show abstract

“…In [3,4], a QC Monte Carlo (QCMC) method and a QC free energy minimization (QCFEM) method were proposed to study equilibrium properties of defects at Enite temperature. Arroyo and Belytschko [6], Zhang et al [7][8][9][10] and Jiang et al [11] have proposed nanoscale continuum theories for carbon nanotubes based on interatomic potentials for carbon. Based on the local harmonic approximation [12], Jiang et al [13] established a Enite-temperature continuum theory directly from the interatomic potential.…”

Section: Introductionmentioning

confidence: 99%