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By utilizing the fourth-, sixth-, eighth-, and tenth-order elastic moduli tensors of graphene a highly nonlinear constitutive model for it is proposed. Subsequently, an accurate analytical formulation, describing the entire tensile behavior of single-walled carbon nanotubes (SWCNTs) from their initial unloaded states through their ideal strengths, is made possible. The angle of twist which is a critical parameter that varies with the tensile loading is also calculated within the current framework. The estimated value of the theoretical strength of SWCNTs with different chiralities and radii as well as that of graphene ranges from 0.39 to 0.44 TPa. Some peculiarities associated with chirality... 

Carbon nanotubes (CNTs) with and without end caps may be used for fluid storage and transport, respectively, referred to as CNT-nanovessel and CNT-nanopipe. The determination of the stiffness in the hoop (circumferential) and radial directions, ideal hoop strength, and hoop stress-strain curve of such nanostructures is of particular interest. Due to the proposed viewpoint, a chiral free-standing single-walled CNT (SWCNT) has a natural angle of twist and natural extension along the axis of the tube. For example, for the SWCNT (9,3) with diameter of 0.85 nm and chirality angle of 13.9°, the natural angle of twist per unit length is 1.45×10-3 rad/nm. Previously, only Vercosa et al. (2010) who... 

Nowadays, two-dimensional materials due to their vast engineering and biomedical applications have been the focus of many researches. The present paper proposes a large-deformation theory for thin plates with application to one-atom-thick layers (OATLs). The deformation is formulated exactly in the mathematical framework of Lagrangian description. In particular, an exact finite strain analysis is given - in addition to the usual strain tensor associated to the middle surface, the second and third fundamental forms of the middle surface of the deformed thin plate are also maintained in the analysis. Exact closed-form solutions for a uniaxially curved thin plate due to pure bending in one case... 

By considering a single-walled carbon nanotube (SWCNT) as a two-dimensional elastica obtained from the roll-up of a graphene sheet into a circular tube, the present paper develops a precise well-posed continuum theory for describing the entire torsional behavior of SWCNTs from an initial unloaded state through their ultimate levels of loading. In addition, the proposed approach can capture the dual ideal shear strengths as well as the asymmetrical behavior of chiral tubes with respect to the direction of the applied torsional loading. The theory incorporates a highly nonlinear constitutive equation which provides information about the nanoscopic morphological parameters of the tubes. As it... 

The elastica is referred to the shape of the curve into which the centreline of a flexible lamina is bent. Hence, single-walled carbon nanotubes (SWCNTs) are treated as the elastica obtained from bending of graphene. The corresponding large deformation accompanies both the material and geometrical non-linearities. The morphology of the free-standing SWCNTs such as the natural angle of twist, bond lengths, tube radius and wall thickness are determined. Moreover, it is shown that the induced self-equilibriated strain field has a remarkable impact on the mechanical behaviour of the nanotube. Utilization of an appropriate non-linear continuum constitutive relation for graphene leads to exact... 

To date, the existing theories pertinent to the determination of the scattered fields of an inhomogeneity have been limited to certain topological symmetries for which the method of wave-function expansion is widely used. In the literature the wave-function expansion method has also been employed to the case involving concentric coated fiber. An alternative approach is the dynamic equivalent inclusion method (DEIM) proposed by Fu and Mura [L.S. Fu, T. Mura, The determination of elastodynamic fields of an ellipsoidal inhomogeneity. ASME J. Appl. Mech. 50 (1983) 390-396.] who found the scattered field of a single spheroidal inhomogeneity. The pioneering work of Eshelby [J.D. Eshelby, The... 

The inadequacy of traditional theory of elasticity in describing such a phenomenon as dispersion associated to a propagating wave with wavelength comparable to the intrinsic length of the medium of interest is well-known. Moreover, under certain circumstances it is incapable of capturing all the propagating waves. A remedy to such dilemmas is the employment of the more accurate higher order continuum theories which give rise to the appearance of at least one new characteristic length in the formulation. The experimental evidences as well as lattice dynamic analysis suggest that, although higher order continuum theories result in some improvements, but cannot fully overcome the...