Torsional Characteristics of Carbon Nanotubes: Micropolar Elasticity Models and Molecular Dynamics Simulation

Abstract

Efficient application of carbon nanotubes (CNTs) in nano-devices and nano-materials requires comprehensive understanding of their mechanical properties. As observations suggest size dependent behaviour, non-classical theories preserving the memory of body’s internal structure via additional material parameters offer great potential when a continuum modelling is to be preferred. In the present study, micropolar theory of elasticity is adopted due to its peculiar character allowing for incorporation of scale effects through additional kinematic descriptors and work-conjugated stress measures. An optimisation approach is presented to provide unified material parameters for two specific class of single-walled carbon nanotubes (e.g., armchair and zigzag) by minimizing the difference between the apparent shear modulus obtained from molecular dynamics (MD) simulation and micropolar beam model considering both solid and tubular cross-sections. The results clearly reveal that micropolar theory is more suitable compared to internally constraint couple stress theory, due to the essentiality of having skew-symmetric stress and strain measures, as well as to the classical local theory (Cauchy of Grade 1), which cannot accounts for scale effects. To the best of authors’ knowledge, this is the first time that unified material parameters of CNTs are derived through a combined MD-micropolar continuum theory.

Beam Theory of Thermal–Electro-Mechanical Coupling for Single-Wall Carbon Nanotubes

“…For the tube hinged at both ends, the boundary conditions of w in Equations ( 12) and ( 13) are consistent with Equation (9). Using MD calculations, the extensional and bending stiffnesses are obtained as…”

“…For the mechanical problems of singlewalled carbon nanotubes (SWCNTs), there are two extensively discussed topics: first, the small-scale effect, i.e., the mechanical properties are dependent on the geometrical dimension [4,[8][9][10]; second, how to determine the bending stiffness [3,11]. There is plenty of research on the small-scale effect, but these studies simultaneously introduce many controversies [4,9,[12][13][14]. In most existing research, the classical beam model is modified through non-local theories to consider the small-scale effect [4,14,15].…”

Analytical solutions of the cylindrical bending problem for the relaxed micromorphic continuum and other generalized continua

“…The strain energy for the isotropic Cosserat continuum in dislocation tensor format (curvature energy expressed in terms of CurlA) can be written as [3,8,13,14,18,21,26,27,29] W (Du, A, Curl A) = µ macro sym Du…”

“…In this paper we continue our investigation of analytical solutions for isotropic the relaxed micromorphic model (and other isotropic generalized continuum models). It follows our recent exposition of analytical solutions for the simple shear [27], bending [26], and torsion problem [13,28]. Here, we consider the uniaxial extension problem, which, in classical isotropic linear elasticity, allows to determine the size-independent longitudinal modulus M macro = λ macro + 2µ macro .…”

Time-History Analysis of Composite Materials with Rectangular Microstructure under Shear Actions

“…Thanks to advances in nanostructures and nanotechnologies fields, nanomaterials are progressively commercialized. Materials with structure at the nanoscale generally have peculiar thermophysical and mechanical properties, and non-local theories, of an "explicit" or "implicit" kind, are usually applied to tackle the dynamical behavior of composites such as nanowires [34], nanobeams [35,36], nanorods [37], nanotubes [38][39][40][41], nanoplates [42] and composite beams [43] and plates [44,45].…”