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.
Highlights
Discovered by Iijima [1,2], carbon nanotubes (CNTs) have received great attention due to their superior mechanical, optical, thermal and electrical properties [3,4,5,6,7]
A unified parameter set, as well as thickness, of equivalent continuum model is derived for each class of SWCNTs chirality by comparing the corresponding data obtained from discrete molecular dynamics (MD) and continuum models by virtue of a non-linear optimisation approach
As the non-vanishing non-symmetric stress and couple stress measures expressed in Equation (9) are independent of θ and z, only the following relation corresponding to angular equilibrium equation in radial direction remains:
Summary
Discovered by Iijima [1,2], carbon nanotubes (CNTs) have received great attention due to their superior mechanical, optical, thermal and electrical properties [3,4,5,6,7]. Classical theory of elasticity (Cauchy of Grade 1), on the other hand, fails to accurately homogenize the discrete nature into a continuum medium for a structure having comparable internal and external lengths [22,23]. A unified parameter set, as well as thickness, of equivalent continuum model is derived for each class of SWCNTs chirality by comparing the corresponding data obtained from discrete MD and continuum models (micropolar, couple stress and classical) by virtue of a non-linear optimisation approach. To the best of authors’ knowledge this is the first time that a combined MD-micropolar continuum theory is employed to model the size-dependent mechanical behaviour of CNTs. The rest of the paper is organised as follows; Section 2 describes the details on MD simulation and presents the primary obtained results.
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