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Summary: Rippling and a phase-transforming mesoscopic
model for multiwalled carbon nanotubes
M. Arroyo I. Arias
Department of Applied Mathematics 3, LaC`aN
Universitat Polit`ecnica de Catalunya (UPC), Barcelona 08034, Spain
Abstract
We propose to model thick multiwalled carbon nanotubes as beams with non-
convex curvature energy. Such models develop stressed phase mixtures composed of
smoothly bent sections and rippled sections. This model is motivated by experimen-
tal observations and large-scale atomistic-based simulations. The model is analyzed,
validated against large-scale simulations, and exercised in examples of interest. It
is shown that modelling MWCNTs as linear elastic beams can result in poor ap-
proximations that overestimate the elastic restoring force considerably, particularly
for thick tubes. In contrast, the proposed model produces very accurate predictions
both of the restoring force and of the phase pattern. The size effect in the bending
response of MWCNTs is also discussed.
Key words: A. buckling, A. phase transformation, B. beams and columns, B.
finite strain, B. multiwalled carbon nanotubes
1 Introduction
Since their discovery in 1991 (Iijima, 1991), carbon nanotubes (CNTs) have
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