J. Y. Parks and S. Im
Physical Review B, 77, 184109 (2008).
This paper presents an adaptive multiscale simulation of deformations of curved crystalline structures such as carbon nanotubes (CNTs). It is based on quasicontinuum approach, which is a coarse-graining method. For fully nonlocal quasicontinuum, high-order interpolation functions are adopted to locate the deformed positions of atoms on a curved crystal structure. The "cluster" concept, which facilitates accurate energy approximation for crystals, is extended such that the vertices of elements or subdivided regions may be chosen irrespective of the positions of carbon atoms. Defining two remeshing criteria based on the second invariant of the Green's strain tensor and its gradient, an automatic adaptive scheme that provides gradually increasing resolution up to atomistic scale in nonlocal deformations of curved bodies is implemented. Various numerical examples, including a CNT fracture and deformations, demonstrate the effectiveness of the present scheme. This investigation realizes the adaptive simulation of nonlocal deformation for curved, as opposed to rectilinear, crystalline structures.