Adaptive nonlocal quasicontinuum for deformations of curved crystalline structures

Abstract

This paper presents an adaptive multiscale simulation of deformations of curved crystalline structures such as carbon nanotubes ͑CNTs͒. 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.

A quasistatic implementation of the concurrent atomistic-continuum method for FCC crystals

“…For example, the hardness of a nano-thin film is known to be a function of the film thickness, and the nano-indentation process has been widely studied by atomistic simulations. In coarse-graining, however, the lattice deformation at a free surface may not be accurately captured due to its localized nature (Park and Im, 2008): the trilinear interpolation function poses a restriction on the atomic configuration, particularly when a large element is employed. Moreover, the assumption that all atoms in a subregion have the same force/energy is only valid when the deformation gradient within an element remains nearly the same, which is not the case for highly inhomogeneous deformation.…”

Multiscale computations for carbon nanotubes based on a hybrid QM/QC (quantum mechanical and quasicontinuum) approach

“…First, we briefly discuss the formulation and implementation of a generalized QC for CNTs. More details of this scheme are presented in Park and Im (2008).…”

“…1). In the present paper, we adopt the QC as a coupling method for MM and CG as in Park and Im (2008). First, we briefly discuss the formulation and implementation of a generalized QC for CNTs.…”

An efficient three-dimensional adaptive quasicontinuum method using variable-node elements

“…Since the QC was first reported by Tadmor et al [5], the behaviors of various defects and their interactions, such as, cracks, dislocations, grain boundaries and so on, have been successfully studied with the aid of this method [5][6][7][8][9][10]. The QC method may be categorized into two approaches.…”

“…To overcome these limitations, various multiscale simulation methods that is capable of bridging different scales have been explored; to name a few, for example, but not limited to, the references [1][2][3][4][5][6][7][8][9][10]. Among others, the quasicontinuum (QC) method [5][6][7][8][9][10] is one of the most successful multiscale simulation methods. It allocates the full atomic degrees of freedom for the domain called the nonlocal region, where defects occur, such as voids, dislocations or twins etc.…”