Objective quasicontinuum approach for rod problems
Ye. Hakobyan, E. B. Tadmor and R. D. James
Physical Review B, 86, 245435 (2012).

ABSTRACT
An objective quasicontinuum (OQC) method is developed for simulating rodlike
systems that can be represented as a combination of locally objective
structures. An objective structure (OS) is one for which a group of atoms,
called a “fundamental domain” (FD), is repeated using specific rules of
translation and rotation to build a more complex structure. An objective
Cauchy-Born rule defines the kinematics of the OS atoms in terms of a set of
symmetry parameters and the positions of the FD atoms. The computational
advantage lies in the capability of representing a large system of atoms through
a small set of symmetry parameters and FD atom positions. As an illustrative
example, we consider the deformation of a copper single-crystal nanobeam which
can be described as an OS. OQC simulations are performed for uniform and
nonuniform bending for two different orientations (nanobeam axis oriented along
[111] and [100]) and compared with elastica results. In the uniform bending
case, the [111]-oriented single-crystal nanobeam experiences elongation, while
the [100]-oriented nanobeam experiences contraction in total length. The
nonuniform bending allows for stretching, contraction, and bending as
deformation. Under certain loading conditions, dislocation nucleation is
observed within the FD.