PIRE - mathematics, mechanics, materials science

Science at the triple point between
mathematics, mechanics and materials science

Publication 54

Objective Quasicontinuum Approach for Rod Problems


Ye. Hakobyan
Cornell University

MinnesotaE. B. Tadmor
Department of Aerospace Engineering and Mechanics
University of Minnesota
Minneapolis, Minnesota

MinnesotaRichard D. James
Department of Aerospace Engineering and Mechanics
107 Akerman Hall
University of Minnesota
Minneapolis, MN 55455, USA

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.
Get the paper in its entirety

Back to Publications