TY - JOUR
T1 - Objective quasicontinuum approach for rod problems
AU - Hakobyan, Ye
AU - Tadmor, E. B.
AU - James, R. D.
PY - 2012/12/28
Y1 - 2012/12/28
N2 - 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.
AB - 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.
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U2 - 10.1103/PhysRevB.86.245435
DO - 10.1103/PhysRevB.86.245435
M3 - Article
AN - SCOPUS:84871738712
SN - 1098-0121
VL - 86
JO - Physical Review B - Condensed Matter and Materials Physics
JF - Physical Review B - Condensed Matter and Materials Physics
IS - 24
M1 - 245435
ER -