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Stability and size-dependency of Cauchy-Born hypothesis in three-dimensional applications

Aghaeia, A. and Qomia, M. J. Abdolhosseini and Kazemia, M. T. and Khoei, A. R. (2009) Stability and size-dependency of Cauchy-Born hypothesis in three-dimensional applications. International Journal of Solids and Structures, 46 (9). 1925-1936 . ISSN 0020-7683

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Abstract

The Cauchy-Born hypothesis (CB) provides a hierarchical approach in the molecular theory of crystal elasticity to relate the continuum and atomic deformations. This kinematic theory has been extensively used as the constitutive law of continuum regions in multi-scale models. In these models, the fine scale is proposed to describe the real behavior or crystalline structure wherever the continuum description fails. The main objective of this article is to investigate the stability and size-dependency of CB hypothesis in three-dimensional applications by direct comparison of information between atomistic and continuous description of a medium. The Sutton-Chen many-body potential is used for the gold metal to consider the real metallic behavior in numerical simulations. Two failure criteria are introduced in the strain and stress domains; the validity surfaces are derived for the Cauchy-Born hypothesis; and the size effect of specimens is investigated on the convergency of results, It is shown that the gold crystal deforms homogeneously inside the validity surface, in which the material is elastic and the CB has remained valid. It is observed that although the deformation is inhomogeneous and the CB is invalid outside the validity surface, the crystalline structure may exhibit elastic or plastic behavior in this region. Moreover, it is numerically shown that the size-dependency of validity surface decreases with the increase of the size of specimens. These observations are meticulously investigated by loading and unloading several cubic specimens using molecular dynamics simulation. (C) 2009 Elsevier Ltd. All rights reserved.

Item Type:Article
Subjects:Physical Science > Nanophysics
Physical Science > Nano objects
Material Science > Nanochemistry
Material Science > Nanostructured materials
Divisions:Faculty of Engineering, Science and Mathematics > School of Physics
Faculty of Engineering, Science and Mathematics > School of Chemistry
ID Code:7325
Deposited By:JNCASR
Deposited On:04 Nov 2009 07:48
Last Modified:04 Nov 2009 07:48

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