Multi‐scale modeling of plastic deformations in nano‐scale materials; Transition to plastic limit |
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| Authors: | A. R. Khoei M. Jahanshahi |
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| Affiliation: | 1. Center of Excellence in Structures and Earthquake Engineering, Department of Civil Engineering, Sharif University of Technology, Tehran, Iran;2. Department of Civil Engineering, School of Science and Engineering, Sharif University of Technology, International Campus, Kish Island, Iran |
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| Abstract: | A large amount of research in computational mechanics has biased toward atomistic simulations. This trend, on one hand, is due to the increased demand to perform computations in nanoscale and, on the other hand, is due to the rather simple applications of pairwise potentials in modeling the interactions between atoms of a given crystal. The Cauchy–Born (CB) hypothesis has been used effectively to model the behavior of crystals under different loading conditions, in which the comparison with molecular dynamics simulations presents desirable coincidence between the results. A number of research works have been devoted to the validity of CB hypothesis and its application in post‐elastic limit. However, the range of application of CB hypothesis is limited, and it remains questionable whether it is still applicable beyond the validity limit. In this paper, a multi‐scale technique is developed for modeling of plastic deformations in nanoscale materials. The deformation gradient is decomposed into the plastic and elastic parts, i.e., F = F p F e. This decomposition is in contrast to the conventional decomposition, F = F e F p, generally encountered in continuum and crystal plasticity. It is shown that the former decomposition is more appropriate for the problem dealt within this work. Inspired by crystal plasticity, the plastic part is determined from the slip on potential slip systems. Based on the assumption that the CB hypothesis remains valid in the homogeneous deformation, the elastic deformation gradient resulting from the aforementioned decomposition is employed in conjunction with the CB hypothesis to update the state variables for face‐centered cubic crystals. The assumption of homogeneity of elastic deformation gradient is justified by the fact that elastic deformations are considerably smaller than the plastic deformations. The computational algorithms are derived in details, and numerical simulations are presented through several examples to demonstrate the capability of the proposed computational algorithm in the modeling of golden crystals under different loading conditions. Copyright © 2016 John Wiley & Sons, Ltd. |
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| Keywords: | Cauchy– Born hypothesis surface effects multi‐scale modeling nonlinear finite element crystal plasticity slip systems |
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