Commun. Comput. Phys., 15 (2014), pp. 470-486.


A Constrained Cauchy-Born Elasticity Accelerated Multigrid Method for Nanoindentation

Jingrun Chen 1, Pingbing Ming 2, Jerry Zhijian Yang 3*

1 Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, Chinese Academy of Sciences, Beijing, 100190, P.R. China.
2 LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, Chinese Academy of Sciences, No. 55 East Road Zhong-Guan-Cun, Beijing, 100190, P.R. China.
3 School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, P.R. China.

Received 2 September 2012; Accepted (in revised version) 15 July 2013
Available online 10 September 2013
doi:10.4208/cicp.020912.150713a

Abstract

We introduce a new multigrid method to study the lattice statics model arising from nanoindentation. A constrained Cauchy-Born elasticity model is used as the coarse-grid operator. This method accelerates the relaxation process and considerably reduces the computational cost. In particular, it saves quite a bit when dislocations nucleate and move, as demonstrated by the simulation results.

AMS subject classifications: 65B99, 65N30, 65Z05, 74G15, 74G65, 74S05

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Key words: Multigrid method, constrained Cauchy-Born elasticity, nanoindentation, Cauchy-Born rule.

*Corresponding author.
Email: chenjr@lsec.cc.ac.cn (J. Chen), mpb@lsec.cc.ac.cn (P. B. Ming), zjyang.math@whu.edu.cn (J. Z. Yang)
 

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