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
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.
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