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the authors of this paper would like to thank the financial supports provided by the national natural sciences foundation (grant no. 11232012 and 11372320).(2)
the authors are grateful for the support of the national natural science foundation of china through grant numbers 11202215 and 11332011. this project was also supported by the youth innovation promotion association cas (2015015).(1)
the authors would like to appreciate the financial supports from the national natural science foundation of china (11572325) and from the strategic priority research program of the chinese academy of sciences (xdb22040503, xdb22020201).(1)
the investigations presented in this paper have been supported by national natural science foundation of china under contract 51376190, 11572330, and 51306013. the authors also acknowledge national supercomputer centre in tianjin for providing computational resource.(1)
this paper is funded by the national key research and development program under 2016yfb1200506.(1)
this research was sponsored by national natural science foundation of china under contract 11332011 and 11202215. this project was also supported by the youth innovation promotion association cas (2015015).(1)
this work is based on the research sponsored by the national key research and development program of china (2016yfa0401200) and the national natural science foundation of china (grant nos. 91441103, 11372330, and 11472278). the authors would like to thank the supercomputing center of the chinese academy of sciences (sccaa) and the tianjin supercomputer center (tsc) for providing computer time.(1)
this work is supported by the national natural science foundation of china (grant no. 11642022).(1)
this work was financially supported by hebei natural science foundation (e2014210020) and hebei provincial education department scientific research project (qn20131067) fund.(1)
this work was financially supported by nsfc under grant nos. 11472286, 11572328, and 11672313, the 973 program of china under grant nos. 2012cb932203 and 2012cb937500, and the strategic priority research program of the chinese academy of sciences under grant no. xdb22040503. y.z. was supported by the us army research office (w911 nf-12-1-0009), the us national science foundation (dmt-1104667), and the nanjing university of science and technology. this paper is dedicated to professor koch's tms symposium 2017(mechanical behavior of advanced materials). this symposium will honor the outstanding contributions of professor carl c. koch to many fields in materials science in the last 50 years and celebrate his 80th birthday.(1)
this work was financially supported by the qingkehengan new material limited company, tanyuan, shanxi, 030006, china.(1)
this work was supported by advanced rail transportation special plan in national key r&d program of china under 2016yfb1200601-b13. and computing facility for computational mechanics institute of mechanics, chinese academy of sciences is gratefully acknowledged.(1)
this work was supported by the national natural science foundation of china (11472277 and 11232011), strategic priority research program, cas (xdb22040104), key research program of frontier sciences, cas (qyzdj-ssw-sys002), science challenge program (jcky2016212a501) and the 973 program of china (2013cb834100). jgd would like to thank professor lian-ping wang at university of delaware, usa for the discussion and help during the work of this paper. the anonymous reviewers are much appreciated for the constructive suggestions to improve the manuscript.(1)
this work was supported by the national natural science foundation of china (grant nos. 11232012, 11372319, 11602273) and the strategic priority research program (type-b) of cas (grant no. xdb22030000).(1)
we would like to thank s. semenov for helpful discussions. this work was financially supported by the national natural science foundation of china (grants no. 11532015, no. 11302236), by the strategic priority research program on space science, chinese academy of sciences (grants no. xda04073000, xda04020202-02), and by the cnes (centre national d'etudes spatiales). the work was conducted within the framework of a joint doctoral training program (dpp) between chinese academy of sciences (cas) and centre national de la recherche scientifique (cnrs). funding from the cas and support from the cnrs/cnes are gratefully acknowledged.(1)

 

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