1 Erratum to: Acta Mech Sin (2015) 31(3):364–372 DOI 10.1007/s10409-015-0405-x

The acknowledgments were left out in the publication due to the negligence of the author’s proofreading, the supplementary corrections are as follows:

The research was supported by the National Basic Research Program of China (Grant 2012CB937500), the National Natural Science Foundation of China (Grants 91216108, 11432014), and the CAS/SAFEA International Partnership Program for Creative Research Teams.