caa a22 4500 44581148X CHVBK 20180317145213.0 cr unu---uuuuu 170323e20110901xx s 000 0 eng 10.1007/s00419-010-0489-5 doi (NATIONALLICENCE)springer-10.1007/s00419-010-0489-5 The area contraction and expansion for a nano-void under four different kinds of loading [Elektronische Daten] [Hu Yi-Feng, Yi-Heng Chen] This paper provides an explanation for the authors' recent conclusions as why the M-integral could be negative for a nano-void (hole) in elastic materials under tensile, bi-axes tensile, and bi-axes tensile-compress loadings (Hui T, Chen YH, in ASME J Appl Mech 77:021019-1-9, 2009; 024505-1-5, 2009). Attention is focused on whether the area of the nano-void under each of four different kinds of loading is contractive when compared to the original geometrical area without loading. The four kinds of loading are as follows: (1) simple tensile loading; (2) bi-axes tensile loading; (3) bi-axes tensile-compression loading; and (4) purely shear loading. It is concluded that, unlike those for a macro/micro hole, the area of the nano-void under relatively lower amplitude of the loadings (1) and (2) is always smaller than the original area of the same void before loading. This reduction in the nano-void area is induced from the surface effect including the surface tension and the surface Lamé constants along the nano-void rim. Thus, these two kinds of loading can either decrease or increase the nano-void area depending on the amplitude of the loading. Under a relatively lower tensile loading, the area contraction occurs but not always corresponding to the negative value of the M-integral, whereas under a relatively higher tensile loading, the area expansion occurs but not always corresponding to the positive value of the M-integral. This again verifies that the positive value of the M-integral does not always correspond to the energy release due to the nano-hole expansion, rather, the area contraction might yield the energy release either. Under bi-axes tensile compression or purely shear loading, this feature disappears. Springer-Verlag, 2010 Nano-hole nationallicence Area contraction nationallicence Surface effect nationallicence M -integral nationallicence Neutral loading point nationallicence Yi-Feng Hu School of Aerospace, SVL, Xi'an Jiaotong University, 710049, Xi'an, People's Republic of China aut Chen Yi-Heng School of Aerospace, SVL, Xi'an Jiaotong University, 710049, Xi'an, People's Republic of China aut Archive of Applied Mechanics Springer-Verlag 81/9(2011-09-01), 1323-1331 0939-1533 81:9<1323 2011 81 419 https://doi.org/10.1007/s00419-010-0489-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00419-010-0489-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Yi-Feng Hu School of Aerospace, SVL, Xi'an Jiaotong University, 710049, Xi'an, People's Republic of China aut NATIONALLICENCE 700 1- Chen Yi-Heng School of Aerospace, SVL, Xi'an Jiaotong University, 710049, Xi'an, People's Republic of China aut NATIONALLICENCE 773 0- Archive of Applied Mechanics Springer-Verlag 81/9(2011-09-01), 1323-1331 0939-1533 81:9<1323 2011 81 419 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer