| CONDENSED MATTER: STRUCTURE, MECHANICAL AND THERMAL PROPERTIES |
|
|
|
|
Analysis of Low-Frequency Vibrational Modes and Particle Rearrangements in Marginally Jammed Amorphous Solid under Quasi-Static Shear |
| DONG Yuan-Xiang1, ZHANG Guo-Hua1**, SUN Qi-Cheng2**, ZHAO Xue-Dan1, NIU Xiao-Na1 |
1Department of Physics, University of Science and Technology Beijing, Beijing 100083
2State Key Laboratory for Hydroscience and Engineering, Tsinghua University, Beijing 100084
|
|
| Cite this article: |
|
DONG Yuan-Xiang, ZHANG Guo-Hua, SUN Qi-Cheng et al 2015 Chin. Phys. Lett. 32 126201 |
|
|
|
|
Abstract We present the numerical simulation results of a model granular assembly formed by spherical particles with Hertzian interaction subjected to a simple shear in the athermal quasi-static limit. The stress-strain curve is shown to separate into smooth, elastic branches followed by a subsequent plastic event. Mode analysis shows that the lowest-frequency vibrational mode is more localized, and eigenvalues and participation ratios of low-frequency modes exhibit similar power-law behavior as the system approaches plastic instability, indicating that the nature of plastic events in the granular system is also a saddle node bifurcation. The analysis of projection and spatial structure shows that over 75% contributions to the non-affine displacement field at a plastic instability come from the lowest-frequency mode, and the lowest-frequency mode is strongly spatially correlated with local plastic rearrangements, inferring that the lowest-frequency mode could be used as a predictor for future plastic rearrangements in the disordered system jammed marginally.
|
|
|
Received: 29 July 2015
Published: 05 January 2016
|
|
|
|
|
|
|
|
[1] Reddy K A, Forterre Y and Pouliquen O 2011 Phys. Rev. Lett. 106 108301
[2] Schall P, Weitz D A and Spaepen F 2007 Science 318 1895
[3] Lundberg M, Kapilanjan K, Xu N, O'Hern C S and Dennin M 2008 Phys. Rev. E 77 041505
[4] Tanguy A, Mantisi B and Tsamados M 2010 Europhys. Lett. 90 16004
[5] Lerner E and Procaccia I 2009 Phys. Rev. E 79 066109
[6] Xu N and O'Hern C S 2006 Phys. Rev. E 73 061303
[7] Liu H, Xie X and Xu N 2014 Phys. Rev. Lett. 112 145502
[8] Karmakar S, Lerner E, Procaccia I and Zylberg J 2010 Phys. Rev. E 82 031301
[9] Maloney C E and Lema?tre A 2006 Phys. Rev. E 74 016118
[10] Manning M L and Liu A J 2011 Phys. Rev. Lett. 107 108302
[11] Rottler J, Schoenholz S S and Liu A J 2014 Phys. Rev. E 89 042304
[12] Lacks D J 1998 Phys. Rev. Lett. 80 5385
[13] Karmakar S, Lerner E and Procaccia I 2010 Phys. Rev. E 82 026105
[14] Chen K, Manning M L, Yunker P J, Ellenbroek W G, Zhang Z, Liu A J and Yodh A G 2011 Phys. Rev. Lett. 107 108301
[15] Widmer-Cooper A, Perry H, Harrowell P and Reichman D R 2009 J. Chem. Phys. 131 194508
[16] Brito C and Wyart M 2009 J. Chem. Phys. 131 024504
[17] Ashton D J and Garrahan J P 2009 Eur. Phys. J. E 30 303
[18] Gao G, B ?awzdziewicz J and O'Hern C S 2006 Phys. Rev. E 74 061304
[19] Smith K C, Srivastava I, Fisher T S and Alam M 2014 Phys. Rev. E 89 042203
[20] Maloney C and Lema?tre A 2004 Phys. Rev. Lett. 93 016001
[21] Heussinger C and Barrat J 2009 Phys. Rev. Lett. 102 218303
[22] Karmakar S, Lema?tre A, Lerner E and Procaccia I 2010 Phys. Rev. Lett. 104 215502
[23] Hentschel H G E, Ilyin V and Procaccia I 2012 Europhys. Lett. 99 26003
[24] Hentschel H G E, Karmakar S, Lerner E and Procaccia I 2011 Phys. Rev. E 83 061101
[25] Zhang G, Sun Q, Shi Z, Feng X, Gu Q and Jin F 2014 Chin. Phys. B 23 076301
[26] Xu N 2011 Front. Phys. 6 109
[27] Xu N, Vitelli V, Liu A J and Nagel S R 2010 Europhys. Lett. 90 56001 |
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
