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
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.
2015, Vol. 32 
