Department of Physics and Materials Science, Shimane University, 1060 Nishikawatsu-cho, Matsue 690-8504, Japan.
Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawaoiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan.
Phys Rev E. 2017 Jun;95(6-1):062902. doi: 10.1103/PhysRevE.95.062902. Epub 2017 Jun 14.
The shear modulus of jammed frictional granular materials with harmonic repulsive interaction under an oscillatory shear is numerically investigated. It is confirmed that the storage modulus, the real part of the shear modulus, for frictional grains with sufficiently small strain amplitude γ_{0} discontinuously emerges at the jamming transition point. The storage modulus for small γ_{0} differs from that of frictionless grains even in the zero friction limit, whereas they are almost identical with each other for sufficiently large γ_{0}, where the transition becomes continuous. The stress-strain curve exhibits a hysteresis loop even for a small strain, which connects a linear region for sufficiently small strain to another linear region for larger strain. We propose a scaling law to interpolate between the states of small and large γ_{0}.
数值研究了在振荡剪切下具有调和排斥相互作用的被卡住的摩擦性颗粒材料的剪切模量。结果证实，对于应变幅度 γ_{0}足够小的摩擦性颗粒，存储模量，即剪切模量的实部，在被卡住的转变点处会突然出现。对于小 γ_{0}，存储模量与无摩擦颗粒不同，即使在零摩擦极限下也是如此，而对于足够大的 γ_{0}，它们几乎是相同的，在那里转变是连续的。即使应变很小，应力-应变曲线也会出现滞后环，将小应变的线性区域与大应变的另一个线性区域连接起来。我们提出了一个标度定律来插在小 γ_{0}和大 γ_{0}的状态之间。
