Theory of rigidity and numerical analysis of density of states of two-dimensional amorphous solids with dispersed frictional grains in the linear response regime.
Theory of rigidity and numerical analysis of density of states of two-dimensional amorphous solids with dispersed frictional grains in the linear response regime.
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DOI：
10.1103/physreve.107.054902
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发表时间：
2022-07
期刊：
影响因子：
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通讯作者：
Daisuke Ishima;Kuniyasu Saitoh;M. Otsuki;H. Hayakawa
中科院分区：
文献类型：
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作者：
Daisuke Ishima;Kuniyasu Saitoh;M. Otsuki;H. Hayakawa
利用雅可比矩阵，我们得到了由摩擦颗粒组成的二维非晶固体对无穷小应变线性响应时的刚度和态密度的理论表达式，其中忽略了由接触点滑移过程引起的动力学摩擦.理论刚性与分子动力学模拟结果一致。我们确认，刚度是光滑连接到无摩擦极限的值。我们发现，当切向刚度与法向刚度之比k_{T}/k_{N}足够小时，态密度中存在两个模。旋转模式存在于低频或小特征值处，而平移模式存在于高频或大特征值处。随着k_{T}/k_{N}的增大，转动带的位置向高频区移动，当k_{T}/k_{N}较大时，转动带与平动带变得难以区分。
Using the Jacobian matrix, we obtain a theoretical expression of rigidity and the density of states of two-dimensional amorphous solids consisting of frictional grains in the linear response to an infinitesimal strain, in which we ignore the dynamical friction caused by the slip processes of contact points. The theoretical rigidity agrees with that obtained by molecular dynamics simulations. We confirm that the rigidity is smoothly connected to the value in the frictionless limit. We find that there are two modes in the density of states for sufficiently small k_{T}/k_{N}, which is the ratio of the tangential to normal stiffness. Rotational modes exist at low frequencies or small eigenvalues, whereas translational modes exist at high frequencies or large eigenvalues. The location of the rotational band shifts to the high-frequency region with an increase in k_{T}/k_{N} and becomes indistinguishable from the translational band for large k_{T}/k_{N}.