Tensor electromagnetism and emergent elasticity in jammed solids
Tensor electromagnetism and emergent elasticity in jammed solids
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DOI：
10.1103/physreve.106.065004
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发表时间：
2022-12-26
影响因子：
2.4
通讯作者：
Bhattacharjee, Subhro
中科院分区：
文献类型：
--
作者：
Nampoothiri, Jishnu N.;D'Eon, Michael;Bhattacharjee, Subhro
无序、堵塞固体中的机械响应和应力传递理论提出了几个悬而未决的问题，即非周期网络如何与流体维持剪切的快照明显区分。我们提出了一种仅应力理论，用于堵塞固体中非热非晶态晶粒的组装，其中每个晶粒都受到力和扭矩平衡的机械约束。这些晶粒级约束导致出现 U (1) 张量电磁学的高斯定律，从而解释了此类固体的机械响应。这种非晶弹性的表述有几个直接的后果。机械响应精确地映射到该张量电磁的静态介电响应，而介质的极化率映射到出现的弹性模量。外力充当矢量电荷，而张量磁场则由动量密度产生。电场和磁场的动力学自然地分别转化为刚性堵塞网络和弹道粒子运动的动力学。应力-应力相关性和响应的理论预测均由 2D 和 3D 理论静态极限下无摩擦颗粒填料的数值模拟结果所证实。
The theory of mechanical response and stress transmission in disordered, jammed solids poses several open questions of how nonperiodic networks-apparently indistinguishable from a snapshot of a fluid-sustain shear. We present a stress-only theory of emergent elasticity for a nonthermal amorphous assembly of grains in a jammed solid, where each grain is subjected to mechanical constraints of force and torque balance. These grain-level constraints lead to the Gauss's law of an emergent U (1) tensor electromagnetism, which then accounts for the mechanical response of such solids. This formulation of amorphous elasticity has several immediate consequences. The mechanical response maps exactly to the static, dielectric response of this tensorial electromagnetism with the polarizability of the medium mapping to emergent elastic moduli. External forces act as vector electric charges, whereas the tensorial magnetic fields are sourced by momentum density. The dynamics in the electric and magnetic sectors naturally translate into the dynamics of the rigid jammed network and ballistic particle motion, respectively. The theoretical predictions for both stress-stress correlations and responses are borne out by the results of numerical simulations of frictionless granular packings in the static limit of the theory in both 2D and 3D.