We investigate the mechanical response of packings of purely repulsive, frictionless disks to quasistatic deformations. The deformations include simple shear strain at constant packing fraction and at constant pressure, “polydispersity” strain (in which we change the particle size distribution) at constant packing fraction and at constant pressure, and isotropic compression. For each deformation, we show that there are two classes of changes in the interparticle contact networks: jump changes and point changes. Jump changes occur when a contact network becomes mechanically unstable, particles “rearrange”, and the potential energy (when the strain is applied at constant packing fraction) or enthalpy (when the strain is applied at constant pressure) and all derivatives are discontinuous. During point changes, a single contact is either added to or removed from the contact network. For repulsive linear spring interactions, second- and higher-order derivatives of the potential energy/enthalpy are discontinuous at a point change, while for Hertzian interactions, third- and higher-order derivatives of the potential energy/enthalpy are discontinuous. We illustrate the importance of point changes by studying the transition from a hexagonal crystal to a disordered crystal induced by applying polydispersity strain. During this transition, the system only undergoes point changes, with no jump changes. We emphasize that one must understand point changes, as well as jump changes, to predict the mechanical properties of jammed packings.

中文翻译：

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有序和无序磁盘包装的联系网络变化。

我们研究了纯排斥、无摩擦圆盘填料对准静态变形的机械响应。变形包括在恒定填充率和恒定压力下的简单剪切应变、在恒定填充率和恒定压力下的“多分散性”应变（我们改变粒度分布）以及各向同性压缩。对于每个变形，我们表明粒子间接触网络中有两类变化：跳跃变化和点变化。当接触网络变得机械不稳定时，会发生跳跃变化，粒子“重新排列”，势能（当以恒定填充率施加应变时）或焓（当以恒定压力施加应变时）和所有导数都是不连续的。在点更改期间，单个联系人被添加到联系人网络或从联系人网络中删除。对于排斥性线性弹簧相互作用，势能/焓的二阶和高阶导数在点变化时是不连续的，而对于赫兹相互作用，势能/焓的三阶和高阶导数是不连续的。我们通过研究通过应用多分散性应变诱导的从六方晶体到无序晶体的转变来说明点变化的重要性。在这个过渡过程中，系统只发生点变化，没有跳跃变化。我们强调，必须了解点变化以及跳跃变化，才能预测堵塞填料的机械性能。势能/焓的二阶和高阶导数在点变化时是不连续的，而对于赫兹相互作用，势能/焓的三阶和高阶导数是不连续的。我们通过研究通过应用多分散性应变诱导的从六方晶体到无序晶体的转变来说明点变化的重要性。在这个过渡过程中，系统只发生点变化，没有跳跃变化。我们强调，必须了解点变化以及跳跃变化，才能预测堵塞填料的机械性能。势能/焓的二阶和高阶导数在点变化时是不连续的，而对于赫兹相互作用，势能/焓的三阶和高阶导数是不连续的。我们通过研究通过应用多分散性应变诱导的从六方晶体到无序晶体的转变来说明点变化的重要性。在这个过渡过程中，系统只发生点变化，没有跳跃变化。我们强调，必须了解点变化以及跳跃变化，才能预测堵塞填料的机械性能。我们通过研究通过应用多分散性应变诱导的从六方晶体到无序晶体的转变来说明点变化的重要性。在这个过渡过程中，系统只发生点变化，没有跳跃变化。我们强调，必须了解点变化以及跳跃变化，才能预测堵塞填料的机械性能。我们通过研究通过应用多分散性应变诱导的从六方晶体到无序晶体的转变来说明点变化的重要性。在这个过渡过程中，系统只发生点变化，没有跳跃变化。我们强调，必须了解点变化以及跳跃变化，才能预测堵塞填料的机械性能。