The mechanical response of packings of purely repulsive, spherical particles to athermal, quasistatic simple shear near jamming onset is highly nonlinear. Previous studies have shown that, at small pressure p, the ensemble-averaged static shear modulus ⟨G-G_{0}⟩ scales with p^{α}, where α≈1, but above a characteristic pressure p^{**}, ⟨G-G_{0}⟩∼p^{β}, where β≈0.5. However, we find that the shear modulus G^{i} for an individual packing typically decreases linearly with p along a geometrical family where the contact network does not change. We resolve this discrepancy by showing that, while the shear modulus does decrease linearly within geometrical families, ⟨G⟩ also depends on a contribution from discontinuous jumps in ⟨G⟩ that occur at the transitions between geometrical families. For p>p^{**}, geometrical-family and rearrangement contributions to ⟨G⟩ are of opposite signs and remain comparable for all system sizes. ⟨G⟩ can be described by a scaling function that smoothly transitions between two power-law exponents α and β. We also demonstrate the phenomenon of compression unjamming, where a jammed packing unjams via isotropic compression.

中文翻译：

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无摩擦球形颗粒堵塞填料的压力相关剪切响应。

纯排斥性球形颗粒填料在干扰开始附近对无热准静态简单剪切的机械响应是高度非线性的。先前的研究表明，在小压力 p 下，整体平均静态剪切模量⟨G-G_{0}⟩ 与 p^{α} 成比例，其中 α≈1，但高于特征压力 p^{**} , ⟨G-G_{0}⟩∼p^{β}，其中 β≈0.5。然而，我们发现单个填料的剪切模量 G^{i} 通常沿接触网络不变的几何族随 p 线性下降。我们通过证明，虽然剪切模量确实在几何族内线性下降，但我们解决了这种差异，⟨G⟩ 还取决于在几何族之间的过渡处发生的 ⟨G⟩ 中的不连续跳跃的贡献。对于 p>p^{**}，⟨G⟩ 的几何族和重排贡献具有相反的符号，并且对于所有系统大小都保持可比性。⟨G⟩ 可以通过在两个幂律指数 α 和 β 之间平滑转换的缩放函数来描述。我们还展示了压缩解卡现象，其中被卡住的包装通过各向同性压缩解卡。