Granular packings display the remarkable phenomenon of dilatancy, wherein their volume increases upon shear deformation. Conventional wisdom and previous results suggest that dilatancy, also being the related phenomenon of shear-induced jamming, requires frictional interactions. Here, we show that the occurrence of isotropic jamming densities ϕ_j above the minimal density (or the J-point density) ϕ_J leads both to the emergence of shear-induced jamming and dilatancy in frictionless packings. Under constant pressure shear, the system evolves into a steady-state at sufficiently large strains, whose density only depends on the pressure and is insensitive to the initial jamming density ϕ_j. In the limit of vanishing pressure, the steady-state exhibits critical behavior at ϕ_J. While packings with different ϕ_j values display equivalent scaling properties under compression, they exhibit striking differences in rheological behaviour under shear. The yield stress under constant volume shear increases discontinuously with density when ϕ_j > ϕ_J, contrary to the continuous behaviour in generic packings that jam at ϕ_J. Our results thus lead to a more coherent, generalised picture of jamming in frictionless packings, which also have important implications on how dilatancy is understood in the context of frictional granular matter.

中文翻译：

---

无摩擦球填料的剪胀，剪力堵塞和广义堵塞相图

粒状填料表现出显着的膨胀现象，其中，其体积在剪切变形时增加。传统观点和先前的结果表明，剪胀也是剪切引起的卡塞现象的相关现象，需要摩擦相互作用。在这里，我们表明，高于最小密度（或J点密度）ϕ _J的各向同性堵塞密度ϕ _j的出现会导致无摩擦填料中出现剪切引起的堵塞和膨胀。在恒定压力下的剪切，该系统演变成稳态在足够大的应变，其密度仅取决于压力和不敏感的初始干扰密度φ _Ĵ。在消失压力的极限下，稳态在ϕ _J处表现出临界行为。尽管具有不同ϕ _j值的填料在压缩下显示出相同的结垢特性，但它们在剪切下的流变行为却表现出惊人的差异。当ϕ _j > ϕ _J时，恒定体积剪切力下的屈服应力随密度不连续增加，这与卡在ϕ _J的普通填料的连续行为相反。因此，我们的结果导致了在无摩擦填料中发生堵塞的更连贯，更全面的图景，这对于如何在摩擦颗粒物质中理解膨胀性也具有重要意义。