Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, China.
Department of Physics, Yale University, New Haven, Connecticut 06520, USA.
Soft Matter. 2019 Dec 4;15(47):9751-9761. doi: 10.1039/c9sm01932d.
We carry out numerical studies of static packings of frictionless superellipsoidal particles in three spatial dimensions. We consider more than 200 different particle shapes by varying the three shape parameters that define superellipsoids. We characterize the structural and mechanical properties of both disordered and ordered packings using two packing-generation protocols. We perform athermal quasi-static compression simulations starting from either random, dilute configurations (Protocol 1) or thermalized, dense configurations (Protocol 2), which allows us to tune the orientational order of the packings. In general, we find that superellipsoid packings are hypostatic, with coordination number zJ < ziso, where ziso = 2df and df = 5 or 6 depending on whether the particles are axi-symmetric or not. Over the full range of orientational order, we find that the number of quartic modes of the dynamical matrix for the packings always matches the number of missing contacts relative to the isostatic value. This result suggests that there are no mechanically redundant contacts for ordered, yet hypostatic packings of superellipsoidal particles. Additionally, we find that the packing fraction at jamming onset for disordered packings of superellipsoidal depends on at least two particle shape parameters, e.g. the asphericity A and reduced aspect ratio β of the particles.
我们进行了无摩擦超椭圆粒子在三维空间中静态堆积的数值研究。通过改变定义超椭圆的三个形状参数，我们考虑了 200 多种不同的粒子形状。我们使用两种堆积生成协议来描述无序和有序堆积的结构和力学性质。我们从随机、稀疏的构型（协议 1）或热化、密集的构型（协议 2）开始进行非平衡准静态压缩模拟，这允许我们调整堆积的取向有序度。一般来说，我们发现超椭圆堆积是亚稳态的，配位数 zJ < ziso，其中 ziso = 2df，df = 5 或 6，具体取决于粒子是否轴对称。在整个取向有序范围内，我们发现堆积的动力矩阵的四次模式数总是与相对于等静压值缺失的接触数相匹配。这个结果表明，对于有序但仍然是亚稳态的超椭圆粒子堆积，没有机械上冗余的接触。此外，我们发现无序超椭圆粒子堆积的阻塞起始时的堆积分数至少取决于两个粒子形状参数，例如粒子的非球形度 A 和相对纵横比 β。
