Hypostatic Jammed Packings of Frictionless Nonspherical Particles

We perform numerical simulations to study jammed packings containing a variety of nonspherical particle shapes (e.g. dimers, circulo-lines, circulo-polygons, ellipses, and dumbbells) in two spatial dimensions. By analyzing these packings, we propose criteria that particle shapes must satisfy to give rise to hypostatic jammed packings, with fewer contacts than degrees of freedom using naive constraint counting arguments. We show the packing fraction $\phi$ and coordination number $z$ for jammed packings of the particle shapes under study. In particular, we find that $\phi$ and $z$ obey a master curve for different particle shapes when they are plotted as a function of the asphericity ${\cal A} = p^2/4\pi a$, where $p$ and $a$ are the perimeter and area of the particles. We also calculate the principal curvatures of the particle contact constraint surfaces in high-dimensional configuration space to identify specific contacts in packings of spherocylinders that allow them to be jammed, yet hypostatic.