Jammed packings of deformable and rigid 2D spherocylinders and spheropolygons

We study mechanically stable packings of deformable and rigid 2D spheropolygons using computer simulation. A 2D sphereopolygon is a particle shape formed by the collection of all points within a perpendicular distance $r$ from the edge of a polygon. It is a generalization of the 2D spherocylinder and a circle, which are the collection of all points within a distance $r$ from a line and a point. In our model, the spheropolygon can be deformable. The lengths of the sides are fixed, but the angles are only constrained by the requirement that the shape factor, $S=$4$\pi A$/$p^{\mathrm{2}}$ is fixed, where $A$ is the area of the polygon and $p$ is the perimeter. The particles can be made rigid by requiring that the shape factor is the maximum possible for the edge length ratios. For example, the maximum for a square is $S=\pi $/4. We present densities and average contact numbers for collections of mono- and bi-disperse packings of spheropolygons for a range of shape factors, edge numbers, and system sizes. We find mechically stable packings with fewer than isostatic contacts.