| Popis: |
We investigate the mechanical response of jammed packings of circulo-lines in two spatial dimensions, interacting via purely repulsive, linear spring forces, as a function of pressure $P$ during athermal, quasistatic isotropic compression. The surface of a circulo-line is defined as the collection of points that is equidistant to a line; circulo-lines are composed of a rectangular central shaft with two semicircular end caps. Prior work has shown that the ensemble-averaged shear modulus for jammed disk packings scales as a power law, $\ensuremath{\langle}G(P)\ensuremath{\rangle}\ensuremath{\sim}{P}^{\ensuremath{\beta}}$, with $\ensuremath{\beta}\ensuremath{\sim}0.5$, over a wide range of pressure. For packings of circulo-lines, we also find robust power-law scaling of $\ensuremath{\langle}G(P)\ensuremath{\rangle}$ over the same range of pressure for aspect ratios $\mathcal{R}\ensuremath{\gtrsim}1.2$. However, the power-law scaling exponent $\ensuremath{\beta}\ensuremath{\sim}0.8$--0.9 is much larger than that for jammed disk packings. To understand the origin of this behavior, we decompose $\ensuremath{\langle}G\ensuremath{\rangle}$ into separate contributions from geometrical families, ${G}_{f}$, and from changes in the interparticle contact network, ${G}_{r}$, such that $\ensuremath{\langle}G\ensuremath{\rangle}=\ensuremath{\langle}{G}_{f}\ensuremath{\rangle}+\ensuremath{\langle}{G}_{r}\ensuremath{\rangle}$. We show that the shear modulus for low-pressure geometrical families for jammed packings of circulo-lines can both increase and decrease with pressure, whereas the shear modulus for low-pressure geometrical families for jammed disk packings only decreases with pressure. For this reason, the geometrical family contribution $\ensuremath{\langle}{G}_{f}\ensuremath{\rangle}$ is much larger for jammed packings of circulo-lines than for jammed disk packings at finite pressure, causing the increase in the power-law scaling exponent for $\ensuremath{\langle}G(P)\ensuremath{\rangle}$. |
