Jammed solids with pins: Thresholds, Force networks and Elasticity

TL;DR

This study investigates how fixed particles ('pins') influence the jamming threshold, force networks, and elasticity in soft particle systems, revealing universal and geometry-dependent effects on packing density and force organization.

Contribution

It demonstrates that pins lower the jamming threshold and alter force networks and elasticity, with effects depending on pin density and geometry, extending understanding of jamming with fixed degrees of freedom.

Findings

Pins lower the jamming threshold universally at low densities.

Force networks become more heterogeneous with pins, showing both weak and strong forces.

Bond-orientational order and force distribution influence elastic moduli.

Abstract

The role of fixed degrees of freedom in soft/granular matter systems has broad applicability and theoretical interest. Here we address questions of the geometrical role that a scaffolding of fixed particles plays in tuning the threshold volume fraction and force network in the vicinity of jamming. Our 2d simulated system consists of soft particles and fixed "pins", both of which harmonically repel overlaps. On one hand, we find that many of the critical scalings associated with jamming in the absence of pins continue to hold in the presence of even dense pin latices. On the other hand, the presence of pins lowers the jamming threshold, in a universal way at low pin densities and a geometry-dependent manner at high pin densities, producing packings with lower densities and fewer contacts between particles. The onset of strong lattice dependence coincides with the development of bond-orientational order. Furthermore, the presence of pins dramatically modifies the network of forces, with both unusually weak and unusually strong forces becoming more abundant. The spatial organization of this force network depends on pin geometry and is described in detail. Using persistent homology we demonstrate that pins modify the topology of the network. Finally, we observe clear signatures of this developing bond-orientational order and broad force distribution in the elastic moduli which characterize the linear response of these packings to strain.