Jammed solids with pins: Thresholds, force networks, and elasticity

Area of Science:

• Soft and granular matter physics
• Statistical mechanics
• Materials science

Background:

• Fixed degrees of freedom play a crucial role in the behavior of soft and granular matter.
• Understanding jamming, the transition to a rigid state, is key to characterizing these systems.
• The geometric influence of fixed elements on jamming properties is not fully understood.

Purpose of the Study:

• To investigate the geometrical role of fixed particles (pins) in tuning jamming thresholds and force networks.
• To analyze how pins affect critical scalings and material properties near jamming.
• To explore the impact of pin geometry on the resulting particle packings and their mechanical response.

Main Methods:

• Two-dimensional simulations of soft particles interacting with fixed harmonic repulsions.
• Systematic variation of pin density and lattice geometry.
• Analysis of jamming threshold, particle contact networks, force distributions, and topological properties using persistent homology.
• Characterization of elastic moduli to probe linear response to strain.

Main Results:

• Critical scalings associated with jamming persist in the presence of pins.
• Pins universally lower the jamming threshold at low densities and geometrically-dependently at high densities.
• Pins lead to lower particle densities, fewer contacts, and the development of bond-orientational order.
• Force networks are dramatically modified, with increased abundance of weak and strong forces, dependent on pin geometry.
• Persistent homology reveals topological modifications induced by pins.
• Bond-orientational order and broad force distributions are reflected in the elastic moduli.

Conclusions:

• Fixed particles significantly alter jamming behavior and mechanical properties of soft matter.
• Pin geometry dictates the extent of jamming threshold reduction and force network organization.
• The interplay between fixed elements, particle interactions, and emergent order governs the macroscopic response of jammed systems.