Minimal contact number for structural rigidity in PAMs

Determine the minimal contact number per particle Z0 required for structural rigidity in three-dimensional polycatenated architected materials (PAMs), quantifying how Z0 depends on inter-particle friction, particle geometry, and catenation topology, to characterize the jamming threshold in these catenated granular systems.

Background

To relate macroscale strain-stiffening to particle-scale densification, the authors plot apparent compressive modulus E* as a function of mean contact number (Z) offset by a minimal contact number per particle (Z0), which marks structural rigidity. While setting Z0=5 collapsed data across protocols and strains, the precise value and its dependence on system parameters were not established.

Establishing Z0 is essential to formalize the jamming threshold in PAMs and to connect their strain-stiffening behavior to contact network statistics across particle shapes, frictional properties, and catenation topologies.

References

Zo depends on many factors such as particle friction, geometry, and catenation topology and is unknown for these catenated granular systems.

— Polycatenated Architected Materials  (2406.00316 - Zhou et al., 2024) in Main Text, Mechanical characterization of PAMs (paragraph discussing E* vs (Z)−Z0, near Fig. 2L)

The present coordination analysis supports, but does not independently prove, brush-mediated angular resistance or a unique reduced rigidity threshold.

— Rheology and Dynamic Arrest in Colloidal Depletion Gels Mediated by Surface Brush Density  (2608.17764 - Zhuang et al., 18 Aug 2026) in Conclusion