Tunable critical jamming fraction and designed mechanical properties in disordered packings

Jamming is a well-known phenomenon in particulate matter, with the exact phase transition point strongly dependent on the preparation protocol. Constructing jamming configurations at prescribed critical packing fractions provides important insight for both fundamental research and practical applications. In this talk, we will demonstrate how to efficiently generate disordered structures of polydisperse disks with a continuous range of critical packing fractions. In overjammed soft packings, the geometric principle of sterically optimal packings governs the energy levels of metastable states. Based on this geometric principle, we develop a novel annealing algorithm that involves a temporary transformation of particle packings to a network structure with additional transient degrees of freedom. This approach generates metastable states at target energy levels with minimal computational costs. Upon decompression of such overjammed packings down to jamming, we observe a strong correlation between metastable state energy and critical packing fractions, with low energy states undergoing jamming transition at exceptionally high packing densities. These high critical packing fraction jamming configurations exhibit remarkable resilience to external deformations, highlighting their special mechanical properties. Our findings emphasize the close relationship between metastable state energy, jamming transitions, and emergent mechanical behavior, offering a potential strategy for rational design of particulate materials with desired properties.