Microscopic Reversibility and Emergent Elasticity in Ultrastable Granular Systems

TL;DR

This study investigates the mechanical response and elasticity of ultrastable shear-jammed granular states, revealing a power-law relation between shear modulus and pressure, and validating the Vector Charge Theory of Granular mechanics with experimental data.

Contribution

It provides the first detailed analysis of local and global responses in ultrastable granular states, linking experimental observations to theoretical models of emergent elasticity.

Findings

Ultrastable states follow a power-law shear modulus-pressure relation with exponent ~0.5.

Two types of contacts are identified: non-persistent and persistent, with non-persistent contacts contributing to shear modulus.

Experimental results align well with the Vector Charge Theory of Granular mechanics, indicating more isotropic responses after shear.

Abstract

In a recent paper [Phys. Rev. X 12, 031021], we reported experimental observations of ``ultrastable'' states in a shear-jammed granular system subjected to small-amplitude cyclic shear. In such states, all the particle positions and contact forces are reproduced after each shear cycle so that a strobed image of the stresses and particle positions appears static. In the present work, we report further analyses of data from those experiments to characterize both global and local responses of ultrastable states within a shear cycle, not just the strobed dynamics. We find that ultrastable states follow a power-law relation between shear modulus and pressure with an exponent $\beta\approx 0.5$, reminiscent of critical scaling laws near jamming. We also examine the evolution of contact forces measured using photoelasticimetry. We find that there are two types of contacts: non-persistent contacts that reversibly open and close; and persistent contacts that never open \yiqiu{and display no measurable sliding}. We show that the non-persistent contacts make a non-negligible contribution to the emergent shear modulus. We also analyze the spatial correlations of the stress tensor and compare them to the predictions of a recent theory of the emergent elasticity of granular solids, the Vector Charge Theory of Granular mechanics and dynamics (VCTG) [Phys. Rev. Lett. 125, 118002, arXiv:2204.11811]. We show that our experimental results can be fit well by VCTG, assuming uniaxial symmetry of the contact networks. The fits reveal that the response of the ultrastable states to additional applied stress is substantially more isotropic than that of the original shear-jammed states. Our results provide important insight into the mechanical properties of frictional granular solids created by shear.