Cohesion-induced hysteresis and breakdown of marginal stability in jammed granular materials

Abstract

The dependence of mechanical properties on microscopic interactions remains a central problem in the physics of disordered solids near the jamming transition. We numerically and theoretically investigate the mechanical response of jammed cohesive granular materials using discrete element simulations and effective medium theory (EMT). We find that the shear modulus exhibits pronounced hysteresis under compression and decompression, even though the interparticle force law itself is strictly history-independent. While such hysteresis disappears for purely repulsive particles when mechanical properties are characterized in terms of pressure, it persists in cohesive packings, indicating that pressure is not a unique state variable for cohesive particles. Extending EMT to cohesive interactions, we show that the functional form of the shear modulus remains the same for both repulsive and cohesive particles, but that attractive interactions violate marginal stability. The resulting deviation from marginal stability generates excess rigidity, as predicted by a scaling relation. This prediction is quantitatively verified by numerical simulations and explains the persistent hysteresis in cohesive packings.

Figures (12)

• Figure 1: (a) Pressure $p$ as a function of the packing fraction $\phi$ for cohesive particles (main panel) and repulsive particles (inset). (b) Shear modulus $G$ as a function of $\phi$ for cohesive particles (main panel) and repulsive particles (inset). (c) Shear modulus $G$ as a function of $p^{1/2}$ for cohesive and repulsive particles. Compression and decompression data are shown by open and closed symbols, respectively. The packing fraction $\phi_{p=0}$ where the pressure vanishes is indicated by black pentagons. The solid line in (c) indicates the expected scaling $G \propto p^{1/2}$ for repulsive particles.
• Figure 2: Schematic of the static interparticle force $f(r)$ as a function of the interparticle distance $r$. The repulsive (i), stabilizing attractive (ii), and locally destabilizing (iii) regimes are indicated by different shaded regions.
• Figure 3: Marginal stability and its breakdown in repulsive ($\alpha=0$) and cohesive ($\alpha>0$) packings, compared with EMT predictions. Open and closed symbols correspond to decompression and compression, respectively. (a) Pressure $p$ as a function of $Z-Z_{\rm iso}$. The solid line indicates the marginal-stability condition $p=p_{\rm c}(Z)$. The shaded region indicates EMT-stable states satisfying $p\le p_{\rm c}(Z)$. (Inset) vDOS $D(\omega)$ for cohesive particles at $\phi=0.60$ during compression. The symbols and solid line represent the spectra obtained from the original and unstressed Hessians, respectively. (b) Shear modulus $G$ as a function of $Z-Z_{\rm iso}$. The solid line represents the bare shear modulus $G=G_0(Z)$ introduced in EMT. (c) Scaling plot of the excess rigidity $(G-G_0)/G_0$ as a function of the deviation from marginal stability $(p_{\rm c}-p)/p_{\rm c}$ for cohesive packings, testing the EMT prediction. The solid line represents the EMT prediction, Eq. \ref{['eq:general_scaling']}. The color of the symbols represents the packing fraction $\phi$.
• Figure S1: Enlarged view of the low-pressure regime of Fig. \ref{['P_G']}(a), showing the pressure $p$ as a function of the packing fraction $\phi$. Compression and decompression data are shown by open and closed symbols, respectively. The packing fraction $\phi_{p=0}$ where the pressure vanishes is indicated by black pentagons.
• Figure S2: Shear modulus $G$ as a function of the pressure $p$ for cohesive particles. The region with negative pressure ($p<0$) is highlighted by the blue shaded area.