Experimental and numerical verification of anomalous screening theory in granular matter

Abstract

The concept of mechanical screening is widely applied in solid-state systems. Examples include nucleation of defects in crystalline materials, scars and pleats in curved crystals, wrinkles in strongly confined thin sheets, and cell-rearrangements in biological tissue. Available theories of such screening usually contain a crucial ingredient, which is the existence of an ordered reference state, with respect to which screening elements nucleate to release stresses. In contradistinction, amorphous materials in which a unique reference state does not exist, nevertheless exhibits plastic events that act as screening geometric charges with significant implications on the mechanical response. In a recent paper [Phys. Rev. E 104, 024904] it was proposed that mechanical strains in amorphous solids can be either weakly or strongly screened by the formation of low or high density of plastic events. At low densities the screening effect is reminiscent of the role of dipoles in dielectrics, in only renormalizing the elastic moduli. The effect of high density screening has no immediate electrostatic analog and is expected to change qualitatively the mechanical response, as seen for example in the displacement field. On the basis of experiments and simulations, we show that in granular matter, strong screening results in significant deviation from elasticity theory. The theoretical analysis, which accounts for an emergent inherent length scale, the experimental measurements and the numerical simulations of frictional granular amorphous assemblies are in agreement with each other, and provide a strong support for the novel continuum theory.