Connecting shear localization with the long-range correlated polarized stress fields in granular materials

Abstract

One long-lasting puzzle in amorphous solids is shear localization, where local plastic deformation involves cooperative particle rearrangements in small regions of a few inter-particle distances, self-organizing into shear bands and eventually leading to the material failure. Understanding the connection between the structure and dynamics of amorphous solids is essential in physics, material sciences, geotechnical and civil engineering, and geophysics. Here we show a deep connection between shear localization and the intrinsic structures of internal stresses in an isotropically jammed granular material subject to shear. Specifically, we find strong (anti)correlations between the micro shear bands and two polarized stress fields along two directions of maximal shear. By exploring the tensorial characteristics and the rotational symmetry of force network, we reveal that such profound connection is a result of symmetry breaking by shear. Finally, we provide the solid experimental evidence of longrange correlated inherent shear stress in an isotropically jammed granular system.

Critical behaviors of jamming in cyclically sheared frictional hard granular particles

“…where u is the displacement at a given position and time, ζ is a drag coefficient, the first term on the right-hand side (r.h.s) represents a noise term with a mean strength υ 0 and random orientation n [43], and the second term on r.h.s represents force from a continuous elastic field. In the case of granular material, we can think the first term on r.h.s as a simplified model of the particle-particle interaction due to random fluctuations of unbalanced contact forces by neglecting its spatial structure and we can think this second term on r.h.s as a mean-field-type effective elastic field, which is consistent with the stress theories of amorphous materials [45][46][47]49] and the recent experimental verification [48]. 2.2.…”

“…where u is the displacement, ζ is a drag coefficient, the first term on the right-hand side (r.h.s) represents a noise term with a mean strength υ 0 and random orientation n [43], and the second term on r.h.s represents force from a continuous elastic field. For granular materials, we can think the first term on r.h.s as a simplified model of the random fluctuations of contact forces due to cyclic shear and this second term on r.h.s as a mean-field-type effec- tive elastic medium [45][46][47][48][49]. This model predicts that the spectrum E T (k) or E L (k) shall ∝ k −2 when the transverse or longitudinal correlation length, i.e.…”

Vibrational density of states of amorphous solids with long-ranged power-law correlated disorder in elasticity

“…Independent evidence supporting the existence of power-law spatially decaying correlations in elasticity have been shown in recent works [69,70]. All these facts point towards the importance of properly accounting for long-ranged power-law elastic correlations in the description of the vibrational properties of disordered systems.…”

Sound attenuation derived from quenched disorder in solids

“…The first successful theoretical prediction of this generalized Rayleigh scattering law for glasses has been achieved in Ref. [26], by implementing anistropic long-ranged power-law correlations of elasticity, which is supported by recent experimental and theoretical works [27,28].…”