Kuniyasu Saitoh (Tohoku University)
Microscopic theory for discontinuous shear thickening of frictional granular disks
Granular materials are ubiquitous in nature and the understanding of their flow properties
is crucial to industry and science.
Different from usual fluids, the constituents of granular materials are macroscale discrete particles
such that thermal fluctuations are negligibly small
for their individual motions and inelastic interactions between them cause the dissipation of kinetic energy.
As a result, the rheology of granular materials strongly depends not only on the shear rate applied to the system,
but also on the volume or area fraction of the constituent particles.
For example, if the fraction is sufficiently small, granular materials behave like gases,
where Bagnold's scaling of shear stress predicted by kinetic theory well describes the flow behavior.
On the other hand, if the fraction exceeds a critical value, i.e. the so-called jamming point,
kinetic theory breaks down as we observe a finite yield stress in a quasi-static limit of shear deformations,
where the shear stress becomes almost rate-independent (the "critical state" in the literature on soil mechanics).
In such jammed states of granular materials, force-chain networks are fully developed
in the system such that the contact contribution to the stress governs the mechanical responses,
where many constitutive models have been proposed (e.g. the so-called mu-I rheology, the non-local model for slow flows,
the order-parameter descriptions of phase-coexistent flows, etc.).
However, the microscopic insight into dense granular flows is not fully understood and the physics
of granular materials completely lack the connection
between the microscale mechanics and the macroscale flow behavior of jammed states.
In addition, it is recently found that frictional forces between the particles in contacts drastically change the dense granular rheology,
where the shear stress jumps from Bagnold?s scaling to the rate-independent jammed states and the system exhibits the strong history dependence,
i.e the discontinuous shear thickening (DST). So far, none of theoretical models have succeeded in predicting the DST of frictional granular materials.
In this study, we propose a microscopic theory for the DST of frictional granular materials, where the Liouville theory of frictionless granular particles (K. Suzuki and H. Hayakawa, Phys. Rev. Lett. 115 (2015) 098001) is extended to dense flows of frictional granular particles. Employing the Sllod equation of motions and adopting a frictional contact model with the Coulomb friction, we generalize the Liouville operator to the case of frictional grains. We explain the microscopic origin of the DST and predict the hysteresis-loop of the flow curve of frictional granular materials by our microscopic theory.