Emergent Elasticity in Jammed Solids: Constraints and a Gauge Theory of Non-Brownian Rheology

There is emerging consensus that shear-thickening in dense suspensions is controlled by the kinetic constraints imposed on the motion of grains: transitions from lubricated to frictional or adhesive contacts change these constraints. A continuum theory of rheology must  account correctly for such kinetic constraints while incorporating microscale information about the structural and contact disorder. Recently, we have succeeded in constructing such a theoretical framework for the elasticity of jammed solids [Phys. Rev. Lett. 125, 118002 (2020)]. Central to this theory is a gauge theoretic structure that arises from the lack of a unique zero-stress reference state, and, the local constraints of mechanical equilibrium on each grain. The latter serves as a “Gauss’s law’’ for a tensorial electric field, which maps on to the stress tensor, and the elastic moduli emerge from the microscopic properties of the networks. The complete gauge-theoretic structure allows for flowing states through the presence of the analog of a magnetic sector to the electric one, which describes static jammed states. In this talk, we will discuss shear-thickening rheology from the perspective of this gauge theory. This work has been supported by NSF-CBET 1916877 and NSF-DMR 2026834.