Continuum thermomechanics of the nonlocal granular rheology

• We derive a nonlocal continuum theory for granular plasticity.
• The final form correctly describes a vast amount experimental granular flow data.
• The approach utilizes a scalar order parameter, called the granular fluidity.
• The theory is formulated using the principle of virtual power.

We formulate a nonlocal, or scale-dependent, elasto-viscoplastic continuum model for granular materials, consistent with the principles of modern continuum thermomechanics. Importantly, the theory contains a scalar, energetic order parameter, referred to as the granular fluidity. We assume power to be expended over the rate of change of the fluidity and its gradient and undertake a derivation based upon the principle of virtual power in the style of Gurtin (1996). This approach results in a non-standard microforce balance, which when combined with our choice of specific constitutive equations, takes the form of a partial differential relation that the fluidity must obey. Finally, we simplify the equations into a form appropriate for steady granular flows. The resulting boundary-value problem was previously shown to be capable of describing a wide array of experimental granular flow data.