Joe Goddard, jgoddard@ucsd.edu
Continuum modeling of granular media
This talk summarizes a recent survey [1] of the interesting phenomenology and the prominent régimes of
granular flow which also offers a unified mathematical synthesis of continuum modeling. The unification is
based on “parametric” viscoelasticity and hypoplasticity involving elastic and inelastic potentials. Fully nonlinear, anisotropic visco-elastoplastic models are achieved by expressing the potentials as functions of the joint
isotropic invariants of kinematic and structural tensors. These take on the role of evolutionary parameters or
internal variables, whose evolution equations are derived from the internal balance of generalized forces. The
resulting continuum models encompass most of the mechanical constitutive equations currently employed for
granular media. Moreover, these models are readily modified to include Cosserat and other multipolar effects.
Several outstanding questions are identified as to the contribution of parameter evolution to dissipation, the
distinction between quasi-elastic and inelastic models of material instability, and the role of multipolar effects
in material instability, dense rapid flow and particle migration phenomena.
References
[1] J. Goddard, Appl. Mech. Rev. 64:5, 2014.