From discrete particles to continuum theory and applications
Particle systems are different from 'classical' atomistic systems; they are neither fluid nor solid, but often both at the same time. There is no generally accepted continuum theory that can be used for industrial or geophysical applications on the large scale, only few promising first attempts have been recently proposed. Empirical first attempts will be followed by more sound mathematical formulations, physical and mechanical insights, as well as calibration and validation procedures for continuum or multi-scale models.
One reason for this challenge is that energy is lost irreversibly due to contacts, and the state of the system depends an the amount and kind of energy inserted. This fact already leads to non-trivial flow mechanisms and is the origin of the unusual dynamics of granular matter. Homogenization to a continuum scale also invokes complications due to the finite size of grains. Adding attractive forces like van der Waals interactions or liquid bridges widens the scope of applications and enriches the phenomenology even further. Dependent on the conditions, particles can flow like a fluid, jam and un-jam, or behave as a solid with anisotropy due to contact- and force-networks. The interplay between strain, stress, structural re-arrangements, and anisotropy leads to dilatancy and ‘memory’ effects within the packing. All these items, ideally, have to be addressed by a multi-purpose continuum theory.
See also MS-3.10 - The Physics of Dense Granular Media