Towards modelling granular -- machine/vehicle/structure interaction
systems: a micromechanical continuum theory of granular media

Antoinette Tordesillas

Department of Mathematics and Statistics

The University of Melbourne

Victoria 3010

AUSTRALIA

Our past research program focused on the modelling of granular-solid
interaction systems from a Contact Mechanics perspective. Of primary
interest was the soil-tyre interaction system in which a classical
plasticity model was used to represent the soil. The study yielded a new
modelling approach that obviated the need for *a-priori* information on
the contact properties (*i.e.* contact area, and forces and
displacements of points therein). In the past, it was common practice to
adopt simplifying assumptions on these properties -- effectively
limiting the predictive capabilities of the interaction model. From the
constitutive viewpoint, we learnt an important lesson: classical
plasticity models of granular media could not provide reliable
predictions of the interaction process for two reasons: (a) such models
have no length scale to accommodate key microstructural mechanisms,
known to govern bulk behaviour of soils, (b) the associated boundary
value problems are ill-posed (*i.e.* non-unique solutions) and,
consequently, finite element simulations of the interaction process
suffered severe mesh sensitivity (*i.e.* mesh size and alignment
dependence).

In this talk, we describe advancements from our current research program
aimed at the development of a micromechanical continuum theory for
granular media. The methodology being developed weaves together
Thermomechanical and Micropolar principles and techniques. Guided by
experiments and discrete element (DEM) simulations, a new breed of
constitutive models was constructed with several distinct advantages
over past models. The models have 'high-resolution' predictive
capability for both local behaviour (*e.g.* critical microstructures
like shear bands) and global behaviour, due to the underlying
homogenisation scheme, devised on the scale of only a few particles
(*i.e.* a particle and its first ring of neighbours). The models can
account for the most influential mechanisms governing granular
deformation, including particle rotations, rolling resistance, and
evolution of force and contact anisotropies. In contrast with the
majority of phenomenological continuum models, these models are
expressed in terms of physical properties of the particles, and their
interactions (*e.g.* particle size, stiffness coefficients, rolling
resistance and sliding friction). Similarly, internal variables with
clear physical meaning (*e.g.* fluctuations in particle displacements
and rotations), and which are consistent with the laws of
thermodynamics, may be introduced. Moreover, the models share the same
material parameters as DEM, allowing a direct comparison to be made
between the two methodologies.

Despite these promising advances, many critical problems remain. Our
existing micromechanical models are mainly confined to small
deformations of two-dimensional assemblies of uniformly sized circular
particles. Studies on the effects of particle size distribution and
angularity are in its nascent stages. The effects of damping,
demonstrated by DEM studies to be a necessary source of dissipation,
have not yet been accounted for. Moreover, we need a better
understanding of what the internal variables, which account for the
irreversible changes in the internal structure of a deforming granular
material, are meant to represent. Ongoing efforts to address these
problems, as well as recent results from finite element (FEM)
implementations of our existing models to benchmark experiments, will be
presented. A comparison between the FEM and DEM predictions will be
made.