MGM stands for Micromechanics of Granular Media.

Complexity in everyday materials

    In recent years there has been a concentrated effort to understand the complex behaviour of various everyday materials known as soft matter and granular materials. Examples of soft matter include foams, emulsions, colloids, liquid crystals, slurries, gels, polymers and biological macromolecules such as DNA and proteins. Examples of granular materials include sand, powders, cereals, woodchip, fertilizers and grains. Some of the many reasons for the strong growth in research in this area are due to the broad range of applications of these materials, especially for the food, biomedical, environmental and mining industries and the potential for exploiting the new physics displayed by these materials. A unifying feature of these materials is structural evolution on a number of different length and time scales. Furthermore, they are not easily characterised as a solid or a liquid, often having quite complex rheological properties governed by intermediate scale structure (between macro or continuum scale and the atomic scale). This intermediate scale is referred to as the microscale or more recently mesoscale (e.g. bubbles and films form froth's microscale). Long-range pattern formation (order from disorder), the build-up and relaxation of stress via structural reorganization and non-local effects typify this class of material.

Granular materials

    Granular materials share much of the complex behaviour common to soft matter, for example, segregation and pattern formation, flow by rearrangement of structure (grains), and solid and liquid-like behaviour. It should be no surprise that granular media are often mentioned in the same context as soft matter. What is surprising is that, although soft matter and granular media constitute many everyday materials (cornflakes, rice, milkshakes, ice-cream, hair gel etc.) and the interaction of the microstructure is usually well known from basic physics, we have only just begun to understand these materials. For example, the physics of two interacting grains in a granular assembly is well understood, however the complexity arising from the interaction of an ensemble of grains is not well understood. Hence, the common goal of those studying granular materials and soft matter is to relate macrostructural behaviour to the underlying microstructural dynamics and kinematics.

Methodologies for modelling granular media

    The great majority of existing models of granular media were developed using classical continuum theory. Classical continuum models, although readily accessible and in widespread use, possess no length scale and so cannot accommodate microstructure. Unfortunately, there is now overwhelming experimental evidence which shows that microstructural mechanisms govern bulk behaviour of granular media. An alternate approach, called the discrete element method (DEM), deals explicitly with the microstructure. DEM uses the techniques of molecular dynamics simulation to govern the motion of every particle in a large assembly. However, the number of particles that can be simulated in DEM is limited by computer power, such that many engineering scale processes are beyond the reach of DEM. Recently, an effort has been made in formulating a third class of models, known as micromechanical models, with the combined strengths of continuum models and DEM. It is this hybrid that we are interested in developing. The basic idea in micromechanics is to relate the microstructural/discrete parameters (e.g. forces, moments, displacements and rotations at interparticle contacts), to macrostructural/continuum parameters (e.g. stresses and strains) using a homogenisation or averaging procedure.
    Micromechanical models are based on two theories: micropolar or Cosserat theory and higher gradient theories. In micro-polar theory, a continuum body consists of material points each possessing the full degrees of freedom of a rigid body: three translatory and three rotational degrees of freedom. Higher gradient theories, on the other hand, are designed to model the effects of heterogeneous strain fields. We are developing a higher gradient micropolar theory in conjunction with a new homogenisation procedure. This yields a methodology for developing a constitutive law that can capture non-local effects on the scale of a particle and its local void space, thereby possessing the correct level of resolution for capturing key microstructural mechanisms of only a few particles in length scale (e.g. shear bands and force chains).