Granular materials – which include everything from coal to coco pops – are physical substances that don’t quite fit into any of the known phases of matter: solid, liquid, or gas.
Keep the grains under pressure, vacuum-packed coffee for example, and you have solid-like behaviour; open the pack and pour it into a container and suddenly the grains flow freely like a liquid.
The changing personalities of granular materials can have devastating implications, for example the disturbance of the earth following an earthquake can be enough to trigger solid ground to turn to mush with catastrophic consequences.
Dr. Antoinette Tordesillas, a senior lecturer at the Department of Mathematics and Statistics at the University of Melbourne says, “Even a fractional advance in our understanding of how granular media behave can have a profound impact on the economic and general well-being of nations worldwide.”
Yet, despite being second only to water on the scale of priorities of human activities, and believed to account for ten per cent of all energy consumed on Earth, the physics behind granular materials remain largely unknown.
Dr. Tordesillas says, “The reason for this is that these seemingly simple materials exhibit a rich and complex rheology.”
Scientists have generally turned to the continuum theory for predicting the behaviours of solids and liquids – it looks at an object as a whole rather than the sum of its parts.
However, the theory collapses when applied to granular materials because information about the properties of the material at the particle level is missing – it treats a bag of sand as a solid block and does not contain information about the individual grains and how easily they rub and roll against each other.
An alternative is to model every single grain, which is what the discrete element method (DEM) does, but this technique is computationally intensive and extremely costly, and a handful of sand is about as much as current supercomputers can handle.
A more recent model, the enriched continuum model, is a hybrid of the continuum and DEM.
It uses the basic form of the continuum model but enriches it with information at the microstructural level, so the equation that describes a bag of sand is penetrated with information about the individual grains and how they interact with each other.
Dr. Tordesillas says, “The result is a picture that has a much higher resolution than that offered by continuum theory.”
“At the correct level of resolution it is possible to see critical microstructures, called ‘shear-bands’, which give insight into the failure properties and personality shifts of such materials.”
“In a sense, we are endeavouring to understand what triggers the personality change in granular materials and the shear band is the key or signature microstructure that these materials manifest as they undergo a transition from solid to liquid.”
Nobody has successfully managed to understand the nature of shear bands to date.
Now, the Mechanics and Granular Media Group of the Department of Mathematics and Statistics at the University of Melbourne, led by Dr. Tordesillas, have pioneered the first enriched continuum model capable of seeing shear bands.
Dr. Tordesillas says, “We have found a way to capture and predict not only the split personality but also the key transition mechanism.”
“This entirely new level of predictive capability is unmatched by any other continuum model developed to date, and the beauty of it is that not only is it more computationally efficient than DEM, but all the underlying physics at the microscale level are there, fully exposed in the equations.”
“By implementing this new breed of material model in computer simulations of granular processes, we hope to gain more accurate predictions and therefore better control of granular behaviour in real world situations.”
The findings are published in the journals Powder Technology, Geotechnique, Acta Mechanica, Granular Matter, International Journal for Analytical and Numerical Methods in Geomechanics, BIT Numerik Mathematik, and the International Journal of Solids and Structures.