Areas of Interest

•      Micromechanics of Granular Media
•      Soil-tyre interaction
•      Discrete element method
•      Thermomechanics / Hyper-Plasticity
•      C-FEM
•      Lunar and Martian micromechanics

Micromechanics of Granular Media

Although examples of granular media exist all around us, to date there is no widely accepted constitutive model describing the behaviour of these materials. The MGM group is creating new models of granular behaviour using a "micromechanical approach". The micromechanical approach is a method for developing models of granular behaviour from a consideration of the interactions between the assembly's constituent particles. In its simplest form this approach involves two separate scales: a macro-scale on which continuum properties of the assembly are described; and a micro-scale on which particle-scale properties are described. By expressing the macroscopic constitutive response in terms of micro-scale behaviour, this "bottom up" approach develops material models based on measurable particle properties, obviating the need for parameters based on the material's bulk behaviour.

Related Articles:

• Walsh SDC, Tordesillas A. and Peters JF, "Development of micromechanical models for granular media", Granular Matter (2005 submitted).
• Gardiner, BS and Tordesillas, A. (2005) “Micromechanical constitutive modelling of granular media: evolution and loss of contact in particle clusters.” J Eng Mathematics 52, pp 93-106.
• Tordesillas, A, Walsh, SDC, Gardiner, BS (2004) "Bridging the length scales: micromechanics of granular media” BIT Numerik Mathematik, 44, pp 539-556.

Soil-Tyre Interaction

Soil-tyre interaction has huge economic significance for Australia: road corrugations cost the Australian taxpayer over a billion dollars every year and Australia spends $5.5 million per day on road maintenance! By studying the soil-tyre interaction system the group hopes to contribute to:

• better management of roads
• improvement of vehicle and tyre design
• reduction for the need for field testing of vehicles
• reduction in damage to the environment

Models of soil-tyre interaction are at the heart of computer simulations of vehicle-terrain interaction. Many industries, as well as the military, depend on these simulations for decision making: for example, the US-Army uses a Virtual Reality Program of Vehicle-Terrain Interaction as a tool in just about every level of decision making from vehicle design, manufacturing and procurement through to driver training. (see also http://mobility.wes.army.mil/ )

Related Articles:

• Tordesillas, A. and Shi, J. (2000), "The rolling contact of a rigid circular cylinder on a semi-infinite granular material", Special Issue in Honour of Prof AJM Spencer FRS of the Journal of Engineering Mathematics 37, 231-252.
• Tordesillas, A. and Shi, J. (1999), "Stresses, flow and deformation of soils in contact with metallic and/or rubber-like bodies" Proceedings, 13th International Conference of the ISTVS 1, 201-208.
• Tordesillas, A. (1994), "A contact mechanics approach to the soil-tyre interaction problem", Proceedings, First North American Workshop on Modeling the Mechanics of Off-Road Mobility. Paper GL-94-30 U.S. Army Corps of Engineers, Waterways Experiment Station, Vicksburg, Mississippi USA.

Discrete Element Methods

The Discrete Element Method or DEM is a popular numerical technique used for simulating granular behaviour. At the heart of most DEM simulations lies a finite difference formulation of the equations of motion governing the assembly's constituent particles. By modelling the motion of individual grains, discrete element models accurately replicate the behaviour of real assemblies at the particle scale.

DEM is an essential complement to experiments – it provides a virtual laboratory that allows the modeler to perform experiments that would be difficult or impossible to undertake in a physical laboratory. DEM models can be used to extract information on the evolution of material behavior at all stages of the loading history: this includes statistical distributions of contact forces as well as the evolution of internal particle-scale structures.

Related Articles:

• Muthuswamy, M, and Tordesillas, A, “Multiscale analysis of the effects of changing gravity on stress propagation in a material subject to an indenting rigid flat punch” Earth and Space 2006 Proceedings, 10th Aerospace Division of International Conference on Engineering, Construction and Operations in Challenging Environments.
• Bosko, J and Tordesillas, A “ Evolution of Contact Forces, Fabric, and Their Collective Behavior in Granular Media under Deformation: a DEM Study” Earth and Space 2006 Proceedings, 10th Aerospace Division of International Conference on Engineering, Construction and Operations in Challenging Environments.
• Peters, JP, Muthuswamy, M, Wibowo, J. and Tordesillas, A, (2005) “Characterization of force chains in granular material. Phys. Rev. E 72: 041307.

Thermomechanics / Hyper-plasticity

A major concern which arises when developing a new constitutive model (particularly one based on a non-standard continuum) is ensuring that the model complies with physical laws. The difficulty of this task is compounded when dealing with geotechnical materials, which often demonstrate behaviours that lie outside the scope of classical modelling techniques. Typically a model's compliance with physical laws is tested after its development, through a (hopefully) rigorous check of the constitutive relations. An alternative "thermomechanical" approach builds the constitutive relations from a basic consideration of the fundamental laws of thermodynamics. In this way, compliance with physical laws is ensured from the outset of the model's construction.

Related Articles:

• Walsh, SDC and Tordesillas, A (2004) “A thermomechanical approach to the development of micropolar constitutive models for granular media” Acta Mechanica, 167 (3-4), pp 145-169.

C-FEM

The complexity of micromechanical constitutive laws inevitably leads to a numerical method of implementation, particularly when dealing with engineering scale problems. C-FEM is a Fortran program capable of modelling micromechanical constitutive relations for granular media. C-FEM differs from most existing finite element methods in that it is designed to implement constitutive models based on Cosserat or micropolar continua. Micropolar continua contain an additional degree of freedom not seen in classical continua - the ability for individual material points to rotate independently. The C-FEM code has been designed to implement the constitutive models developed by the MGM group.

Related Articles:

• Walsh SDC and Tordesillas, A, (2005) “Finite element methods for micropolar models of granular materials” Applied Mathematical Modelling (in press)
• Walsh SDC and Tordesillas, A, (2005) “A thermomechanical formulation of finite element schemes for micropolar continua” The ANZIAM Journal 46 (E) pp. C336-C350.
  

Lunar and Martian Micromechanics

A vital element in the success of any Lunar or Martian mission rests on our understanding of the fundamental problem of how a granular material behaves under an indenting solid body (e.g. foundations, penetrometer devices). Not only is this important for applications involving interactions between space vehicles and granular geomaterial, but long-term missions requiring the use of the extraterrestrial regolith as either an in-situ resource, or as a structural foundation, require an understanding of the bulk deformation and failure properties of the granular geomaterial. In Lunar and Martian conditions, smaller gravitational forces result in a less densely packed regolith than on Earth. We have been quantitatively ascertaining the effects and implications of the change in gravitational field on the nature of the force network, and more precisely, on the so-called "force chains" that are the main pathways of force transmission.

Related Articles:

• Muthuswamy, M, and Tordesillas, A, “Multiscale analysis of the effects of changing gravity on stress propagation in a material subject to an indenting rigid flat punch” Earth and Space 2006 Proceedings, 10th Aerospace Division of International Conference on Engineering, Construction and Operations in Challenging Environments.