Multiscale Mechanics of Granular Materials
September 3, 2012 — September 7, 2012
- Kenichi Soga (University of Cambridge, UK)
- Farhang Franck Radjai (Université Montpellier 2, France)
This course provides a general introduction to the mechanics of granular materials with focus on the micromechanics and multi-scale approach. The lectures cover a broad range of topics from macro-scale experimental behavior, commonly taught in civil engineering schools, to the grain-scale description and micro-statistical behaviour, which is becoming essential both for a better understanding of the experimental behavior and for the development of predictive models based on physical internal variables. Recent advances in this field have been mostly inspired by an intensive cross-disciplinary research that integrates various concepts and methods from soil mechanics, materials science, powder technology, soft matter physics and statistical physics in a universal framework. This became possible by new experimental tools, such as 3D imaging techniques and testing devices, as well as discrete element methods (DEM) to simulate large collections of grains.
A multi-scale approach in the field of granular materials should be based on the following three different groups of mathematical concepts; 1) continuum mechanics for the formulation of the macroscopic behavior, 2) statistical physics for the description of disordered granular microstructure, discrete (grain) displacement fields and contact forces, and 3) rigid-body dynamics for a grain-scale description of the statics and dynamics of a collection of grains. A first series of lectures will thus be devoted to each framework in order to present the relevant concepts and mathematical and numerical tools. The second series of lectures will cover both the phenomenological description of the macroscopic behavior as well as the micro-statistical properties of granular materials. These lectures include the quasi-static rheology (stress-strain behaviour), inertial flows, localized and diffuse instabilities and creep behaviour for the former and the statistical descriptors of granular microstructure and force transmission for the latter. The third series of lectures will discuss various micromechanical models and upscaling approaches such as dimensional analysis, averaging techniques, macro-elasticity of a packing of gains and macro-plasticity with physical internal variables. The last series of lectures will cover the influence of grain properties and the micromechanics of clays and cohesive materials with solid and liquid bonding.
The multi-scale modeling of granular media is presently an active area of research. Starting with the most classical aspects of granular mechanics, this course leads very naturally to current modeling challenges and open issues such as the choice of relevant internal variables for granular plasticity, the appropriate coarse-graining volumes and the behaviour of complex granular media in the presence of solid or liquid bonding between grains. This course is of broad interest to researchers and engineers involved in soil mechanics, powder technologies and all kind of granular processing. It addresses doctoral students and young researchers with various backgrounds and applicative areas, with the aim of providing an integrated view of the micromechanics of granular materials.
KEYWORDS: Multiscale Mechanics, Granular Materials, Soil Behaviour, Discret Element Method.