Organized chaos in granular media

The aim of this project is to derive micromechanically based and thermomechanically consistent constitutive models for the behavior of granular media, by taking into account the deterministic chaos that governs the structure and behavior of particulate media at the grain level. This project will address the problem using statistics to describe the chaotic behavior at the microscale, thus resolving the problem of surplus information at the micro-level. To transfer this information to a continuum formulation, averaging based on probability distributions will be used, with emphasis on energy related quantities, namely elastic energy, dissipation and internal energy. Using such measures, thermomechanically consistent elastoplastic formulations can be derived. For the evolution of the internal variables, numerical simulations, both in discrete and continuum domain, are planned.The road map of this 4 year project is:
(1) establish the pdfs of static and kinematic quantities, as well as their evolution using DEM.
(2) Derive the internal energy, the elastic energy and the dissipation
(3) Establish and implement the resulting constitutive law
(4) Validate against attractors.
The approach is general and will result in a methodology, rather than in an isolated model. This methodology can then be applied to other problems, among which grain crushing, segregation in granular flows and the behavior of fractured rock mass are the most obvious.