Generalised Continua and Dislocation Theory. Theoretical Concepts, Computational Methods and Experimental Verification
July 9, 2007 — July 13, 2007
Coordinator:
- Carlo Sansour (University of Nottingham, Nottingham, Great Britain)
The course aims to provide a comprehensive treatment of generalised continua and dislocation theory at multiple scales, that fully covers the theoretical frameworks and the computational methods and provides an insight into the experimental background. The Cosserat continuum with independent rotations, the micromorphic continuum with independent distortional degrees of freedom, and higher gradient theories are to be discussed at the continuum level as well as that of the crystal lattice. Dislocation theory at the continuum and, most importantly, at the discrete level is to be thoroughly treated, which includes complete numerical procedures.
For generalised continua, the kinematics and the theoretical structure will be viewed from the point of transformation groups understood as Lie groups (SO(3), SL(3), and GL(3)). This allows for the unification of many concepts. In their mathematical structures, concepts of generalised continua and continuum dislocation theory are similar and can be treated very much from the same geometric point of view. At the crystal level, the application of concepts of generalised continua enhances the kinematics in crystal plasticity formulations to better describe slip mechanisms at such a level.
The discrete dislocation theory describes inelastic processes at an elementary and fundamental level which makes the understanding of basic deformation mechanisms that give rise to scale effects, possible. Discrete dislocation simulations generate large amount of data that need to be post-treated. Several numerical tools will be presented which explain how to compute the real shape of a plastically deformed volume or how statistical data like dislocation densities, internal stresses or stored energies can be estimated inside a grain. Discrete dislocation simulations are usually used as part of a multiscale modelling of a physical problem and it will be shown how information could be exchanged between different numerical models starting from molecular dynamics at the lowest scale and ending up to finite elements at the continuum level of description.