Seminar of Pr. Marc Geers, March 31th

Short biography:

Marc Geers is full professor in Mechanics of Materials. He obtained his master in Polytechnical Engineering in Belgium in 1987. After 3 years of engineering practice, he started an academic career in 1991 at the civil engineering (and materials) department of the RMA in Brussels. In the period 1992-1996 he combined this position with a PhD at the Eindhoven University of Technology under the supervision of prof. R. de Borst. He was appointed associate professor in Belgium and guest lecturer at the TU/e in 1998. In 2000, he moved to the TU/e in the Netherlands where he was appointed full professor in the Department of Mechanical Engineering. His present interests are damage mechanics, micromechanics, multi-scale mechanics, generalized continua, crystal plasticity and metal forming.

Abstract:

Considerable progress had been made in bridging the mechanics of materials to other disciplines, e.g. downscaling to the field of materials science or upscaling to the field of structural engineering. The steady progress essentially results from the research efforts invested in multi-scale modelling in general, whereby a focus on multi-disciplinary aspects naturally arises. There are various ways to classify multi-scale methods in a general setting. In this presentation, attention is restricted to a particular method that falls in the category of homogenization methods based on integration over short length scales. This category of methods is also called ’coarse graining’ in the physics community. Among the various homogenization techniques proposed, a computational homogenization scheme is probably one of the most accurate techniques in upscaling the nonlinear behaviour of a well-characterized microstructure. This method is essentially based on the construction of a micro-scale boundary value problem, used to determine the local governing behaviour at the macro scale. In case the macro scale boundary value problem is solved simultaneously, a fully nested solution of two boundary value problems is obtained, one at each scale. Though computationally expensive, the procedures developed allow to assess the macroscopic influence of microstructural parameters in a rather straightforward manner.
Several topics will be addressed:

• - First-order computational homogenization: historical overview and key principles
• - Second-order computational homogenization: how to incorporate the size of the underlying microstructure?
• - Continuous-discontinuous multi-scale approach for localization problems: the problem and the solution inspired by embedded localization bands.
• - Multi-physics and coupled problems: the heat conduction problem & thermo-mechanically coupled computational homogenization
  - Thin structures: shells and beams, how to handle flat structures with a complex through-thickness architecture?
  - Computational homogenization towards cohesive zones.

The most important issues are commented for each of the topics addressed, with a particular emphasis on the applicability, and possible limitations of each. The presentation concludes with some general remarks on the added value of computational homogenization techniques as stand-alone tools or in development of alternative multi-scale methods. Finally, some open issues and challenges are summarized.