Microstructure and effective behavior of materials


  • [Plenary Lecture, GAMM Annual Conference 2012, Darmstadt]


Tailor-made materials often take advantage of surprising material behavior which is related to special effects and structures on small length scales. In order to achieve the design goals, a precise understanding of the underlying mechanisms in a mathematical model is indispensable. This contribution presents modern methods in the calculus of variations which are available for the analysis and numerical simulation of systems with multiple scales and illustrates their use in two characteristic model examples.