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AMCS seminar| Asymptotic rigidity and homogenization of layered materials with stiff components

Start Date: April 25, 2017
End Date: April 25, 2017

By Professor Carolin Kreisbeck (Universiteit Utrecht, The Netherland)
 
In the context of finite-strain elastoplasticity, we investigate the effective behavior of variational models for bilayered composite materials featuring large elastic constants in one component. Our particular interest lies in understanding whether the presence of the stiff layers forces a rigid macroscopic material response. The answer to this question is expected to depend on the scaling relation between stiffness and layer thickness. In this talk, we characterize the limit deformations of sequences of uniformly bounded energy as the thickness of the layers tends to zero, and identify two different scaling regimes. If the elastic constants diverge sufficiently fast, the observed macroscopic deformations coincide with those in the special case of completely rigid layers. As it is shown in a previous preprint, the latter correspond exactly to global rotations of shear deformations in layer direction, provided they are locally volume preserving. One major step in the proof is to quantify the layers’ stiffness with the help of the geometric rigidity estimate established by Friesecke, James, and Müller in 2002. To show optimality of this regime, an explicit construction based on bending of the individual stiffer layers is given, which yields macroscopically softer material behavior. These findings serve as a basis for proving a rigorous homogenization result via Γ-convergence. This is joint work with Fabian Christowiak (Universität Regensburg).
 
Biography: since Aug 2016 Assistant professor and Westerdijk fellow at Universiteit Utrecht Sept 2012 - July 2016 Research associate at Universität Regensburg (on leave in summer 2014) Apr 2014 - Sept 2014 Research associate at Weierstraß-Institut Berlin Sept 2011- Aug 2012 Post-doctoral fellow at Universidade Nova de Lisboa Sept 2010- Aug 2011 Post-doctoral fellow at Carnegie Mellon University July 2010 PhD in Mathematics from Universität Regensburg Mar 2007 Diploma in Mathematics from Universität Augsburg Apr 2006 Bachelor in Mathematics from Technische Universität München.
 

More Information:

For more info contact: Prof. Diogo Gomes: email: diogo.gomes@kaust.edu.sa
 
Date: Tuesday 25th Apr 2017
Time:01:00 PM - 02:00 PM
Location: Location: B1-L4-4214
Refreshments: Will be provide at 1 pm