AMCS Seminar : Asymptotic rigidity and homogenization of layered materials with stiff components

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).

Date: Tuesday 25^{th} Apr 2017

Time:01:00 PM - 02:00 PM

Location: B1-L4-4214