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Applied Math Seminar
Effective theories for thin elastic films
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The main topic of this talk is the derivation of effective energy expressions for thin elastic films as variational limits in the sense of Gamma-convergence starting from atomistic models. In the membrane energy regime a rigorous version of a scheme proposed by Friesecke and James in [JMPS 48 (2000)] for general atomic interactions is proven, and qualitative aspects of the resulting continuum theory are discussed. In the realm of finite bending energy I will consider more specific models that will lead to Kirchhoff's plate theory in the continuum limit, augmented with some correction terms for "ultra-thin" layers. Finally, I will give some results on heterogeneous plates and their applications to the self-organized fabrication of nano-tubes by rolling up stessed multilayers. |