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Cy Maor (University of Toronto): Elasticity and curvature: the elastic energy of non-Euclidean thin bodies

Ort: MPI für Mathematik in den Naturwissenschaften Leipzig, Inselstr. 22, A3 01 (Sophus-Lie-SR)

Vortrag in der Reihe: Arbeitsgemeinschaft ANGEWANDTE ANALYSIS\nNon-Euclidean, or incompatible elasticity, is an elastic theory for bodies that do not have a reference (stress-free) configuration. It applies to many systems, in which the elastic body undergoes plastic deformations or inhomogeneous growth (e.g. plants, self-assembled molecules). Mathematically, it is a question of finding the "most isometric" immersion of a Riemannian manifold (M,g) into Euclidean space of the same dimension, by minimizing an appropriate energy functional.\nMuch of the research in non-Euclidean elasticity is concerned with elastic bodies that have one or more slender dimensions (such as leaves), and finding appropriate dimensionally-reduced models for them. In this talk I will give an introduction to non-Euclidean elasticity, and then focus on thin bodies and present some recent results and open problems on the relations between their elastic behavior and their curvature.\nBased on joint work with Asaf Shachar.

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Beginn: May 3, 2019, 11 a.m.

Ende: May 3, 2019, 12:30 p.m.