2D limit models in nonlinear elasticity: membranes, plates and Willmore surfaces

03.11.2022, 14:00-15:30  –  1.22 und Zoom
Geometric Analysis, Differential Geometry and Relativity

Claudia Grabs

Elastic deformations of thin plates include stretching, shearing and compression, as well as bending. As the thickness of the plate goes to zero, different limit theories arise, depending on the scaling of the elastic energy with the thickness of the plate for different deformations. Following an introduction to the basics of 3D nonlinear elasticity, including convexity conditions and existence theorems, we turn to 2D nonlinear elasticity. First we introduce the membrane model, capturing the stretching of an elastic membrane. We show how this is obtained either as Gamma-limit from 3D elasticity or derived from purely 2D conservation laws. For bending deformations of an elastic plate the nonlinear bending theory is obtained by Gamma convergence. As a special case here, the Willmore functional arises.

This talk is part of the seminar Geometric Analysis, Differential Geometry and Relativity organized by Carla Cederbaum (Uni Tübingen), Melanie Graf (Uni Tübingen), and Jan Metzger (Uni Potsdam) . To...