Roberta Marziani (Siena)

Mercoledì, 28 maggio⋅15:00 – 16:00

Sala Professori I livello

Titolo: Gamma-convergence for plane to wrinkles transition region Abstract: Motivated by physical experiments, we consider a variational problem modelling wrinkling effect of a thin annular sheet radially stretched. We start with a brief introduction on elasticity theory for thin films. We then settle a model for an annular domain radially stretched and describe an energy scaling result for low energy wrinkle patterns [Bella-Kohn 2014]. Afterwards, to better characterize the wrinkle pattern, in particular to describe the transition  between flat and wrinkled regions we set up a toy problem and perform an asymptotic analysis, via Gamma-concergence, as the sheet thickness goes to 0.  The limiting problem is scalar and convex, but constrained and posed for measures. The latter are in some sense related to Fourier coefficients of the vertical displacement of the elastic deformation.  Eventually for the limiting problem we show existence of a minimizer and equipartition of the energy for each frequency. This is based on a joint work with Peter Bella (TU Dortmund).