This series of 5 seminars will provide an introduction to the analysis of nonlinear problems in elasticity. Based on examples from recent research works and/or from daily life (such as the inflation of a cylindrical ballon, the shape of human hair, or the hexagonal patterns produced by the elastic Rayleigh-Taylor instability), we will derive the main methods applicable to nonlinear elasticity problems: the calculation of critical loads by a linear bifurcation analysis, the selection of buckling patterns using Koiter's method, the analysis of localized buckling using amplitude equations, etc. We will provide examples of both geometrical instabilities (as Euler's buckling) and material instabilities (as in the striction of bars and other localization phenomena).
2. Analysis of singularities - Tuesday, April 24, 2018 at 12:00PM 115 Gates-Thomas
Thin structures often develop singularities, i.e. small regions called inner/boundary layers where the strain concentrates. By way of illustration, we analyze the boundary layer that forms near the clamped endpoint of a heavy hair. A mathematical analysis is proposed in close analogy with the analysis of Prandtl's boundary layer in a fluid with low viscosity. It proceeds by identifying a non-regularized and a regularized model, by carrying out a dimensional analysis of the layer, and by setting up a matched asymptotic expansion.