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).
4. Amplitude equations - Tuesday, May 8, 2018 at 12:00PM 115 Gates-Thomas
We consider the buckling of an elastic plate floating onto a bath of fluid. The linear stability analysis predicts a well-defined wavelength and a homogenous buckling pattern, similar to the case of a strut on a foundation. Experiments, however, reveal the formation of a strongly localized buckling pattern comprising a single fold. This localization phenomenon is typical of extended systems. It is analyzed by the method of amplitude equations, which was originally developed in the context of pattern formation in fluids.