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).
3. From linear to non-linear buckling analyses - Tuesday, May 1, 2018 at 12:00PM 115 Gates-Thomas
The buckling of an elastic structure entails a bifurcation from a symmetric configuration to a less-symmetric configuration, as in Euler's buckling. We consider the example of the elastic Rayleigh-Taylor instability: by turning over a slab of a soft elastic material that rests initially on a hard surface, so that it ends up hanging from below this surface, one can obtain a hexagonal buckling pattern at the free surface of the slab. We start by carrying out a linear bifurcation analysis of this system, which yields a prediction for the critical load at bifurcation. Next, we present a nonlinear buckling analysis, which explains the formation of hexagons and the discontinuous nature of the bifurcation.