Abstract

The von Karman- Foppl equations are a nonlinear extension of the usual linear elastic plate equations allowing for both in-plane stretching and out-of-plane deformation. The equations are popular in areas of the Physics community and our aim is to solve them both analytically, asymptotically and numerically and then compare to experiments. We use the equations to explore the onset of linear instability and the subsequent nonlinear development of buckling patterns in a flat elastic plate due to an imposed shear or body force such as gravity. In particular the spacing of the buckles, their amplitude and the envelope of their displacement can be identified. For comparison experimental results are also presented for a clamped and sheared sheet of Neoprene rubber and thus we can quantify how effective these equations are at predicting reality. Moving on from this we then consider how an underlying flowing fluid affects wrinkling or buckling and this forms a simple model of flow beneath a solidifying skin such as one sees in some lava flows.

This is joint work with Neil Balmforth & Anja Slim (UBC, Canada)