Buckling profile of a thin rod embedded in a fractured biopolymer matrix

A thin elastic rod embedded in an elastic medium buckles into an exponentially decaying short wavelength profile under compressive loading beyond a critical value. In this study, we report a combined experimental and theoretical investigation of the buckling profile of a thin elastic rod embedded in an elastic gelatin biopolymer network when fracture of the network happens. Prior models have predicted the transverse displacement of the rod under a compressive force in a uniform viscoelastic medium, but it is assumed that the deformation is small and elastic. Thus they cannot capture the main features where there is plastic deformation. Here we use the energy principle to interpret and predict the buckling profile of the superelastic thin rod after fracture of the surrounding gelatin happens due to excessive lateral displacement of the rod in a gelatin medium. Preliminary results indicate that the modeling framework can be used to predict the buckling profile in experiments with certain improvements.