Attenuated short wavelength buckling and force propagation in a biopolymer-reinforced rod

We investigate short wavelength buckling of a thin elastic rod embedded in an elastic gelatin biopolymer network. Using a combination of micro-mechanical testing, microscopic imaging, as well as theory, we show that the buckling penetration depth can be tuned by varying the mechanical properties of the rod and the rod-gel interface. Prior models have predicted a decay length that is dependent on the nonlinear material response of the embedding media. Here we identify a regime where the decay length is governed by the ratio of the bending rigidity of the rod and the linear elastic response of the medium, and show that our experiments are in good quantitative agreement with such a linear model.