Buckling morphology of an elastic beam between two parallel lateral constraints: implication for crawling snake between walls

 Junfeng Xiao and Xi Chen, Journal of Royal Society Interface. 2013, 10(85).  http://dx.doi.org/10.1098/rsif.2013.0399

 
A snake crawling on horizontal surfaces between two parallel walls exhibits a unique wave-like shape, which is different from the normal shape of a snake crawling without constraints. We propose that this intriguing system is analogous to a buckled beam under two lateral constraints. A new theoretical model of beam buckling, which is verified by numerical simulation, is firstly developed to account for the special boundary conditions. Under this theoretical model, the effect of geometrical parameters on the deformation shape, such as the distance between walls, length of the snake and radius of the snake, is examined. The buckling beam model is then applied to explain qualitatively the wave-like shape of the snake. 

 Comparison between real snake and simulation results of buckled beam. In (a), 12 curved sections are found in both experiments and simulations. In (b), 10 curved sections are found in the experiments, which corresponds to the simulation case of 11 curved sections.