Crawling motility on viscous substrates

We study one-dimensional crawlers, namely, model mechanical systems that exploit cyclic shape changes and mechanical interactions with the environment to achieve self-propulsion. We focus on systems that can execute shape changes by propagating stretching or contraction waves along their bodies, and that interact with the substrate through viscous tangential forces. Two distinct rheologies are considered for the substrate: a linear Newtonian one, and a non-linear one of the Bingham type. Different behaviors result from the two rheologies and their implications in terms of motility performance are discussed. We believe that our results contribute to the general understanding of the key principles of limbless locomotion in natural and engineered systems.