Discrete one-dimensional crawlers on viscous substrates: Achievable net displacements and their energy cost

• We analyze model, self-propelled discrete crawlers on viscous substrates.
• Both linear (Newtonian) and nonlinear (Bingham-type) substrates are considered.
• Large strains allow for net advancement even in the case of a linear rheology.
• The direction of motion can be inverted by changing the substrate's rheology.
• Self-propulsion is typically more efficient on a non-linear substrate than on a linear one.

We study model one-dimensional crawlers, namely, model mechanical systems that can achieve self-propulsion by controlled shape changes of their body (extension or contraction of portions of the body), thanks to frictional interactions with a rigid substrate. We evaluate the achievable net displacement and the related energetic cost for self-propulsion by discrete crawlers (i.e., whose body is made of a discrete number of contractile or extensile segments) moving on substrates with either a Newtonian (linear) or a Bingham-type (stick-slip) rheology. Our analysis is aimed at constructing the basic building blocks towards an integrative, multi-scale description of crawling cell motility.