We study model locomotors on a substrate, which derive their propulsive capabilities from the tangential (viscous or frictional) resistance offered by the substrate. Our aim is to develop new tools and insight for future studies of cellular motility by crawling and of collective bacterial motion. The purely viscous case (worm) is relevant for cellular motility by crawling of individual cells. We re-examine some recent results on snail locomotion in order to assess the role of finely regulated adhesion mechanisms in crawling motility. Our main conclusion is that such regulation, although well documented in several biological systems, is not indispensable to accomplish locomotion driven by internal deformations, provided that the crawler may execute sufficiently large body deformations. Thus, there is no snail theorem. Namely, the crawling analog of the scallop theorem of low Reynolds number hydrodynamics does not hold for snail-like crawlers. The frictional case is obtained by assuming that the viscous coefficient governing tangential resistance forces, which act parallel and in the direction opposite to the velocity of the point to which they are applied, depends on the normal force acting at that point. We combine these surface interactions with inertial effects in order to investigate the mechanisms governing the motility of a bristle-robot. This model locomotor is easily manufactured and has been proposed as an effective tool to replicate and study collective bacterial motility.

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A direct theory of a one-dimensional structured continuum is introduced in order to study the postbuckling behavior of thin-walled beams. A simply supported beam bent by end couples is analyzed showing that, in the case of nonsymmetric cross sections, lateral buckling gives rise to imperfection sensitivity. Then an axially loaded beam is studied taking also into account the interaction between torsional and flexural buckling. The results obtained prove that in this case imperfection sensitivity, though slighter than in the previous case, arises also for symmetric cross sections.

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Posterior vitreous detachment is a fairly common condition in elderly people. Tractions exerted by the detached vitreous on the retina may result in retinal tears and detachments. We studied how these tractions can arise from saccadic eye movements. Numerical simulations have been performed on a two-dimensional model of the vitreous chamber within a rigid spherical sclera, subjected to prescribed finite-amplitude rotations about a vertical axis. The vitreous chamber was assumed to be split into two regions: one occupied by the detached vitreous, modeled as an elastic viscous solid, and the other occupied by the separated liquefied vitreous, modeled as a Newtonian fluid. At the interface between the two phases, we also considered the presence of the vitreous cortex, modeled as an elastic membrane. We tested several different configurations of the interface. In all cases, we found that eye rotations generate large tractions on the retina close to the attachment points of the membrane. Comparing them, we identified configurations of the vitreous detachment that exhibit higher tractions. We also investigated how the response to saccadic movements depends on some physical parameters, in particular on the rheological properties of the solid phase and the membrane. The numerical simulations show that the generated tractions may be of the same order of magnitude as the adhesive force between the retina and the pigment epithelium. Therefore, the model provides a sound physical justification for the hypothesis that saccadic movements, in the presence of posterior vitreous detachment, could be responsible for high tractions on the retina, which may trigger retinal tear formation.