How caterpillar crawling gait takes advantage of non-linear elasticity

The vast majority of existing models of caterpillar locomotion successfully uses linear elasticity to describe how these Lepidoptera, at the larval stage, activate and coordinate the movement of the body segments during their crawling gait. Although linear mechanics is extremely effective for capturing the key features of the locomotion of these insects and for providing some helpful analytical results, large deformations actually experienced by the moving caterpillar structures suggest that nonlinear elasticity could play an important role in faithfully and quantitatively predicting their behaviour. To incorporate these experimental evidences, the present study, by employing a discrete lumped-mass model, introduces a neo-Hookean constitutive law for the segmented caterpillar body. Apart from consistency with observations, the proposed hyperelastic approach energetically penalised high compressive stresses and contractions with respect to tensile stresses and stretches, as actually occurs during realistic locomotion, also intrinsically preventing interpenetration between adjacent body tracts at any step of the numerical simulations, so inherently enforcing compatibility conditions that, in linear elastic formulations, would have required the introduction of additional constraints for avoiding unphysical results. In particular, we propose that locomotion is triggered by a localised inelastic muscle contraction of the terminal caterpillar body segment, which interacts with the abdominal prolegs responsible for substrate attachment and detachment, leading to a competition between gripping forces and internal body deformations. The consequence is that detachment and forward progression occur only when the adhesive energy threshold of the abdominal prolegs – modelled as Winkler foundation of elastic springs that disengage upon reaching a critical tensile load – is exceeded. Finally, by uploading inertial and dissipative effects for reproducing dynamic conditions, we demonstrate that caterpillar crawling gait is essentially a steady-state process, however highlighting how nonlinear elastic energy stored during muscle contraction is redistributed and partly converted into kinetic energy during locomotion for activating initial propulsion. It is felt that the results of the present work may contribute to shed new light on the fundamental mechanisms ruling crawling in living organisms, which could also guide the design of next-generation bio–inspired soft robots, capable of exploiting cumulated elastic energy for propulsion and efficient motion while adhering on substrates.