Mathematics

The framework of rate-independent systems, which has found in the last years many successful applications in phenomena such as plasticity and fracture, is also a powerful way to describe the quasi-static evolution of mechanical systems subject to (Coulomb) dry friction. The recently growing interest in the study of biological and bio-inspired crawling locomotors can provide new motivations to this matter, instigating new questions and raising new issues. The aim of this talk is to provide a gentle introduction to such themes. In the first part, I introduce rate-indepentent systems, with the support of a minimal, one-dimensional example. Then, after a brief presentation on crawling locomotion and on the paradigm of soft robotics, we discuss how a toy model of crawler can fit in the framework previously described. To conclude, we have a glance at a more sophisticated application, concerning the genesis of a directionality in friction on hairy surfaces.