ADHESIVE FLEXIBLE MATERIAL STRUCTURES FRANCESCO MADDALENA, DANILO PERCIVALE, FRANCO TOMARELLI Abstract. We study variational problems modeling the adhesion in- teraction with a rigid substrate for elastic strings and rods. We produce conditions characterizing bonded and detached states as well as opti- mality properties with respect to loading and geometry. We show Euler equations for minimizers of the total energy outside self-contact and secondary contact points with the substrate. Contents Introduction 1 1. Adhesion of shearable elastic strings to a rigid substrate 4 2. Adhesion of elastic rods to a rigid substrate 7 3. Euler equations for a detached rod 15 4. Explicit conditions for detachment from a flat substrate 19 References 25 Introduction At the fundamental level of some recent fields of research such as nanoscale engineering and byophysics there is the need of a fine understanding of the behavior of thin flexible material structures involved in complex interac- tions. Indeed, the small scale interactions of material components, governed by surface-tension forces and adhesive forces as one-dimensional nanostruc- tures like nanotubes, nanowires and biopolymers adhering on different mate- rial substrates, are crucial in the study of biological adhesion and the devel- opment of nanoelectronics and nanocomposites as well as MEMS and NEMS devices ([27]), e.g. super coiled DNA molecules, bacteria filaments, gecko in- spired materials, actuators, etc. It has been shown that at the nanoscale, Date : October 27, 2010. 1