Professor Basile Audoly
Institut Polytechnique de Paris
France
will give the lecture
One-dimensional models for highly deformable elastic rods
Abstract:
We are interested in identifying effective mathematical models describing the deformations of rods, i.e., cylindrical elastic bodies whose cross-section dimensions are much smaller than their length. Owing to the separation of scales, their equilibrium is governed by ordinary differential equations which are easier to solve than the partial differential equations applicable in 3D elasticity. These equilibrium equations are well-established as long as the strain remains small, i.e., when the cross-sections remain almost undeformed. In this talk, I will discuss the interesting case of soft rods having highly deformable cross-sections. This includes inflated cylindrical rubber balloons, elastic bars made of very soft gels deforming under the action of surface tension, and carpenter's tapes. I will present a method for deriving the one-dimensional equations governing the equilibrium of these highly deformable rods, and will show that they accurately account for the localization phenomena that are ubiquitous in these systems.