Speaker
Marcelo Dias
(Aarhus University)
Description
In this talk we shall discuss the localization of folds in a
curved tape spring. This phenomena reveals a generalized
mathematical structure with strong links to that of phase
transitions, as seen in a van der Waals’ fluid, for which a
fixed volume contains a mixture of liquid and vapor phases.
This framework also captures phase transformations as
material instabilities, whereby material non-linearities
showcase non-convex energy functionals. To exemplify this
idea, in the context of elasticity, we shall review a simple
one-dimensional for instabilities in elastic bars, namely
the Ericksen bar model. Then, we will construct a
dimensionally reduced shell model in order to approach the
problem of a curved tape spring. An asymptotic derivation of
this model will be explained and demonstrated to be a
possible tool to analyze the localization of folds.
