Mar 20 – 22, 2019
Nordita, Stockholm
Europe/Stockholm timezone

Asymptotic derivation of a higher-order beam model for tape springs

Mar 21, 2019, 9:45 AM
45m
132:028 (Nordita, Stockholm)

132:028

Nordita, Stockholm

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.

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