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15-02-2017 | Active Behavior in Soft Matter and Mechanobiology

Capturing the helical to spiral transitions in thin ribbons of nematic elastomers

Authors: Giuseppe Tomassetti, Valerio Varano

Published in: Meccanica | Issue 14/2017

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Abstract

We provide a quantitative description of the helicoid-to-spiral transition in thin ribbons of nematic elastomers using an elementary calculation based on a Koiter-type plate with incompatible reference configuration. Our calculation confirms that such transition is ruled by the competition between stretching energy and bending energy.

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Notice that the energy (41) depends only on the planar components $C_{\alpha \beta }$ of the Cauchy–Green strain. Moreover, such energy coincides with the relaxation (${{\mathcal {V}}}$ is the translation space of ${{\mathbb {E}}}$):

$$\begin{aligned} \overline{\sigma }_{{\mathsf{Q}}}({{\mathbf {A}}})=\min _{{{\mathbf {a}}}\in {{\mathcal {V}}}}\frac{1}{2} {{\mathbb {A}}}\left[ {{\mathbf {A}}}+{\mathrm{sym}}({{\mathbf {a}}}\otimes {\varvec{e}}_3)\right] \times \left[ {{\mathbf {A}}}+{\mathrm{sym}}({{\mathbf {a}}}\otimes {\varvec{e}}_3)\right] \end{aligned}$$

which appears in rigorous deductions of nonlinear plate models [1, 12, 25].

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Title: Capturing the helical to spiral transitions in thin ribbons of nematic elastomers
Authors: Giuseppe Tomassetti
Valerio Varano
Publication date: 15-02-2017
Publisher: Springer Netherlands
Published in: Meccanica / Issue 14/2017
Print ISSN: 0025-6455
Electronic ISSN: 1572-9648
DOI: https://doi.org/10.1007/s11012-017-0631-3

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