Journal
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 380, Issue 2234, Pages -Publisher
ROYAL SOC
DOI: 10.1098/rsta.2021.0326
Keywords
liquid crystals; elastomers; auxetic behaviour; finite deformation; mathematical modelling
Categories
Funding
- Engineering and Physical Sciences Research Council of Great Britain [EP/R020205/1, EP/S028870/1, EP/M009521/1]
- Leverhulme Trust
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This study develops a mathematical model to describe the nonlinear mechanical response observed in recent experiments on nematic liquid crystal elastomers, where the material becomes thicker in one direction instead of thinning under large strains. The material is modeled using an Ogden-type strain-energy function, and its parameters are calibrated to available datasets, showing that the Ogden strain-energy functions are suitable for modeling nematic elastomers.
We develop a mathematical model that builds on the surprising nonlinear mechanical response observed in recent experiments on nematic liquid crystal elastomers. Namely, under uniaxial tensile loads, the material, rather than thinning in the perpendicular directions, becomes thicker in one direction for a sufficiently large strain, while its volume remains unchanged. Motivated by this unusual large-strain auxetic behaviour, we model the material using an Ogden-type strain-energy function and calibrate its parameters to available datasets. We show that Ogden strain-energy functions are particularly suitable for modelling nematic elastomers because of their mathematical simplicity and their clear formulation in terms of the principal stretches, which have a direct kinematic interpretation.This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.
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