Finite element modeling of viscoelastic liquid crystal elastomers

Ali El Hajj Chehade, Beijun Shen, Chris M. Yakacki, Thao D. Nguyen, Sanjay Govindjee

Research output: Contribution to journalArticlepeer-review

Abstract

Liquid crystal elastomers (LCEs) are elastomeric networks with anisotropic monomers that reorient in response to applied loads, and in particular, thermomechanical loads. LCE complex microstructures translate into complex behaviors, such as soft elasticity, rate-dependency, and hysteresis. In this work, we develop a three-dimensional finite element implementation for monodomain LCEs, with the material modeled as a finite deformation viscoelastic network with a viscous director. The formulation is designed so that the director field can be modeled as an internal variable. Unique to this class of materials is that their deformation response function depends on the full deformation gradient and not just the right-stretch tensor. This results in the material tangent losing its ‘usual’ symmetry properties. Accordingly, this makes the use of a first Piola–Kirchhoff finite element formulation advantageous. We utilize this framework to examine a number of nuances associated with the simulation and design of LCE based systems. In particular, we investigate in some detail the importance of a careful characterization of an LCE's initial director field. Via simulations of separate tension and compression experiments, we highlight the possibility of incorrect predictions when even small perturbations to initial conditions occur. The simulations are also used to illustrate the goodness of the model in replicating simple and complex experimental results, including the first-of-their-kind buckling-like column compression and thick-walled balloon inflation simulations.

Original languageEnglish (US)
Article numbere7510
JournalInternational Journal for Numerical Methods in Engineering
Volume125
Issue number16
DOIs
StatePublished - Aug 30 2024
Externally publishedYes

Keywords

  • first Piola–Kirchhoff form
  • inhomogeneous directors
  • liquid crystal elastomer
  • viscoelasticity
  • viscous director

ASJC Scopus subject areas

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics

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