A nonlinear bending theory for nematic LCE plates

Research output: Contribution to journalResearch articleContributedpeer-review



In this paper, we study an elastic bilayer plate composed of a nematic liquid crystal elastomer in the top layer and a nonlinearly elastic material in the bottom layer. While the bottom layer is assumed to be stress-free in the flat reference configuration, the top layer features an eigenstrain that depends on the local liquid crystal orientation. As a consequence, the plate shows non-flat deformations in equilibrium with a geometry that non-trivially depends on the relative thickness and shape of the plate, material parameters, boundary conditions for the deformation, and anchorings of the liquid crystal orientation. We focus on thin plates in the bending regime and derive a two-dimensional bending model that combines a nonlinear bending energy for the deformation, with a surface Oseen-Frank energy for the director field that describes the local orientation of the liquid crystal elastomer. Both energies are nonlinearly coupled by means of a spontaneous curvature term that effectively describes the nematic-elastic coupling. We rigorously derive this model as a F-limit from three-dimensional, nonlinear elasticity. We also devise a new numerical algorithm to compute stationary points of the two-dimensional model. We conduct numerical experiments and present simulation results that illustrate the practical properties of the proposed scheme as well as the rich mechanical behavior of the system.


Original languageEnglish
Pages (from-to)1437-1516
Number of pages80
JournalMathematical models and methods in applied sciences
Issue number7
Publication statusPublished - 30 Jun 2023

External IDs

WOS 000982041000001


Research priority areas of TU Dresden

DFG Classification of Subject Areas according to Review Boards

Subject groups, research areas, subject areas according to Destatis


  • bending plates, constrained finite element method, Dimension reduction, liquid crystal elastomer, nonlinear elasticity, Bending plates, Liquid crystal elastomer, Constrained finite element method, Nonlinear elasticity

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