Lucas Bouck: Numerical Approximation of a Membrane Model of Liquid Crystal Elastomers

Speaker: Lucas C. Bouck (University of Maryland)
Series of lectures: Seminar für Angewandte Mathematik
Contact: Prof. Dr. Axel Voigt, Dr. Simon Praetorius
Streaming: Zoom https://t1p.de/dldcu

Title: Numerical Approximation of a Membrane Model of Liquid Crystal Elastomers

Abstract: Liquid crystal elastomers are materials where a liquid crystal is coupled with a rubbery material. When actuated with heat or light, the interaction of the liquid crystal with the rubber creates complex shapes. We present a finite element method to compute minimizers of the stretching energy developed by Ozenda, Sonnet, and Virga (2020). One significant challenge is the lack of quasi convexity of such energy; in fact we show that the energy is not rank-one convex. To address the lack of quasiconvexity, we regularize with a term that mimics a higher order bending energy. We prove that the regularization serves as a selection mechanism for computing finite bending configurations that minimize the membrane energy. We illustrate the geometric effects of liquid crystal defects via numerical computations as well as approximate special solutions.