Past Event: Babuška Forum

Liquid Crystal Polymeric Networks: Modeling, Approximation, and Computation

Ricardo Nochetto, Professor, University of Maryland

Abstract

We discuss modeling, numerical analysis and computation of liquid crystal networks (LCNs). These materials couple a nematic liquid crystal with a rubbery material. When actuated with heat or light, the interaction of the liquid crystal with the rubber creates complex shapes. Thin bodies of LCNs are natural candidates for soft robotics applications. We start from the classical 3D trace energy formula and derive a reduced 2D membrane energy as the formal asymptotic limit of vanishing thickness and characterize the zero energy deformations. We design a sound numerical method and prove its Gamma convergence despite the strong nonlinearity and lack of convexity properties of the membrane energy. We present computations showing the geometric effects that arise from liquid crystal defects as well as computations of non-isometric origami within and beyond the theory. This work is joint with L. Bouck and S. Yang.

Biography

Dr. Nochetto's professional journey started in Argentina with a Ph.D from Universidad de Buenos Aires in October 1983. From there he moved to Italy, completing postdoctoral studies at Universita di Pavia.

Nochetto's research interests include numerical methods for PDEs: free boundary problems, nonlinear elasticity, liquid crystals, fully nonlinear PDEs, fractional diffusion and adaptivity. 

Prizes and Awards

Giovanni Sacchi Landriani Prize in ``Numerical Analysis of Partial Differential Equations", Istituto Lombardo (Accademia di Scienze e Lettere), 1993 (Italy)

Invited talk at the International Congress of Mathematicians (ICM) 2010, Hyderabad, India.

SIAM Fellow, 2011.

AMS Fellow, 2012.

Plenary speaker at the International Congress on Industrial and Applied Mathematics (ICIAM), Beijing (China), 2015.