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Ricardo H. Nochetto(University of Maryland): Thermally Actuated Bilayer Plates
We present a simple mathematical model of polymer bilayers that undergo large bending deformations when actuated by non-mechanical stimuli such as thermal effects. The model consists of a nonlinear fourth order problem with a pointwise isometry constraint, which we discretize with either Kirchhoff quadrilaterals or fully discontinuous elements. We prove $Gamma$-convergence of the discrete models and propose iterative methods that decrease their energy and lead to stationary configurations. We investigate performance of the two methods, as well as reduced model capabilities, via several insightful numerical experiments involving large (geometrically nonlinear) deformations. They include the folding of several practically useful compliant structures comprising of thin elastic layers. This work is joint with S. Bartels A. Bonito, and D. Ntogkas.