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Abstract: 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 discontinuous Galerkin methods. We prove $Gamma$-convergence of the discrete model and propose an iterative method that decreases its energy and leads to stationary configurations. We investigate performance, 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.