Liquid crystal elastomers (LCEs) are a novel class of polymer networks with tunable, anisotropic mechanical properties that can be programmed through applied strain, and have demonstrated advantages for actuation, energy absorption and reconfigurable microstructures.  Integrating LCEs into a network of elastomeric beams adds geometric nonlinearity into the stiffness programming hierarchy, further broadening the design space and functionality for architected LCEs. However, the confluence of nonlinearities between the mapping of geometry and local strain, and the mapping between local strain and LCE stiffness programming, presents a large and complex design space to navigate.  To address this challenge, we developed a Bayesian optimization framework that connects the macro and microscales of the programming process to design LCE beams with switchable buckling modes. The LCE beam shape is parameterized with a Fourier series expansion, which controls the periodicity and thickness of the beam as a function of length. A multi-level mechanical analysis is performed at each iteration using a finite element (FE) approach, which calculates the spatial strain distribution, nonlinear strain-to-stiffness mapping, and the post-programming mechanical behavior. Preliminary results indicate geometry regulates the number and type of buckling modes, while the nonlinear stiffness programming regulates mode selectivity, which highlights the importance of design tools to predict the parameter space for specific modes.

Design of Switch States in Liquid Crystal Elastomer Beam Networks

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