Boosting lattice polarization Mixing the perspectives of geometry optimization and cell-augmentation

Abstract

Topologically polarized mechanical metamaterials enjoy a special built-in asymmetry that manifests as a preferred localization of edge states on selected edges. While this property has been shown for a few ideal Maxwell lattices, we currently lack systematic criteria to design families of structural systems exhibiting polarization. Here, we propose a framework to design polarized structural configurations enabled by topology optimization (TO), using both band and mode morphological properties as drivers of the optimization algorithm. Through the lens of TO, we are able to tap into a vast design space, unlocking geometric freedom far beyond what is achievable with canonical lattice architectures. At the same time, we elucidate important criteria that need to be satisfied, beyond the optimization outcome, to ensure robustness of the achieved polarization against perturbations of the edge morphology. These results provide the inspiration to loop back into the realm of ideal lattices in search of new configurations characterized by extreme polarization. The peculiar shape and connectivity of the TO-generated lattice offer a blueprint for identifying a new family of Maxwell trusses based on augmented kagome geometry. We demonstrate the achievement of strong polarization signatures up to a three-count edge state mismatch. For all the cases studied, we show agreement between theory, simulations, and experiments, which include laser vibrometry wave measurements on a waterjet-cut specimen and static tests on a 3D-printed prototype.