Geometry and Mechanics of Shell Growth

Abstract eng:
Understanding and controlling the shape of thin, soft objects has been the focus of significant research efforts among physicists, biologists, and mechanicians over the last decade. These studies aim to utilize advanced materials in novel, adaptive ways to fabricate smart actuators or mimic living tissues. Our recent work investigates how the underlying geometry of thin sheets will morph into shells when exposed to a local isotropic expansion, which may represent several stimuli such as nonuniform heating, local swelling, and differential growth. We present an analytical model built on a framework of differential geometry and mechanics to predict the mean and Gaussian curvatures of the growing shells. We confirm our results through both numerical analysis, and an experimental technique that relies on the residual swelling of soft, geometric composites.

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