Inverse design of multishape metamaterials

Multishape metamaterials exhibit more than one target shape change, e.g. the same metamaterial can have either a positive or negative Poisson's ratio. So far, multishape metamaterials have mostly been obtained by trial-and-error. The inverse design of multiple target deformations in such multishape metamaterials remains a largely open problem. Here, we demonstrate that it is possible to design metamaterials with multiple nonlinear deformations of arbitrary complexity. To this end, we introduce a novel sequential nonlinear method to design multiple target modes. We start by iteratively adding local constraints that match a first specific target mode; we then continue from the obtained geometry by iteratively adding local constraints that match a second target mode; and so on. We apply this sequential method to design up to 3 modes with complex shapes and we show that this method yields at least an 85% success rate. Yet we find that these metamaterials invariably host additional spurious modes, whose number grows with the number of target modes and their complexity, as well as the system size. Our results highlight an inherent trade-off between design freedom and design constraints and pave the way towards multi-functional materials and devices.