Ribbon Gridshells – Soft Elasticity and Inverse Design

In this talk, we discuss the properties of a two-dimensional metamaterial composed of thin inextensible ribbons connected together to form a gridshell. We study both in-plane and out-of-plane deformations of such ribbon gridshells and point out their exotic geometric and mechanical properties. In particular, ribbon gridshells demonstrate anomalous softness with respect to some modes of deformation. At the same time, they are highly rigid with respect to other modes and conserve global geometric invariants. Shaping these objects constitutes a hyperbolic PDE system, and therefore, properly imposing initial conditions on a one-dimensional subset rigidifies them and fully determines their shape. We further show that exploiting structural degrees of freedom in ribbon gridshells allows tuning their soft modes in various ways. In particular, we can encode shapes into them; for example, make a flat object that can be accurately deformed into an arbitrary target surface shape. We demonstrate our results with experiments and suggest functional design and technology applications based on our findings.