Morphing architecture with controll of both metric and curvature

The configuration of a surface is fully characterized by two tensors, a metric tensor and a curvature tensor. Changing its shape generally involves both. With a set of constrains, the Gauss-Codazzi-Mainardi equations, the minimum of total elastic energy will dictate the final shape by setting the right metric and curvature tensor simultaneously.

Here, we develop a versatile technique based on consumer-grade materials assembled in a flat panel, which can be designed to to program both metric and curvature. By performing theoretical analysis and experimental tests, these quantitative results are used to achieve shape-morphing and design programmed surface composed of actuators for specific tasks. Therefore, our study paves the way for a new generation of robotic systems that can tune their shape and function to adapt and even influence their surroundings, leading material machine closer to application.