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A flat sheet programmed with a planar pattern of spontaneous shape changewill morph into a curved surface. Such metric mechanics is seen in growingbiological sheets, and may be engineered in actuating soft matter sheets suchas phase-changing liquid crystal elastomers (LCEs), swelling gels and inflatingbaromorphs. Here, we show how to combine multiple patterns in a sheet bystitching regions of different shape changes together piecewise alonginterfaces. This approach allows simple patterns to be used as building blocks,and enables the design of multi-material or active/passive sheets. We give ageneral condition for an interface to be geometrically compatible, and exploreits consequences for LCE/LCE, gel/gel, and active/passive interfaces. Incontraction/elongation systems such as LCEs, we find an infinite set ofcompatible interfaces between any pair of patterns along which the metric isdiscontinuous, and a finite number across which the metric is continuous. As anexample, we find all possible interfaces between pairs of LCE logarithmicspiral patterns. In contrast, in isotropic systems such as swelling gels, onlya finite number of continuous interfaces are available, greatly limiting thepotential of stitching. In both continuous and discontinuous cases, we find thestitched interfaces generically carry singular Gaussian curvature, leading tointrinsically curved folds in the actuated surface. We give a generalexpression for the distribution of this curvature, and a more specialized formfor interfaces in LCE patterns. The interfaces thus also have rich geometricand mechanical properties in their own right.

Interfacial metric mechanics: stitching patterns of shape change in active sheets