Multistable sheets with rewritable patterns for switchable shape-morphing

Flat sheets patterned with folds, cuts or swelling regions can deform into complex three-dimensional shapes under external stimuli^1-24. However, current strategies require prepatterning and lack intrinsic shape selection^5-24. Moreover, they either rely on permanent deformations^{6,12-14,17,18}, preventing corrections or erasure of a shape, or sustained stimulation^5,7-11,25, thus yielding shapes that are unstable. Here we show that shape-morphing strategies based on mechanical multistability can overcome these limitations. We focus on undulating metasheets that store memories of mechanical stimuli in patterns of self-stabilizing scars. After removing external stimuli, scars persist and force the sheet to switch to sharply selected curved, curled and twisted shapes. These stable shapes can be erased by appropriate forcing, allowing rewritable patterns and repeated and robust actuation. Our strategy is material agnostic, extendable to other undulation patterns and instabilities, and scale-free, allowing applications from miniature to architectural scales.