Sequential Metamaterials

Ordered sequences of motion govern the morphological transitions of a wide variety of natural and man-made systems, while the ability to interpret time-ordered signals underlies future smart materials that can be (re)programmed and process information. Here we introduce two types of mechanical metamaterials, that either exhibit sequential output or are sensitive to sequential input.
First, we obtain metamaterials that translate a global uniform compression into a precise multistep pathway of reconfigurations.
Second, we introduce the notion of non-commuting metamaterials that are sensitive to a sequence of mechanical inputs.
Our work establishes generic principles for infusing metamaterials with sequential input and output.