Non-commuting Mechanical Metamaterials

The elastic response of ordinary materials typically satisfies the principle of superposition, thus rendering the deformation output impervious to the order of actuation inputs. This severely constrains the design of multifunctional programmable metamaterials. Here, we introduce an elegant solution in the form of non-commuting mechanical metamaterials, which are sensitive to the magnitude as well as the order of inputs. We discuss the essential ingredients to design such a non-commuting metamaterial and demonstrate a scalable framework to study them. Our work establishes the groundwork for reprogrammable designer matter with memory.