## Programming and reprogramming metamaterials

The development of mechanical metamaterials rapidly grows and explores multiple strategies to design functional materials. Essentially a function relies on an internal structural property, so that a radical change of function often requires redesigning a new structure from scratch. Pre-encoding several functions in one single structure is a corner stone towards designing truly reprogrammable mechanical metamaterials. In this talk I will present ongoing researches and discuss a new strategy we have investigated. We construct a mechanical metamaterial by assembling non-commuting unit cells. Each unit can be actuated by two external inputs, say A and B such that actuating A then B is different than B then A. We propose a rationale design to encode this non-commuting property within a unit-cell by considering an elastic square frame whose diagonal rest-length can be contracted at will. Depending on the order of contraction (diagonal A or diagonal B), the unit-cell deforms into two different tetrahedra. By assembling a two-dimensional network of m x n unit cells we construct, a non-commuting mechanical metamaterial and I will present some of its emerging properties. I will discuss the case of a 1 x n strip and will present its surprising properties when a sequence of actuations at different sites is achieved. Finally, I will discuss the case of larger system size where the system becomes overconstrained and the non-commuting are mediated in a frustrated energy landscape.