Navigating the landscape of nonlinear mechanical metamaterials for advanced programmability

We consider a flexible mechanical metamaterial comprising an elastomeric matrix with an embedded square array of circular holes. First, we use the deflated continuation technique of bifurcation analysis to explore its complex energy landscape, characterized by multiple bifurcations from which stable and unstable branches emanate. We then investigate how this landscape can be exploited for real-time programmability. We find that the response of the system can be constantly reprogrammed by locally manipulating it to move it from one stable branch to another and that small targeted imperfections can be harnessed to enhance such programmability.