Domain Wall Manipulation by Hierarchy in Multi-Stable Metamaterials

The manipulation of domains is critical to emerging functionalities in multi-stable metamaterials; however, the available strategies for domain control -- especially, those applicable in two-dimensional environments -- are few and, often, limited in their ability to sculpt and stabilize the domain contours. Here, we analyze domain wall motion in hierarchical metamaterial architectures formed by intersecting chains of elastically-coupled multi-stable elements, which establish a tailorable, non-uniform energy landscape for producing the sought-after behavior. The intersections create an energy barrier that impedes (even halts) domain wall motion and, thus, are mechanisms of control of the same. In tailoring the hierarchical structure, an assortment of unusual and complex domain contours can be realized and stabilized. We highlight some applications facilitated by the hierarchical structure.