Floppy modes—deformations that cost zero energy—are central to the mechanics of a wide class of systems.For disordered systems, such as random networks and particle packings, it is well-understood... Show moreFloppy modes—deformations that cost zero energy—are central to the mechanics of a wide class of systems.For disordered systems, such as random networks and particle packings, it is well-understood how the numberof floppy modes is controlled by the topology of the connections. Here we uncover that symmetric geometries,present in, e.g., mechanical metamaterials, can feature an unlimited number of excess floppy modes that areabsent in generic geometries, and in addition can support floppy modes that are multibranched. We study thenumber of excess floppy modes by comparing generic and symmetric geometries with identical topologies,and show that is extensive, peaks at intermediate connection densities, and exhibits mean-field scaling. Wethen develop an approximate yet accurate cluster counting algorithm that captures these findings. Finally, weleverage our insights to design metamaterials with multiple folding mechanisms. Show less
Mechanical metamaterials are man-made materials which derive their unusual properties from their structure rather than their composition. Their structure, or architecture, often consists of... Show moreMechanical metamaterials are man-made materials which derive their unusual properties from their structure rather than their composition. Their structure, or architecture, often consists of periodically arranged building blocks whose mutual interactions realize unusual properties. In this thesis, we investigate the role of two aspects of mechanical metamaterials: The beam ligaments and the microstructures of hinging squares. Both aspects play an important role in mechanical metamaterials, but give rise simultaneously to several open problems. First, although the mechanical behaviour of slender beam ligaments is well understood, the finite-width ligaments that often occur in mechanical metamaterials lead to new physics; wide beams exhibit a negative post-buckling stiffness, characterized by a decreasing force after buckling, which is not well understood. Second, fully filled microstructures of hinging squares constitute an auxetic mechanism, but possible new zero modes derived from (diluted) microstructures with missing squares remain largely unexplored. How does the number of zero modes increases in such diluted systems, can we count these additional modes, and what is their spatial structure? Here we address these open problems, thereby providing the necessary understanding to fully leverage the characteristics of wide beam ligaments and diluted collections of hinging squares for the design of novel mechanical functionalities. Show less
