From soft matter to topological mechanical metamaterials

Soft matter is a crucial area of research in physics, chemistry, and biology. Among these systems, isostatic systems are particularly intriguing as they lie on the verge of mechanical stability and instability, exhibiting a variety of fascinating properties. These systems are ubiquitous in nature and engineering, such as in granular materials, cytoskeletal fibers, and soft robotic metamaterials. Isostatic systems display highly polarized surface mechanics: the surface hosting mechanical floppy modes exhibits softness, while the opposite boundary, hosting states of self-stress, is as rigid as the inner body. Furthermore, this polarized surface elasticity is insensitive to disorder and randomness, demonstrating topological robustness. This gives rise to the burgeoning field of “topological mechanics”. By integrating the fundamental concepts of soft matter, topological band theory, and mechanical metamaterials, this paper reviews the development and latest progress in topological mechanics.