Mechanical criticality, nonlinearity, fracturing, and topological edge modes in fiber networks

Disordered networks of crosslinked fibers capture the essential structure of many materials in nature, such as the cytoskeleton and extracellular matrix as networks of biopolymers, and manmade materials such as hydrogels and aerogels. In this talk, we will discuss a number of remarkable mechanical properties of fiber networks, starting from Maxwell's counting of numbers of degrees of freedom and constraints, which places these fiber networks close to a special mechanical critical point, the so called "isostatic point", leading to highly sensitive changes of elastic properties [1]. We will then proceed to discuss how this point also controls the significant strain-stiffening behavior of these fiber networks in the nonlinear regime [2], as well as special critical phenomena when these materials fail under stress [3]. Moreover, we will show that in two dimensions, floppy modes in these fiber networks are controlled by a topological winding number. Interestingly, when a small active stress changes the network geometry, floppy modes in fiber networks can localize at opposite edges of the network, strongly affects mechanical properties of the network from local stiffness to signal transmission [4]. These unusual mechanical phenomena reveal great potential for both controlling fiber networks in nature such as tissue engineering, and creating new materials with sensitive, topologically protected, mechanical properties.
[1] Broedersz, Mao, MacKintosh and Lubensky, Nature Physics 7, 983 (2011).
[2] Feng, Levine, Mao, and Sander, Physical Review E 91, 042710 (2015); Soft Matter 12, 1419 (2016).
[3] Zhang, Rocklin, Sander, and Mao, Physical Review Materials1, 052602 (2017).
[4] Zhou, Zhang, and Mao, Physical Review Letters 120, 068003 (2018).