Analytic study of the mechanics of random biopolymer networks
How do large-scale properties of materials arise from the complex interplay of their microscopic constituents? Biopolymer networks such as collagen are an important part of connective tissues in animals. However, even if the mechanical properties of single fibers of such networks were precisely known, the disordered nature of the network makes the behavior of the whole system hard to predict. One common model for biopolymer networks are fiber network models, where individual fibers resist both stretching and bending. I have recently developed an analytical approach to understand the elastic behavior of a broad class of under-constrained, disordered systems. This approach also allows to quantitatively understand the macroscopic behavior of fiber networks in the limit of vanishing fiber bending rigidity. This approach now needs to be generalized.
The analytical approach will be generalized to over-constrained systems. This will then be applied to fiber networks with a finite bending rigidity, where the student will study in detail the connections between microscopic structure and macroscopic properties. Finally, the results will be compared to experimental biopolymer gel rheology data.
These questions will be addressed using a combination of analytical studies (continuum mechanics, minimization problems, topological invariants) and numerical studies (implementation and simulation of different kinds of disordered fiber network models).
PhD student’s expected profile
I am looking for a curious and highly motivated student with a master degree in physics or mathematics.