Mechanics of marginal solids: Length, strain, and time scales

Abstract

Network materials, foams, and emulsions are ubiquitous in our daily life. We have a good intuition about how they respond as we handle them, but our theoretical understanding is poor. One of their most interesting features is that they are unusually fragile and appear to switch between solid and liquid state seamlessly. In fact, foams and emulsions undergo a non-equilibrium phase transition as their packing fraction increases - this is the jamming transition. Networks show a similar transition as their connectivity increases, where the material switches from sloppy to rigid. The fact that these materials undergo a phase transition, opens up the theoretical toolset of statistical mechanics. An important part of current research is therefore dedicated to finding diverging length and time scales and investigating the critical behavior of the systems in detail. Because the systems in question are highly disordered, analytical modeling is challenging. At the same time there are significant experimental obstacles to approaching the critical point closely. For this reason, the development of simulation software plays an important role - all data presented in this thesis is generated through simulations. As the subtitle of this dissertation suggests, our findings concern length, strain, and time scales which can be found in the linear response to external forces.