Relationships Between Structure, Dynamics, And Flow In Sheared Amorphous Materials
Amorphous solids, those composed of haphazardly arranged constituents, are found everywhere from our windows as silicate glass, in the ground and foundations as mud and concrete, and our grocery stores as granular piles of oranges. Even though they can be found over a huge range of length scales, it remains a challenge to systematically design their mechanical properties using knowledge of their microstructure. In this thesis, I investigate the link between the microstructure and the mechanical properties of a-thermal solids. First, I probe the particle trajectories for chaotic signatures that relate to bulk rheology. Particles are confirmed to exhibit chaotic, Brownian like motion during cyclic shear, even though the particles are large enough that thermal motion is negligible. I also find that, the average area traced by returning particles is proportional to the amplitude of strain, which could be useful for in situ measurements in industrial, granular, mixing applications. Next, I examine the interconnection between particle dynamics and the arrangements of the constituents. I calculate the characteristic time for particles to shift past each other, called relaxation time, and the configurational entropy of the system in excess of a reference ideal gas. I show that the relaxation time at any given instant is related to the excess entropy a quarter shear cycle later, which implies that the dynamics of particles shape the eventual structure. This means it is possible to take a snapshot of particle positions and infer its mechanical past. Finally, I focus on the interplay between particle positions and bulk yield by using concepts from kinetics, thermodynamics, statistical mechanics, and shear transformation zone theory. I establish a relationship between excess entropy and energy dissipation and uncover a novel definition for the yield transition based on memory signatures within the microstructure. Using these observations, I derive a phenomenological model that links the microstructure to bulk rheology that is physically informed and whose parameters are all quantitatively measurable. This dissertation elucidates how the statistics of particle configurations and dynamics give rise to the macroscopic transition from elasticity to plasticity during yield of amorphous, a-thermal solids.
Douglas J. Jerolmack