Document Type

Dissertation

Date of Award

5-31-2021

Degree Name

Doctor of Philosophy in Mathematical Sciences - (Ph.D.)

Department

Mathematical Sciences

First Advisor

Lou Kondic

Second Advisor

Denis L. Blackmore

Third Advisor

Abram H. Clark

Fourth Advisor

Konstantin Michael Mischaikow

Fifth Advisor

Richard O. Moore

Abstract

Granular particle systems are scattered around the universe, and they can behave like solids when there exist strong force-bearing networks, so that the granular system can resist certain stress without deformation. When such a network is not present, particles yield to small stress and behave like a fluid. A wide range of systems exhibit intermittent dynamics as they are slowly loaded, with different dynamical regimes governing many industrial and natural phenomena. While a significant amount of research on exploring intermittent dynamics of granular systems has been carried out, not much is known about the connection between particle-scale response and the global dynamics. In this work, four different types of systems are investigated both through experiments and numerical simulations to reveal the connection.

At the beginning of this work, a spherical intruder is considered, which is initially buried in a granular column exposed to an upward pullout force. Analysis of the interparticle forces, using both classical and novel methods based on persistent homology, uncovers the details of the failure process. The intruder and the granular particles are essentially static before failure, however, the force network that includes the information about the particle contacts goes through significant changes. The failure occurs through a culmination of temporally intermittent changes that take place predominantly in the proximity to the intruder.

Next, experiments involving a slider moving on top of granular media consisting of photo-elastic particles in two dimensions are investigated. Such systems exhibit various dynamics, from continuous motion to crackling, and stick-slip type of behavior. By applying image analysis and persistence homology, a clear correlation between the slider dynamics and the response of the force network properties is revealed. Furthermore, the correlation is particularly strong in the dynamical regime characterized by well-defined stick-slip type of dynamics.

The stick-slip dynamics of dense granular systems is further investigated via 2D discrete element simulations. The focus of this work is understanding what type of information is needed to be able to predict upcoming events. Both static and dynamic measures are considered. The static measures are obtained from observing the state of the system at a given time, while dynamic measures are obtained by considering the information from system evolution. A set of dynamic measures is identified with a promise to predict slip events.

Finally, the intermittent dynamics of a dense granular system, exposed to slow compression and decompression in three spatial dimensions, is considered. Both compression and decompression involve transitional events involving fast irreversible transitions which are not always associated with rearrangement of particles and contact networks. The analysis of the force networks using the tools of persistent homology shows that the evolution of pressure is strongly correlated with the evolution of the topological measures quantifying loops in the force networks. Frictional effects are found to smoothen system evolution and to decrease both the amplitude and the duration of the transition events that occur during compression or decompression.

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