Description of the project: We propose a set of coordinated experiments, numerical simulations, and theoretical studies to provide predictive and quantitative descriptions of the structural and mechanical properties of static and slowly driven granular materials. Dense granular media are ubiquitous in nature and occur in many industrial applications. However, there is currently no fundamental understanding of how to uniquely characterize the state of a dense granular system using macroscopic descriptors. In our proposed research, we seek such a description using a systematic, bottom-up approach in which we first characterize microstate probabilities of mechanically stable granular packings and then utilize them to predict macroscopic behavior. In our studies of static particle packings, we will measure the probabilities of distinct microscopic states (cataloged by the particle positions) for different packing preparation protocols and particle properties such as shape, friction, and size polydispersity. We will also determine the number of microscopic states corresponding to macroscopic observables, such as the volume fraction, elastic constants and mechanical strength. By combining our results for microstate probabilities and the density of macro-states, we will determine the microstates that contribute significantly to ensembleaveraged quantities. We will also study the evolution of slowly driven systems, in which transitions from one microstate to another occur. In particular, we will measure the transition probabilities in experiments and numerical simulations of tapping excitations and quasi static shear. We will then develop master equation approaches to predict the steady state microstate distributions and corresponding macroscopic variables as a function of the intensity of the driving mechanism.
Intellectual Merit:
An important aspect of this work is that the experiments and numerical simulations will be performed over a range of system sizes. In small systems (up to tens of particles), all static packings will be enumerated, so that we can disentangle the influence of the packing generation protocol from geometrical effects. In moderate sized systems (up to one hundred particles), we will obtain the set of states that are statistically most relevant. We will also gain insight into the macroscopic properties of granular systems in the large-system limit by studying systems with O(103) particles. We thus will be able to develop a unified picture that connects microscopic probability distributions of mechanically stable (MS) packings to macroscopic properties. Another key feature of this proposal is that we propose integrated experiments, simulations, and theoretical studies. At each stage, we will compare the packing distributions from experiments and simulations to understand the nature of the MS packings and the effect of the packing generation protocol. Simple theoretical models will also be developed to identify the dominant physical mechanisms.
Broader Impacts:
While our investigations are focused on the properties of granular media under quasistatic conditions, our results will also contribute to a better understanding of material properties of other amorphous systems, such as molecular and colloidal glasses and emulsions and foams. In particular, our research will be relevant for theories describing slow dynamics in glass-forming fluids in terms of the statistics of inherent structures. Apart from the fundamental importance, the knowledge gained from the proposed studies will have impact on practical applications. Potential industrial applications include development of efficient technologies for storage, mixing, separation, and conveying of granular matter, and design of modern glassy materials of desired properties (e.g., high-strength metallic glasses). The proposed investigations will provide research opportunities for graduate and undergraduate students (in particular, we will mentor talented minority students from the STARS program at Yale and the diverse student body at CCNY). We will participate in programs at two high schools in New York City to involve high school students in our research program. Our project will also promote iternational knowledge transfer through the proposed collaboration with several scientists from the Institute of Fundamental Technological Research in Poland.
In this collaborative award, co-PIs O'Hern and Shattuck performed combined computational and experimental studies of mechanicaly stable packings of model granular materials. The main questions on which we have focused during the grant period are: 1) What determines the probability with which mechanically stable frictionless packings occur, and can the probabilities for individual packings be calculated in the large-system limit; 2) What is the characteristic packing fraction that signals the onset of nonaffine particle motion, limit cycles, and irreversibility in systems undergoing cyclic deformations; and 3) What controls the crossover from random close packing at low friction to random loose packing at high friction. We have also carried out preliminary experimental studies of packings of long rods and avian nests to determine their structural and mechanical properties. This work has led to 5 published manuscripts in Physical Review E, Physical Review Letters, and Nature Materials. We mentored 5 undergraduates, 5 graduate students (2 from Yale and 3 from CCNY), and one postdoctoral research associate. Outreach and broader impacts from this grant include Shattuck's participation as a lecturer for the Hands-on School in Complex Systems in Cameroon and China in 2010 and 2012 and O'Hern's participation in the Pathways to Science outreach events to New Haven public school students.
