Dissertations, Theses, and Capstone Projects

Date of Degree


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Mark D. Shattuck

Subject Categories



avalanches; granular materials


We explore the microscopic interactions and properties of dry granular materials in the plane using experiments and simulations. We use statistics of this microscopic information to better understand and predict the bulk behavior and evolution of granular materials.

In the first part, we study the geometric structure of mechanically stable packings of frictional disks in configuration space. Our experimental setup contains frictional disks confined in a vertical plane and subject to a series of small amplitude vibrations that compact the system by reducing the friction between contacts during each vibration step. We find that the evolution of the packings forms a tree-like structure in the configuration space and that the particles move in the direction of gravity projected onto the null space of the rigidity matrix determined from the contact network of the packing. We suggest that this formalism can also be used to explain the evolution of frictional packings under other forcing conditions.

In the second part, we address the question of universality in granular avalanches. We set up an experiment made from a quasi-two-dimensional rotating drum half-filled with a mono-layer of stainless-steel spheres. We measure the size of the avalanches created by the increased gravitational stress on the pile as we rotate. We find that the size and duration of the avalanches follow a power law and that the avalanche shapes are self-similar and nearly parabolic. This indicates that the avalanches belong to a universality class, which has been predicted by mean field theory.

Finally we look at granular phase transitions from gas to crystal and ask which local properties best describe the granular phase transition in mono-disperse disks from gas to crystal. We perform two-dimensional numerical simulations with different boundary conditions and driving mechanisms, in which we measure the local area fraction, bond order, and anisotropy.

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