This CAREER award supports theoretical and computational research aimed at understanding the relationships between plasticity of amorphous solids and the jamming transition. It is generally accepted that the mechanical properties of crystals are controlled by their defects; however for amorphous solids, no such consensus has been reached. There is now mounting evidence for two different kinds of critical behavior in athermal, repulsive systems such as suspensions of soft particles or granular materials. On one hand, amorphous solids exhibit a kind of dynamical critical behavior similar to other depinning systems as they are driven at vanishing shear rate. On the other hand, confined random packings of repulsive particles exhibit critical behavior in their elastic response as the confining pressure vanishes. The key issue of the interplay between these behaviors during slow shear at low confinement pressure remains relatively unexplored.
The PI will perform massively parallel computer simulations of suspensions of soft and hard particle systems under shear to identify the mechanisms for stress buildup and relaxation in various regimes of particle stiffness, packing density, and shearing rate. The spatio-temporal structure of these processes will be studied using emerging tools developed for supercooled liquids and glasses. The PI will address whether the dynamically critical behavior observed in systems above jamming persists at the jamming transition and, more generally, how proximity to the jamming transition affects spatio-temporal structures that allow shear.
The educational activities lie along three main thrusts:
1) The undergraduate curriculum development will involve the infusion of numerical modeling into core upper division coursework.
2) The graduate curriculum development will involve the design and implementation of an introduction to statistical physics for engineering and theoretical mechanics students.
3) The secondary education outreach will be done in conjunction with the Pittsburgh Supercomputing Center in the context of a program which involves high school teachers from the Pittsburgh public schools.
NON-TECHNICAL SUMMARY
This CAREER award supports theoretical and computational research aimed at a fundamental understanding of how amorphous materials behave when subjected to external forces. Many amorphous materials behave like ordinary solids without external forces. Even though they lack any underlying crystalline order, they hold their shape. A few of the many examples from everyday experience include windows (made of glass or plexiglass), mayonnaise, and sand on the beach. When the external forces become sufficiently large, the particles which make up these solids start to flow as if the material were a liquid and the material is said to undergo "plastic yield". In crystalline materials, plastic yielding has been understood for many decades to be governed by extended defects in the crystal structure known as "dislocations". In the amorphous solids, a microscopic understanding of plastic yielding is only beginning to emerge.
In a certain subclass of these amorphous solids, e.g. the grains of sand, the constituent particles interact through purely repulsive forces. In this repulsive case, the materials can only behave like a solid when external forces confine the particles and force them to interact with each other. In such a confined state, the particles are said to be "jammed". At the transition point when the confinement is just about to be released, the elastic properties of the material are known to be completely anomalous, unlike anything observed in ordinary solids. Therefore, it is important to ask whether the system will yield via the same mechanism near jamming. The PI will perform very large-scale computer simulations and theoretical analysis to address this question.
The educational activities lie along three main thrusts:
1) The undergraduate curriculum development will involve the infusion of numerical modeling into core upper division coursework.
2) The graduate curriculum development will involve the design and implementation of an introduction to statistical physics for engineering and theoretical mechanics students.
3) The secondary education outreach will be done in conjunction with the Pittsburgh Supercomputing Center in the context of a program which involves high school teachers from the Pittsburgh public schools.
