COLLEGE OF ARTS AND SCIENCES Department of Mathematics and Statistics
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Joint Colloquium: Discrete Models for Granular Materials


11:00am Sloan 233

Matthew R. Kuhn

Abstract: Granular materials exhibit interesting and unusual phenomena, whether they are viewed at the micro, meso, and macro-scales. As such, they present an excellent context for multi-scale modeling, particularly since the micro-scale behavior is amenable to discrete, finite-dimensional analysis. The presentation gives examples of phenomena that, as of yet, have not been adequately explained or modeled at more than a single scale. We then focus on the micro-scale and show that some of these phenomena are expressed in entirely counter-intuitive ways, which is probably due to micro-scale instabilities in the motions and interactions of particle clusters. A consistent framework is then presented for discrete, finite-dimensional analysis using the direct stiffness method.This framework addresses two issues that arise in granular deformation--stability and uniqueness--and the manner in which these issues can be resolved through discrete analysis. The framework is applied to regular packings of particles and to meso-scale simulations of random media.