CRITICAL SCALING AND STRUCTURE AT THE YIELDING TRANSITION IN PARTICULATE MEDIA

Particulate materials (amorphous, athermal substances such as dry grains, foams, emulsions, and colloids) are commonplace in industry and defense, second only to water in their ubiquity. These materials can transition from solid-like to liquid-like in unexpected ways, with failure in one section of a large system rapidly leading to failure across the entire system and giving rise to significant consequences in phenomena as disparate as impact resistance, geological fault interface behavior, soil liquefaction, pharmaceuticals, crater formation, glacier flow, avalanches and landslides. These complex behaviors are the result of simple interaction laws (e.g., Hooke’s law) applied to thousands or more of individual particles. Since no complete theory of flow in these materials exists, accurately predicting or engineering the onset of these transitions can be challenging. Using extensive computer simulations, we show that shear flows occur in particulate materials due to a correlation length (a measure of the distance over which rearrangements propagate) that diverges at the material yield condition. Large ensembles of simulated systems are sheared, and statistics are gathered on the average initial flow distance, slip avalanche distance, and the average internal shear stress at each shear strain step. These properties are found to vary in a manner consistent with a diverging correlation length. My results will be useful in deriving a more complete theory of flow in these materialhttp://archive.org/details/criticalscalinga1094563512Lieutenant, United States NavyApproved for public release; distribution is unlimited