Swarm/Mob Concepts Applied to Materials Modeling

Rebecca Brannon, Ph.D.
Emeritus Associate Professor
Department of Mechanical Engineering
University of Utah

Friday, Aug. 24, 3:15 pm
Sidney & Marian Green Classroom (3550 MEK)
Free & Open to the Public | Reception to follow at 4:15 pm

Abstract: Mob or swarm dynamics is a generic term for any theory that homogenizes the net behavior of many entities (panicky people, eddies, migrating birds, atoms, planets, etc.). Each entity obeys a set of simple rules to nevertheless produce intoxicatingly complex, path-dependent, and often fractal or fluid-like behavior. Viewing continuum mechanics from this perspective, microcracks, pores, fibers, dipoles, dislocations, grains, or any other “subscale’’ (smaller than finite element) morphological features are homogenized to obtain governing equations at larger scales that are significantly different from the generally simpler equations of each constituent.

The resulting composite is a “representative volume element (RVE)’’ if it is sufficiently large in size for “aleatory uncertainty’’ in subscale morphology (such as variable fiber orientation) to be inconsequential to a given engineering analysis. In statistical continuum mechanics, a “statistical volume element (SVE)’’ is large enough for homogenization to be meaningful, but not quite large enough to be an RVE. Case studies are used to illustrate benefits of treating each finite element as an SVE rather than an RVE. To introduce concepts, a simple (freshman-level) buckling hinge is placed in series with a nonlinear spring to provide a “micromorphology-dependent’’ force-displacement curve so that perturbations in that curve can be induced from perturbations in the hinge geometry.

Thousands of these component systems acting in parallel provide a foundation model that exhibits decreased peak strength as geometry perturbations are increased, reminding us of the similar observation that real columns buckle at a lower force than predicted with Euler theory. A similar result is found in damage theories that idealize a material to contain a “swarm’’ of penny-shaped cracks, in which morphological perturbations arise from natural variability in crack sizes and orientations. For any of these so-called first-principles theories to be of use in everyday engineering, they must be scaled up to finite elements that would have literally trillions of internal variables. As this is not practical even with exascale computing, a novel coarse-graining (binning) method is described.

Bio: Dr. Brannon is an ASME fellow with 25+ years of experience in computational and theoretical mechanics, emphasizing high-rate destructive deformations of metals, ceramics, and rocks. Her models are applied to armor, ceramic hip-replacements, single-use batteries, bunker surety, and shaped-charge jet well-bore completion. She is also known for her monographs on mathematics, dwarfed only by her stunning collection of Christmas ornaments.