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Continuum Mechanics: Research Questions for the Classroom

Continuum Mechanics: Research Questions for the Classroom. Michael Dennin U. C. Irvine Department of Physics and Astronomy. “One of the oddities of contemporary physics education is the nearly complete absence of continuum mechanics in the typical undergraduate or graduate curriculum.”

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Continuum Mechanics: Research Questions for the Classroom

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  1. Continuum Mechanics: Research Questions for the Classroom Michael Dennin U. C. Irvine Department of Physics and Astronomy

  2. “One of the oddities of contemporary physics education is the nearly complete absence of continuum mechanics in the typical undergraduate or graduate curriculum.” Jerry Gollub, Reference Frame, Physics Today, Dec. 2003.

  3. What do we teach? • Single particle classical • Rigid body classical • EM • Quantum • Waves (strings) • Relativity WHY DO WE TEACH THESE TOPICS?

  4. JAMMING PHASE DIAGRAM Liu and Nagel How does it help understand … FLOW JAMMING VERSUS

  5. What happened to continuum mechanics? • Two Big Questions in Physics: • Transition from quantum to classical. • Transition from single particle to continuum.

  6. Educational Benefits • Physically accessible tensors: stress/strain. • Practice with differential equations (ODE AND PDE). • Exposure to CLASSICAL FIELD THEORY. • Fun Demonstrations!! • Relevance for undergrads moving into engineering positions • CRITICAL BACKGROUND FOR CURRENT RESEARCH AREAS!!!

  7. Jamming Phase Diagram • Plasticity in “molecular” systems • Glassy behavior in liquids • Flow of “multiphase” materials: granular, foams, colloids, pastes, etc.. The “J-point” Liu and Nagel, Nature v 396, 1998

  8. WHAT ABOUT FOAMS? http://www.joiff.com/technical/infoamation.htm FOAM: gas bubbles with liquid walls Size: microns to millimeters Useful parameter: Liquid fraction or gas fraction Durian, UPENN

  9. Main Features of Sheared foam • Initial elastic response (yield stress) • Flowing regimes: • Slow shear: “irregular” stress response • Fast shear: “smooth” flow BUBBLES PLAYS CENTRAL ROLE

  10. Definition of Terms: Part I T1 event: Neighbor switching

  11. Definition of Terms: Part II Outer barrier moves with V flowing stress Ds elastic Dr Strain:g =Dx/Dr Strain Rate: dg/dt = v/Dr Viscosity:h = stress/(strain rate) strain Shear stress:sxy = F/L (two-dimensions) Stress drop:Ds

  12. Apparatus

  13. Schematic of Apparatus Inner radius ri: 3.84 cm Outer radius ro: 7.43 cm Area fraction: 0.95 Boundary conditions: no slip at both walls, but inner cylinder is free to move.

  14. Basic measurements • Stress on inner cylinder • Individual bubble motions • Automatic tracking gives average properties and topological rearrangements

  15. Bubble Motions

  16. One problem in continuum mechanics: What is a solid and a fluid? (Is there a simple understanding of a broad range of collective behavior?)

  17. Continuum Facts: Part I Couette Geometry: average stress, s, proportional to 1/r2 Sample stress curve Yield Stress shear rate is a continuous function of r.

  18. Effective Viscosity: stress/(strain rate)

  19. Shear Discontinuity Yield stress fluid “solid” Power law fluid J. Lauridsen, G. Chanan, M. Dennin, PRL, 2004

  20. Another view Exponential

  21. Is this a “phase” transition? THREE DIMENSIONAL Coussot, Raynaud, et al., PRL 88, 218301 (2002)

  22. What are the questions? • Correct description of fluctuations: • Statistical mechanics? • Chaos theory? • Spatial fluctuations? • Something else?

  23. How can we understand the average velocity behavior? • Why does it converge so quickly? • What sets the critical radius? • What is the role of T1 events?

  24. T1Events

  25. # of neighbors • distribution of neighbors • changes in distribution • size separation? • ordering/disorder?

  26. Conclusions • Even continuum mechanics has interesting physics questions left. • We need to inspire our students with exciting, challenging QUESTIONS, not just elegant past solutions. • One such question – Can we describe collective behavior based on simple principles?

  27. Thanks to … Michael Twardos John Lauridsen Gregory Chanan Yuhong Wang Kapil Krishan Funded by: Department of Energy grant DE-FG02-03ED46071, Sloan Foundation, Petroleum Research Fund, and UCI UROP

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