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Departamento de Gravitación y Teoría de CamposSeminarios 2011 |
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Instituto de Ciencias Nucleares, UNAM |
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Departamento de Gravitación y Teoría de CamposSeminarios 2011 |
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Instituto de Ciencias Nucleares, UNAM |
Jueves 8 de Diciembre, a las 17:00 hrs en la sala de seminarios del ICN
James Hanna (University of Massachusetts)
Covariant elasticity with strains or constraints?
| Continuum mechanics makes many people very angry and stressed, in part due to disagreements over method, technique, and notation. This talk will be a modest attempt to demonstrate that there are at least two useful ways to think about the elasticity of thin objects, in particular if one is not the progenitor of either world-view. As merely an impartial practitioner, I will present a pair of examples. The first is a programming problem, namely that of making a general surface by imposing a two-dimensional "target metric" or "eigenstrain" on a thin gel sheet. Nontrivial sheet thickness, or nonexistence of a smooth immersion of this metric, leads to significant equilibrium strains and a complicated post-buckled global balance of stretching and bending. Here a stress is constructed from the mid-surface strains and curvatures, and vanishes if both strains and thickness vanish. The second example involves the motion of a string or chain, a curve on which strains are set to zero with a Lagrange multiplier field whose form provides much qualitative information about the dynamics, whether viscous or inertial. I will show that, in an inertial regime, gradients in this field may lead to startling macroscopic structures in the presence of microscopic noise. Here a stress is identified with the multiplier. As both approaches seem to work just fine, I conclude that one should refrain from imposing one's stress on other people. |
