Plates20 - 12.005 Lecture Notes 20 Plates Rock rheology...

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12.005 Lecture Notes 20 Plates Rock rheology function of T ; T increases with depth. ± Thin region near surface remains elastic on geologic times. Below this, mantle behaves as a viscous fluid. Plate theory: Assume plate thickness h L , with L a characteristic length scale 3-D equations simplify Applications: Figure 20.1 Trench Subduction Zone Folding Laccolith Magma Fore-arc bulge λ Seamount Loading Figure by MIT OCW.
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Figure 20.2 “Fiber stresses” large compare to tractions applied to surfaces. Neutral surface – smooth and centered Kirchoff’s assumption – approximate, but useful. 0 yy yx yz σ σ σ = = = , xx zz σ σ linearly through 2 2 h h y or every straight line originally perpendicular to neutral plane remains straight and perpendicular More accurate formulations lead to nonlinear coupled equations, not solvable analytically. y x h Neutral surface Main Feature Fibers compressed Fibers extended z } } Figure by MIT OCW.
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To derive plate equations – consider the following figures: Figure 20.3 Figure 20.4 V – shear force / unit length P – horizontal force / unit length
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