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Unformatted text preview: 12.005 Lecture Notes 15 Elasticity So far: Stress angle of repose vs accretionary wedge → → Strain reaction to stress → but how? Constitutive relations τ ij = τ ij ε kl ( ) ; ε ij = ε ij τ kl ( ) For example, Elasticity Isotropic Anisotropic Viscous flow Isotropic Anisotropic Power law creep Viscoelasticity Trade offs: simplicity ↔ realism constant variable isotropic anisotropic elastic, viscous viscoelastic history independent history dependent Tensors Most physical quantities that are important in continuum mechanics like temperature, force, and stress can be represented by a tensor. Temperature can be specified by stating a single numerical value called a scalar and is called a zeroth-order tensor. A force, however, must be specified by stating both a magnitude and direction. It is an example of a first-order tensor. Specifying a stress is even more complicated and requires stating a magnitude and two directions—the direction of a force vector and the direction of the...
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- Fall '10