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Unformatted text preview: 4. Justify our step in the derivation of the local form of the rst law of thermodynamics for deforming bodies where we assumed: u i ij = ij ij u j i.e., demonstrate that the double scalar product (full contraction) of a symmetric tensor A = A T , with an arbitrary tensor B amounts to contracting A with the symmetric part of B : 1 B sym = B + B T 2 (Hint: Decompose B into its symmetric and antisymmetric parts and show that the contraction of a symmetric tensor A with the antisymmetric part of B : 1 B antisym = B B T 2 is zero. 5. Obtain the relationships between the engineering elastic constants ( E, ) and the Lam e constants ( 1 , 2 ). 2...
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This note was uploaded on 11/07/2011 for the course AERO 16.21 taught by Professor Dffs during the Fall '10 term at MIT.
 Fall '10
 dffs

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