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Unformatted text preview: EN0175 10 / 19 / 06 Mechanical Behavior of Solids Linear Elastic solids E = (1D) kl ijkl ij C = or kl ijkl ij S = (3D) where C is sometimes called the stiffness tensor and S is sometimes called the compliance tensor. Both of them are 4 th order elastic moduli tensors. Symmetry of elastic moduli tensors: jikl ijkl C C = , (minor symmetry) ijlk ijkl C C = The minor symmetries reduce the independent elastic constants from 81 to 36. There is also a major symmetr in elastic moduli klij ijkl C C = , which reduces the number of independent elastic constants from 36 to 21. We use the concept of energy & work to demonstrate the major symmetry of C and S : u F , Assume an increment of displacement at the bar end, u u u + The work done by the applied load should equal to the stored energy in the material, ( ) V Al l A u F W = = = = = = V W w should be the stored elastic energy per unit volume, which is also called the strain energy density. ( ) w w = , = w , ( ) = d w 1 EN0175 10 / 19 / 06 Generalize to 3D S V f v t v ( ) ( ) V w V V u V u f V u f V u V u f S u n V u f S u t V u f S u t w V V ij ij V j i ij i V i j ij i V i V j i ij i V i i S j ij i V i i S i V S d...
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This note was uploaded on 01/10/2010 for the course EN 0175 taught by Professor Huajiangao during the Spring '06 term at Brown.
 Spring '06
 HUAJIANGAO

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