EN0175-14

EN0175-14 - EN0175 10 / 19 / 06 Mechanical Behavior of...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This note was uploaded on 01/10/2010 for the course EN 0175 taught by Professor Huajiangao during the Spring '06 term at Brown.

Page1 / 7

EN0175-14 - EN0175 10 / 19 / 06 Mechanical Behavior of...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online