Hw2sol - Materials Science and Engineering 765 mechanical behavior of materials Spring 2005 Homework 2 solutions(including revisions and hints and

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1/4 Anderson G4:Users:peterand:Central files:Courses:MSE 765:2005:hw2sol.doc Materials Science and Engineering 765 mechanical behavior of materials Spring 2005 Homework 2 (including revisions and hints 4/21/05) and solutions Due: At 5pm on Monday, April 25, 2005. Please show all work necessary to arrive at your answers. Slide the homework under the FL 345 office door if closed. 1. Symmetry of C ij The strain energy stored in elastic materials is independent of the path of loading. Consider a composite material with orthotropic symmetry and which deforms in a linear-elastic manner at small stress. Show that C 12 = C 21 . To do so, compute the elastic energy stored in the material using two different paths: path A involves deformation from (0, 0) to ( ε 1 , 0) and then from ( ε 1 , 0) to ( ε 1 , ε 2 ) while path B involves deformation from (0, 0) to (0, ε 2 ) and then from (0, ε 2 ) to ( ε 1 , ε 2 ). Show that if the stored elastic energy is the same in both cases, then C 12 = C 21 . 2. The effect of cracking on the symmetry of C ij Suppose that the composite material above is overloaded, so that internal delamination (cracking) occurs. Is C 12 = C 21 for the damaged material? Discuss
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This note was uploaded on 07/17/2008 for the course MSE 765 taught by Professor Anderson during the Spring '05 term at Ohio State.

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Hw2sol - Materials Science and Engineering 765 mechanical behavior of materials Spring 2005 Homework 2 solutions(including revisions and hints and

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