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Unformatted text preview: AE 321 Homework #6 Due: Friday October 24, 2008 Chapter 4: Material Behavior 1. (Old exam question) (a) Determine the slope of the x vs. x curve in the elastic range if an isotropic homogeneous material is tested under the following stress state: x = 2 y = 3 z (b) Show that for a linear, elastic, isotropic homogeneous solid, strain energy density W can be expressed in terms of stresses as: W = 1 + 2 E ij ij 2 E k k ( ) 2 2. For a linearly elastic isotropic material starting from ij = 2 ij + ij kk , where , are the Lam moduli, show that E ij = 1 + ( ) ij ij kk , where E , are the Youngs modulus and Poissons ratio, respectively. 3. (a) Show that the principal axes for stress and strain coincide for a linearly elastic isotropic material. (b) Under what condition do the principal axes for stress and strain coincide for an orthotropic solid? 4. This exercise is based on the laboratory demonstrations that you had. Data for three tension 4....
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This note was uploaded on 03/07/2011 for the course AE 311 taught by Professor Dutton,j during the Spring '08 term at University of Illinois, Urbana Champaign.
- Spring '08