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HW6 - AE 321 – Homework#6 Due Friday Chapter 4 Material...

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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 μ ¢ ij + £¤ ij ¢ kk , where £ , μ are the Lamé moduli, show that E ¡ ij = 1 + ¢ ( ) £ ij ¤ ¢¥ ij £ kk , where E , ¤ are the Young’s modulus and Poisson’s 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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HW6 - AE 321 – Homework#6 Due Friday Chapter 4 Material...

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