1. (Linear elastic isotropic material) Derive G = E / 2 (1+v) for linear elastic isotropic materials. E, G (or according to the Bower textbook), and v are Young’s modulus, shear modulus, and Poisson’s ratio, respectively.
2. (Constitutive relationship) Derive constitutive relationship under the plane strain and stress conditions (i.e., derive expressions in Sec. 3.2.3. in the Bower book from the full 3D expressions).
3. (Constitutive relationship) Given a state of strain at a point in an isotropic material,
é 0.001 0.001 -0.002 ù
e = ê 0.001 0 0.005 ú
ê-0.0020.005 0 ú ëû
Determine stress tensor. Assume E = 200 GPa and v = 0.3.
4. (Coordinate transformation) An equi-triangular strain rosette is mounted on the surface of a body as shown below.
The strain gauge readings are:
𝜀0° = 0.005,
Out: Oct. 26, 2021 Due: Nov. 2, 2021
𝜀60° = 0.002,
𝜀120° = −0.001
The material properties are E = 200 GPa and v = 0.3. Find the stress tensor along the xy axes at point O.
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