Description
1. [20 points] (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. [30 points] (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. [20 points] (Constitutive relationship) Given a state of strain at a point in an isotropic material,
e =
0.001 0.001 -0.002
0.001 0 0.005
-0.002 0.005 0
é
ë
ê
ê
ê
ù
û
ú
ú
ú
Determine stress tensor. Assume E = 200 GPa and v = 0.3.
4. [30 points] (Coordinate transformation) An equi-triangular strain rosette is mounted on the
surface of a body as shown below.
AA 530: SOLID MECHANICS Out: Oct. 26, 2021
HW #3 Due: Nov. 2, 2021
2
The strain gauge readings are:
𝜀0° = 0.005, 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.
