Problem 2, 17pts

An isotropic elastic body ( E_{y} = 207GPa ; p=79.2GPa) has a uniform state of stress given by:

[T] = [[100, 40, 60], [40, - 200, 0], [60, 0, 200]] (MPa)

(a) What are the strain components? Use the infinitesimal strain.

(b) What is the total change of volume for a five-centimeter cube of the material?

Problem 3, 18pts

For the following displacement fields in cylindrical coordinates:

(1) u_{r} = u_{theta} = 0 u_{x} = A + B * r ^ 2

(2) sint/r. u_{theta} = u_{z} = 0

(3) u_{r} = r ^ 2 * sin theta / 2 u_{theta} = r ^ 2 * cos theta / 2 u_{z} = 0

(a) Calculate the deformation gradient F.

(b) Calculate the Green Lagrange E.

(c) Calculate the infinitesimal strain E.