A solid with Young's modulus E = 70 GPa and Poissonâ's ratio = 0.3 is in a state of plane strain parallel to the xy-plane. The in-plane strain components are measured as follows: Epsilon-xx = 0.007, epsilon-yy = -0.008, and epsilon-xy = 0.02.
(a) Compute the principal strains and corresponding principal strain directions.
(b) Compute the stresses including szz, corresponding to the above strains.
(c) Determine the principal stresses and corresponding principal stress directions. Are the principal stress and principal strain directions the same?
(d) Show that the principal stresses could have been obtained from the principal strains using the stress-strain relations.
(e) Compute the strain energy density using the stress and strain components in xy-coordinate system.
(f) Compute the strain energy density using the principal stresses and principal strains.