A solid with Young's modulus \(E=70 \mathrm{GPa}\) and Poisson's ratio \(=0.3\) is in a state of plane strain parallel to the xyplane. The inplane strain components are measured as: \(\varepsilon_{x x}=\) \(0.007, \varepsilon_{y y}=-0.008\), and \(\gamma_{x y}=0.02\).

a. Compute the principal strains and corresponding principal strain directions.

b. Compute the stresses, including \(\sigma_{z z}\), 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 the principal stresses could have been obtained from the principal strains using the stressstrain relations.

e. Compute the strain energy density using the stress and strain components in the xy coordinate system.

f. Compute the strain energy density using the principal stresses and principal strains.