Consider the following displacement field in a plane solid:

a. Compute the infinitesimal strain components \(\varepsilon_{x}, \varepsilon_{y}\), and \(\gamma_{x y}\). Is this a state of uniform strain?

b. Determine the principal strains and their corresponding directions. Express the principal strain directions in terms of the angles (in degrees) the directions make with the \(x\) axis.

c. What is the normal strain at \((x, y)\) in a direction \(45^{\circ}\) to the \(x\) axis?

u(x,y)=0.4-0.09x+0.06y, v(x,y) = 0.6+0.04x+0.15y.