Response to the following problems:
1. Draw a representative volume element (RVE) for an epoxy matrix filled with cylindrical steel rods arranged in a rectangular array. Compute the volume fraction Vf as a function of the fiber diameter df and the spacing between the centers of the fibers ax and ay in the two directions (center to center).
2. Write a definition for Representative Volume Element. Draw a set of fibers in an hexagonal array: six fibers at the vertices of an hexagon plus one in the center, with the fibers touching each other. Draw the smallest RVE for this arrangement. Compute the fiber volume fraction.