For a unidirectional composite with a rectangular fiber array (Figure 3.18), use the equations of elasticity to set up the displacement boundary value problem for the determination of the transverse modulus, \(E_{2}\). That is, find the governing partial differential equations for displacements \(u\) and \(v\) in the RVE, and specify the boundary and continuity conditions. Assume plane strain \(\left(\varepsilon_{z}=0\right)\). Do not attempt to solve the equations, but explain briefly how \(E_{2}\) would be found. Assume that both fiber and matrix are isotropic.

FIGURE 3.18