Figure 3.15 shows an RVE for an elementary mechanics of materials model of the same type as shown in Figure 3.7, but with transverse deformation along the 2 direction prevented by rigid supports along the top and bottom edges. For an applied longitudinal normal stress as shown in Figure 3.15, find a micromechanics equation for the longitudinal modulus \(E_{1}\). Do not neglect the Poisson strains in the general derivation, and show what happens to the general equation for \(E_{1}\) when the Poisson's ratios for composite, fiber, and matrix are all equal.

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Matrix 2 1 Fiber Matrix FIGURE 3.15 RVE for elementary mechanics of materials model with rigid supports that prevent transverse deformation.