Using the result from Problem 6.2, develop an expression for the longitudinal modulus of the RVE shown in Figure 6.2a that includes the effect of the matrix material at the fiber ends.

Problem 6.2

A short-fiber composite is to be modeled using the RVE in Figure 6.2b. Assuming that the matrix is rigid plastic in shear but that both the fiber and matrix are elastic in extension, develop an equation for the longitudinal modulus of the RVE. What values of the longitudinal modulus does the model give as the fiber length becomes-very large or very small?

Figure 6.2b

Figure 6.2a

(b) Matrix Fiber D