Question

Problem 4: A short-fiber composite is to be modeled using the RVE in the figure below. 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? (a and b are comparable and much smaller than L.) Matrix Fiber

Answer 1

Answer! distauce foom The d'agram a Eb are comparable a eb much &imilar Thau b (x - dinection) normal stoes stres g Chaug Ju shear stoel Ceuyh of differeutdal eleumeut :dx The directien of x SFx - (ot do) xa xb-6xa xb -2(2X (atb) xdx -) ab + ab(dr)-cab- (2ta+276) dx =0 Gabtab (dr) - ab - (2 7a+ 206) dx=0 dr dx 2T (a 4b) ab