You are given the following material properties for a stiff, particulate filler material (aggregate) and a lightweight (but not so stiff) matrix (binder). E_agg= 30GPa, E_matrix =1.55 GPa, p_agg= 2400 kg/m3, P_matrix=1050 kg/m3
For your particular application, it is important to have a stiff material but also one that is lightweight. In fact, the optimum stiffness to unit weight ratio is 11.1 MPa/kg/m^3. Determine the optimum volume fractions (0 to 1) for the matrix and the particulate if the composite stiffness behaves according to the following models:
a) series
b) parallel
c) Hirsch with x = 0.2, x = 0.4, x = 0.8