“…The bulk elastic modulus of the ultrasonic cast Al 6061 –WS 2 composites was analytically calculated using continuum micromechanics Hashin–Shtrikman lower bound model. [ 35,36 ] This model is appropriate for isotropic composites reinforced by randomly distributed particles, as observed in the present case (Figure 5). According to this model, the elastic modulus of the composite is given bywhere E (GPa) is the elastic modulus, V is the volume fraction, and the subscripts c, m, and r stand for composite, matrix, and reinforcement, respectively.…”