Computation of the bounds on the elastic moduli of a fiber-reinforced composite by Monte Carlo simulations

Bounds on the effective elastic moduli of a fiber-reinforced composite are studied. The composite is composed of infinitely long, parallel, equal-sized circular cylinders (fibers) randomly embedded in a matrix. Based on the variational principles and by employing the cylindrical inclusion solutions as trial functions, the bounds are determined through Monte Carlo simulations. Comparisons are made with the second-order and third-order perturbation bounds. Because the shape of the inclusion has been explicitly taken into consideration, it is found that the bounds computed by the present approach are the sharpest in terms of the width of the bound pair. Specifically, when the fibers are stiffer than the matrix, the present lower bounds coincide with the second-order lower bounds at low concentrations and are slightly higher than the second-order lower bounds at high concentrations, while the upper bounds are far below the corresponding second-order and third-order perturbation bounds. In many cases, the present bound pair is very close and thus provides accurate prediction on the effective properties of this class of composites.