The Effective Elastic Modulus of Fiber-Reinforced Composites

This paper presents an application of the boundary element method to model the mechanical response of fully three-dimensional, multiparticle, whisker (or short-fiber-reinforced) composites. In the physical systems examined, up to 64 rigid rod-like particles are embedded in an elastic matrix, with the limit in the number of particles being imposed by the limitations in computer memory. The reduction in dimensionality achieved by the boundary element method, combined with the use of modern supercomputers, makes feasible the numerical modeling of very complex geometrical configurations of particles. This frees the analysis from the restrictive assumption of macroscopic homogeneity that is typical in previous analytical or numerical work. Results for multiparticle, three-dimensional systems are compared with two-dimensional particle-in-cell models. With the fully three-dimensional models, we analyze the effects of the particle aspect ratio, volume fraction, degree of alignment and spatial configuration in a system that simulates a bar tensile test. The composite stiffness depends on the placement of particles, with each configuration resulting in a different overall value of stiffness. Therefore, numerical "measurements" of the effective properties of the composite scatter about a mean, the magnitude of which increases with increasing volume fraction of particles. Over the range of our calculations, the mean effective modulus of the composite increases with volume fraction, as anticipated. However, the scatter in the calculated moduli is seen to decrease with an increase in the number of particles when the rest of the parameters are held constant. Composites with fibers aligned in the tensile direction yielded the highest effective moduli. At a fixed concentration, the effective stiffness of the composite increases rapidly with the aspect ratio of the reinforcing rods.