Role of exterior statistics-based boundary conditions for property-based statistically equivalent representative volume elements of polydispersed elastic composites

The property-based statistically equivalent RVE or P-SERVE has been introduced in the literature as the smallest microstructural volume element in non-uniform microstructures that has effective material properties equivalent to those of the entire microstructure. An important consideration is the application of appropriate boundary conditions for optimal property-based statistically equivalent representative volume element domains. The exterior statistics-based boundary conditions have been developed, accounting for the statistics of fiber distributions and interactions in the domain exterior to the property-based statistically equivalent representative volume element. This paper is intended to validate the efficacy of the exterior statistics-based boundary condition-based property-based statistically equivalent representative volume elements for evaluating homogenized stiffnesses of a unidirectional polymer matrix composite with a polydispersed microstructure characterized by nonuniform dispersion of carbon fibers of varying sizes in an epoxy matrix. Experimental tests and microstructural characterization of the polymer matrix composite are conducted for calibration and validation of the model. Statistically equivalent microstructural volume elements are constructed from experimental micrographs for direct numerical simulations. The performance of the property-based statistically equivalent representative volume element with exterior statistics-based boundary conditions is compared with other boundary conditions, as well as with the statistical volume elements. The tests clearly show the significant advantages of the exterior statistics-based boundary conditions in terms of accuracy of the homogenized stiffness and efficiency.