A sequential addition and migration method for generating microstructures of short fibers with prescribed length distribution

We describe an algorithm for generating fiber-filled volume elements for use in computational homogenization schemes. The algorithm permits to prescribe both a length distribution and a fiber-orientation tensor of second order, and composites with industrial filler fraction can be generated. Typically, for short-fiber composites, data on the fiber-length distribution and on the volume-weighted fiber-orientation tensor of second order is available. We consider a model where the fiber orientation and the fiber length distributions are independent, i.e., uncoupled. We discuss the use of closure approximations for this case and report on identifying the describing parameters of the frequently used Weibull distribution for modeling the fiber-length distribution. We discuss how to integrate these procedures in the Sequential Addition and Migration algorithm, developed for fibers of equal length, and work out algorithmic modifications accounting for possibly rather long fibers. We investigate the capabilities of the introduced methodology for industrial short-fiber composites, demonstrating the rather low dispersion of the effective elastic moduli for the generated unit cells.