On the Influence of the Fiber Curvature on the Stiffness of Long Fiber Reinforced Composites

The degree of curvature of fiber inclusions in fiber-reinforced composites impacts the elastic properties of the composite, butnumerical studies of this effect are limited by the lack of efficient microstructure generators with fiber curvature control. Wepropose an extension to the fused Sequential Addition and Migration algorithm (Int. J. Numer. Methods Eng., 125(22), e7573,2024) to allow for the direct control of the average fiber curvature. To this end, we prescribe an averaged curvature parameterfor the entire microstructure, while also constraining local curvature for every fiber to a maximum value. While local curvature isunambiguously defined, the choice of the averaged curvature parameter is not obvious. We introduce as a novel curvature measurethe deviation from straight curve (DSC), which computes as the trace of the local second-order fiber orientation tensor’s covariancefor a single fiber. Averaging this over all fibers leads to a scalar averaged curvature parameter. Using this parameter, we definean optimization procedure for generating curved-fiber reinforced microstructures. We compare the microstructure generationcapabilities of the proposed extension with the prior algorithm without curvature control and find that the extended algorithmis capable of realizing a significantly wider spectrum of curvatures. ... mehrFinally, we study the influence of fiber curvature on elasticproperties, and find that for an example composite of glass-fiber reinforced polypropylene, increased fiber curvature leads to areduction of the Young’s modulus by as much as 10%.