Minimum potential method appropriate to generate 2D RVEs of composites with high fiber volume fraction

Abstract

This work proposes a novel method, entitled minimum potential method, to generate Representative Volume Elements (RVEs) of unidirectional fibers composites with high fiber volume fractions (FVFs, generally ≥70.0%). In the proposed method, a given VF of random and periodic fibers are initially created within the matrix and the fiber overlap is allowed, and then the fiber overlap is gradually removed by adjusting the fiber centroids based on the principle of the minimum overall potential. In the process of fiber overlap removal, the fiber periodicity and the fibers completely or partly contained in the matrix are preserved. The overall potential of the fibers consists of fiber overlap potential, fiber position potential and fiber periodicity potential, and is minimized using the gradient descent method. The numerical implementation of the proposed method is detailed, and the RVEs of the composites with various FVFs are generated. Through the probability distribution function of the nearest neighbor distance, the cumulative probability distribution function of the nearest neighbor orientation angle, the second-order intensity and pair correlation functions, the fiber distribution in the generated RVEs is analyzed, and the results indicate a completely random distribution of the fibers in the generated RVEs. Comparing with the available experimental test, the literature and the Double-Inclusion model, the proposed method to generate RVEs of the composites with high FVFs is validated.