Modeling Random Short Nanofiber- and Microfiber-Reinforced Composites Using the Extended Finite-Element Method

Abstract

This manuscript presents the formulation and implementation of an extended finite-element method (XFEM) for random short fiber-reinforced composite materials. A new enrichment function is proposed to incorporate the effect of random fiber inclusions within the XFEM framework to eliminate the need of using finite-element meshes compliant with fiber inclusions. The motion of the fiber inclusions are modeled by constraining the deformation field along the domain of the fiber inclusions. Coupling the XFEM along with the new enrichment function and constraint equations formulate the elastic response of short fiber-reinforced composites. Numerical integration procedures are provided for accurate evaluation of the system response for fiber tips that lie on arbitrary positions within the problem domain. The performance of the proposed model is verified against the direct finite-element method.