The increased utilization of composite materials in recent years and concomitant struggles in optimizing their properties while avoiding unrequested properties directed attention to accurate material design. Due to their cost efficiency in parameter studies, Finite Element (FE) simulation could play an important role, if appropriate material models are evolved. In this work, quantum mechanical tunnelling is implemented as a user element in numerical simulations to investigate the electric properties of a composite of insulating matrix material (polyetherimide) and conducting spherical inclusions (exfoliated, unfunctionalized graphite). While the algorithm's functionality is proven by accordance with determined correlation length exponents with theoretical literature values, the utilization of a homogenization technique leads to reasonable effective conductivities of the composite material acknowledging the quality of the algorithm.