Systems and methods are described for performing mechanical analysis of particulate systems by describing particle morphology of particles within the system using Non-Uniform Rational Basis Spline (NURBS). One embodiment includes generating a NURBS description for the particle morphology of a plurality of particles within a particulate system, determining contact points between at least two particles based on the NURBS description, determining a magnitude of the contact between the at least two particles based on the NURBS description, determining normal forces and associated moments based upon the contact points and the magnitude of the contact between the at least two particles, determining tangential forces and associated moments based upon the contact points and the magnitude of the contact between the at least two particles, and performing mechanical analysis of the particulate system based on the contact between the at least two particles and the resulting forces and associated moments.