Discontinuous deformation analysis for ellipsoids using cone complementary formulation

Abstract

Abstract A new computational framework for discontinuous deformation analysis (DDA) of ellipsoidal particles is developed by taking full advantage of the geometric convexity of the ellipsoid. To identify the contact points and contact directions between ellipsoidal bodies analytically and efficiently, a semi-analytic geometry iteration (SAGI) algorithm is proposed based on parametric equation of the ellipsoid, which is also extended to cylindrical and conical boundaries. The controlling equations of motion of the bodies are established in the context of discontinuous deformation analysis. To reinforce the constraint of frictional contacts in the discrete system, a linearized cone complementarity formulation is proposed to solve the contact forces using a fixed point iteration algorithm, which is the key ingredient to conserve energy, linear and angular momentums in the new numerical framework. The accuracy, computational efficiency, and application prospects of the proposed methodologies are demonstrated through some numerical examples.