A finite deformation method for discrete modeling: particle rotation and parameter calibration

We present a finite deformation method for 3-D discrete element modeling. In this method particle rotation is explicitly represented using quaternion and a complete set of interactions is permitted between two bonded particles, i.e., normal and tangent forces, rolling and torsional torques. Relative rotation between two particles is decomposed into two sequence-independent rotations, such that an overall torsional and rolling angle can be distinguished and torques caused by relative rotations are uniquely determined. Forces and torques are calculated in a finite deformation fashion, rather than incrementally. Compared with the incremental methods our algorithm is numerically more stable while it is consistent with the non-commutativity of finite rotations. We study the macroscopic elastic properties of a regularly arranged 2-D and 3-D lattice. Using a micro-to-macro approach based on the existence of a homogeneous displacement field, we study the problem of how to choose the particle-scale parameters (normal, tangent, rolling and torsional stiffness) given the macroscopic elastic parameters and geometry of lattice arrangement. The method is validated by reproducing the wing crack propagation and the fracture patterns under uniaxial compression. This study will provide a theoretical basis for the calibration of the DEM parameters required in engineering applications.