Discontinuous deformation analysis for SH-body

Based on micro X-ray computed tomography data, the spherical harmonic (SH) function can be employed to reconstruct the nature sand particle, referred to as SH-body. Thus, the sand particle micromorphology can be described by analytic functions. Thanks to these analytic functions, the closest points between SH-bodies for contact detection can be identified by using a second-order geometric iteration algorithm. Meanwhile, the equivalent variational inequality is formulated to determine the inter-particle contact forces for the three-dimensional cases. To capture the kinematics and kinetics of SH-bodies, this study deduces discontinuous deformation analysis (DDA) formula based on the principle of minimum potential energy. The study establishes a framework for simulating the dynamic behavior of SH-bodies, and the proposed methodology is validated through numerical examples.