Consistent control of energy dissipation in non-spherical particle contact via a structure-preserving formulation

Abstract: The control of energy dissipation in non-spherical particle contact remains an unresolved problem. Unlike spherical contact, where the interaction reduces to a one-dimensional normal oscillator, both the effective inertia and the effective stiffness depend on the evolving contact geometry, and the impact dynamics are intrinsically coupled across translational, rotational, and tangential directions. Classical damping formulations are therefore structurally incompatible with the contact dynamics they are intended to represent. This work addresses the problem from first principles. By projecting the dynamics onto contact degrees of freedom, the interaction is shown to be governed by an instantaneous contact dynamics with a configuration-dependent projected mass and intrinsic translational--rotational coupling. Building on the exact energy--phase transformation for monotone conservative contact, we show that consistent dissipation requires a unique damping structure aligned with the underlying contact energy. The analysis leads to two central consequences. First, the admissible damping law is not empirical but fixed by the harmonic structure revealed in transformed space. Second, the appropriate coefficient of restitution for non-spherical particles is the contact-point restitution $e_{cn}$, whereas the total energy restitution $e_E$ is a geometry-dependent outcome that includes coupling-induced energy transfer. Numerical evidence based on smooth single-contact impacts confirms the theory: the resulting formulation controls $e_{cn}$ consistently across impact configurations, while the apparent variability of $e_E$ follows directly from the coupled dynamics.