Geometric Contact Mechanics for Particle Systems

This book, for the first time, establishes particle contact mechanics as a branch of modern mechanics. It moves beyond empirical formulations and places the discrete element method (DEM) on the rigorous footing of classical analytical mechanics. On this foundation, the Energy-Conserving Contact (ECC) principle formulates contact as a geometric variational structure on configuration space: scalar potentials generate consistent interactions, the Contact Kinematic Identity governs geometric evolution, and the conservative dynamics take Hamiltonian form. The book develops three rigid ECC models, the Enriched Spectral Discrete Element Method (eS-DEM), Instantaneous Contact Dynamics with breathing contact inertia, an exact energy–phase transformation, a universal damping law and adaptive damping for 3D contact. The book is written for researchers, research students, engineers and code developers seeking a coherent theoretical and computational foundation for modelling particulate systems.