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.

Y. T. Feng is Professor at the Zienkiewicz Institute for Modelling, Data and AI, Swansea University, UK, where he has worked for more than three decades. He holds a first degree in Mechanical Engineering and a PhD in Computational Mechanics. His research spans computational engineering, the finite and discrete element methods, the mechanics of multi-fracturing solids, and the modelling of complex particulate systems.

For more than two decades, his work has centred on the discrete element method and particle contact mechanics, with particular emphasis on the fundamental and theoretical aspects of the field. He has made original contributions to energy-conserving contact theory, contact modelling for arbitrarily shaped particles, coupled particle–fluid and particle–thermal methods, and multiscale particulate modelling.

Professor Feng has published more than 250 peer-reviewed papers and delivered more than ten plenary and keynote lectures at major international conferences. He leads an internationally recognised research group working on finite element modelling of multi-fracturing solids and discrete element modelling of discontinuous systems. He remains personally and actively engaged in frontier research in the discrete element method.

His current research includes a general contact theory for non-spherical discrete elements, coarse-graining methods for large-scale particulate systems and data-driven modelling of granular media. This book consolidates and extends his long-term research on energy-conserving contact mechanics into a unified theoretical and computational framework for discrete element formulations.