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This book shows how continuum mechanics can be extended to describe phenomena that lie beyond the scope of classical mechanics and traditional constitutive theory. In many applications, the classical translational degrees of freedom are not sufficient. Rotational motion, internal variables, particle density, and physics-based concepts from mixture theory provide additional degrees of freedom that are needed to capture the behavior of complex materials. The book also introduces several recently developed concepts, including a producible microinertia tensor field that allows structural changes to be described directly at the continuum level.

Besides the classical balance laws, the book discusses generalized balance equations, such as strain balances, and their role in continuum modeling. It also presents continuum formulations for electromagnetic phenomena and shows how these can be combined with mechanical descriptions within a common theoretical framework. The relation between microscopic models and macroscopic continuum theories is examined, and homogenization methods are used to establish the connection between these different levels of description.

The concepts presented are applied to a broad range of problems, including granular materials, damage and fracture, phase transitions, and electrodynamic phenomena. The book is intended for researchers and graduate students in continuum mechanics, applied mathematics, physics, and engineering who are interested in modern extensions of continuum theory and their applications.