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.

Elena N. Vilchevskaya’s research focuses on mechanical modeling, with an emphasis on general and applied micromechanics, mechanochemistry, and biomechanics. She was working as a Leading Scientist at the Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences and as a Professor at the Department of Physics and Mechanics, St. Petersburg State Polytechnic University. Most recently she was awarded a Mercator Followship by the German Research Foundation (DFG) and is acting as a Guest Professor at Technische Universität Berlin.

Wolfgang H. Müller’s research focuses on theoretical engineering and materials science, with an emphasis on the mechanics and modeling of materials and structures. After appointments as a Lecturer of Structural Engineering at Paderborn University (Germany), he became a Professor of Mechanical Engineering at Heriot-Watt University in Edinburgh (UK) and finally a Full Professor of Continuum Mechanics and Constitutive Theory at Technische Universität Berlin.

Elena A. Ivanova’s research focuses on continuum mechanics with an emphasis on generalized continua and their application to modeling of physical phenomena. She is a Professor at the Department of Theoretical Mechanics and Mathematical Physics, Peter the Great St. Petersburg Polytechnic University, and a Leading Scientist at the Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences.