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Fundamentals of Continuum Mechanics provides a clear and rigorous presentation of continuum mechanics for engineers, physicists, and materials scientists. This book uses a first-principles-based approach to continuum-level characterization, design, and modeling. While emphasizing modern materials research, it also devotes special attention to constrained materials (for example, incompressible fluids) and the continuum characterization of TEMM smart materials. A wealth of carefully chosen examples and exercises illuminate the subject matter and facilitate self-study. It uses direct notation for a clear and straightforward math presentation, leading to better understanding of the underlying physics. It covers high-interest research areas such as constrained materials and characterization of smart materials used in intelligent systems and structures. It offers a unique approach to covering thermo mechanical constraints, based on the authors' own research.