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This contributed volume explores the applications of various topics in modern differential geometry to the foundations of continuum mechanics. In particular, the contributors use notions from areas such as global analysis, algebraic topology, and geometric measure theory. Chapter authors are experts in their respective areas, and provide important insights from the most recent research. Organized into two parts, the book first covers kinematics, forces, and stress theory, and then addresses defects, uniformity, and homogeneity. Specific topics covered include:
Part I: Kinematics, Forces, and Stress Theory.- Manifolds of Mappings for Continuum Mechanics.- Notes on Global Stress and Hyper-Stress Theories.- Applications of Algebraic Topology in Elasticity.- De Donder Construction for Higher Jets.- Part II: Defects, Uniformity, and Homogeneity.- Regular and Singular Dislocations.- Homogenization of Edge-Dislocations as a Weak Limit of de-Rham Currents.- A Kinematics of Defects in Solid Crystals.- Limits of Distributed Dislocations in Geometric and Constitutive Paradigms.- On the Homogeneity of Non-Uniform Material Bodies.
Description
This contributed volume explores the applications of various topics in modern differential geometry to the foundations of continuum mechanics. In particular, the contributors use notions from areas such as global analysis, algebraic topology, and geometric measure theory. Chapter authors are experts in their respective areas, and provide important insights from the most recent research. Organized into two parts, the book first covers kinematics, forces, and stress theory, and then addresses defects, uniformity, and homogeneity. Specific topics covered include:
