Machine generated contents note: 10.7. The Momentum 1.2. The Equilibrium Problem -- 1.3. Remarks About Equilibrium Boundary Problems -- 1.4. Variational Formulation of Equilibrium -- 1.5. Isotropic Elastic Materials -- 1.6. Homogeneous Deformations -- 1.7. Homothetic Deformation -- 1.8. Simple Extension of a Rectangular Block -- 1.9. Simple Shear of a Rectangular Block -- 1.10. Universal Static Solutions -- 1.11. Constitutive Equations in Nonlinear Elasticity -- 1.12. Treolar's Experiments -- 1.13. Rivlin and Saunders' Experiment -- 1.14. Nondimensional Analysis of Equilibrium -- 1.15. Signorini's Perturbation Method for Mixed Problems -- 1.16. Signorini's Method for Traction Problems -- 1.17. Loads with an Equilibrium Axis -- 1.18. Second-Order Hyperelasticity -- 1.19. A Simple Application of Signorini's Method -- 1.20. Van Buren's Theorem -- 1.21. An Extension of Signorini's Method to Live Loads -- 1.22. Second-Order Singular Surfaces -- 1.23. Singular Waves in Nonlinear Elasticity -- 1.24. Principal Waves in Isotropic Compressible Elastic Materials -- 1.25. A Perturbation Method for Waves in Compressible Media -- 1.26. A Perturbation Method for Analyzing Ordinary Waves in Incompressible Media -- 2.1. Preliminary Considerations -- 2.2. Kinematics of a Micropolar Continuum -- 2.3. Mechanical Balance Equations -- 2.4. Energy and Entropy -- 2.5. Elastic Micropolar Systems -- 2.6. The Objectivity Principle -- 2.7. Some Remarks on Boundary Value Problems -- 2.8. Asymmetric Elasticity -- 3.1. Introduction -- 3.2. Velocity of a Moving Surface -- 3.3. Velocity of a Moving Curve -- 3.4. Thomas' Derivative and Other Formulae -- 3.5. Differentiation Formulae -- 3.6. Balance Laws -- 3.7. Entropy Inequality and Gibbs Potential -- 3.8. Other Balance Equations -- 3.9. Integral Form of Maxwell's Equations -- 4.1. Boundary Value Problems in Phase Equilibrium -- 4.2. Some Phenomenological Results of Changes in State -- 4.3. Equilibrium of Fluid Phases with a Planar Interface -- 4.4. Equilibrium of Fluid Phases with a Spherical Interface -- 4.5. Variational Formulation of Phase Equilibrium -- 4.6. Phase Equilibrium in Crystals -- 4.7. Wulff's Construction -- 5.1. The Problem of Continuous Casting -- 5.2. On the Evolution of the Solid-Liquid Phase Change -- 5.3. On the Evolution of the Liquid-Vapor Phase Change -- 5.4. The Case of a Perfect Gas -- 6.1. Balance Laws -- 6.2. Classical Mixtures -- 6.3. Nonclassical Mixtures -- 6.4. Balance Equations of Binary Fluid Mixtures -- 6.5. Constitutive Equations -- 6.6. Phase Equilibrium and Gibbs' Principle -- 6.7. Evaporation of a Fluid into a Gas -- 7.1. Integral Balance Laws -- 7.2. Electromagnetic Fields in Rigid Bodies at Rest -- 7.3. Constitutive Equations for Isotropic Rigid Bodies -- 7.4. Approximate Constitutive Equations for Isotropic Bodies -- 7.5. Maxwell's Equations and the Principle of Relativity -- 7.6. Quasi-electrostatic and Quasi-magnetostatic Approximations -- 7.7. Balance Equations for Quasi-electrostatics -- 7.8. Isotropic and Anisotropic Constitutive Equations -- 7.9. Polarization Fields and the Equations of Quasi-electrostatics -- 7.10. More General Constitutive Equations -- 7.11. Lagrangian Formulation of Quasi-electrostatics -- 7.12. Variational Formulation for Equilibrium in Quasi-electrostatics -- 8.1. An Evolution Equation for the Magnetic Field -- 8.2. Balance Equations in Magnetofluid Dynamics -- 8.3. Equivalent Form of the Balance Equations -- 8.4. Constitutive Equations -- 8.5. Ordinary Waves in Magnetofluid Dynamics -- 8.6. Alfven's Theorems -- 8.7. Laminar Motion Between Two Parallel Plates -- 8.8. Law of Isorotation -- 9.1. Ferromagnetism and Micromagnetism -- 9.2. A Ferromagnetic Crystal as a Continuum with an Interface -- 9.3. Variations in Surfaces of Discontinuity -- 9.4. Variational Formulation of Weiss Domains -- 9.5. Weiss Domain Structure -- 9.6. Weiss Domains in the Absence of a Magnetic Field -- 9.7. Weiss Domains in Uniaxial Crystals -- 9.8. A Variational Principle for Elastic Ferromagnetic Crystals -- 9.9. Weiss Domains in Elastic Uniaxial Crystals -- 9.10. A Possible Weiss Domain Distribution in Elastic Uniaxial Crystals -- 9.11. A More General Variational Principle -- 9.12. Weiss Domain Branching -- 9.13. Weiss Domains in an Applied Magnetic Field -- 10.1. Lorentz Transformations -- 10.2. The Principle of Relativity -- 10.3. Minkowski Spacetime -- 10.4. Physical Meaning of Minkowski Spacetime -- 10.5. Four-Dimensional Equation of Motion -- 10.6. Integral Balance Laws -- 10.7. The Momentum
Summary:
"This book offers a broad overview of the potential of continuum mechanics to describe a wide range of macroscopic phenomena in real-world problems. Building on the fundamentals presented in the authors' previous book, Continuum Mechanics using Mathematica±, this new work explores interesting models of continuum mechanics, with an emphasis on exploring the flexibility of their applications in a wide variety of fields. Specific topics. which have been chosen to show the power of continuum mechanics to characterize the experimental behavior of real phenomena, include: -Various aspects of nonlinear elasticity, including equilibrium equations and their variational formulation, nonlinear constitutive equations, existence and uniqueness theorems of Van Buren and Stoppelli, and Signorini's method with some extensions to live loads and acceleration waves. -A model of a continuum with a nonmaterial moving interface. -Mixture theory: The Gibbs Rule in a binary mixture. -Interaction between electric or magnetic fields with matter. -Continua in special relativity and relativistic interactions between matter and electromagnetic fields. Appendices are included to provide background information on topics such as surface geometry, first-order PDEs, and weak solutions to models. Mathematica± notebooks also accompanying the text are available for download at http://www.birkhauser.com/ 978-0-8176-4869-5. Aimed at advanced graduate students, applied mathematicians, mathematical physicists, and engineers, the work will he an excellent self-study reference or supplementary textbook in graduate-level courses focusing on advanced topics and research trends in continuum mechanics. "--Book jacket.
Series:
Modeling and simulation in science, engineering and technology
This resource is supported by the Institute of Museum and Library Services under the provisions of the Library Services and Technology Act as administered by State Library of Iowa.