Opis: Advanced Mechanics of Continua - Karan Surana

Explore the Computational Methods and Mathematical Models That Are Possible through Continuum Mechanics Formulations Mathematically demanding, but also rigorous, precise, and written using very clear language, Advanced Mechanics of Continua provides a thorough understanding of continuum mechanics. This book explores the foundation of continuum mechanics and constitutive theories of materials using understandable notations. It does not stick to one specific form, but instead provides a mix of notations that while in many instances are different than those used in current practice, are a natural choice for the information that they represent. The book places special emphasis on both matrix and vector notations, and presents material using these notations whenever possible. The author explores the development of mathematical descriptions and constitutive theories for deforming solids, fluids, and polymeric fluids-both compressible and incompressible with clear distinction between Lagrangian and Eulerian descriptions as well as co- and contravariant bases. He also establishes the tensorial nature of strain measures and influence of rotation of frames on various measures, illustrates the physical meaning of the components of strains, presents the polar decomposition of deformation, and provides the definitions and measures of stress. Comprised of 16 chapters, this text covers: * Einstein's notation * Index notations * Matrix and vector notations * Basic definitions and concepts * Mathematical preliminaries * Tensor calculus and transformations using co- and contra-variant bases * Differential calculus of tensors * Development of mathematical descriptions and constitutive theories Advanced Mechanics of Continua prepares graduate students for fundamental and basic research work in engineering and sciences, provides detailed and consistent derivations with clarity, and can be used for self-study. "... this comprehensive and self-sufficient monograph, written on a very strict mathemat- ical level and clear physical background, contains a detailed and well-structured description of the advanced mechanics of continua. This book should be very useful to students and teachers in the fields of engineering and mathematical physics." -Zentralblatt MATH,1326 "The book Advanced Mechanics of Continua is a complete reference for both students and researchers in the field of material sciences and applied mechanics. It contains comprehensive and detailed representation for the mechanical behavior of solids and fluids. The constitutive laws for different types of materials are presented separately in this book which helps the readers to understand the concepts without confusion. The choice of gradually developing formulations for different subjects eases the grasping of material for the readers and makes the book an excellent reference for graduate students. -George Z. Voyiadjis, Louisiana State University, Baton Rouge, USA "This textbook gives a very rigorous analysis of continuum mechanics covering complex topics in Eulerian and Lagrangian kinematics and stress measures for finite deformation problems. ... The book covers all the key topics required to gain a foothold on the complex concepts of continuum mechanics. ... The discussion on kinematics provides a rigorous analysis of kinematics in different reference frames. This is often treated briefly in other comparable textbooks. ... The author has succeeded in providing an exhaustive resource for advanced graduate students and researchers interest[ed] in mastering continuum mechanics." -William S. Oates, Florida State University, Tallahassee, USAIntroduction Concepts and Mathematical Preliminaries Introduction Summation Convention Dummy Index and Dummy Variables Free Indices Vector and Matrix Notation Index Notation and Kronecker Delta Permutation Tensor Operations Using Vector, Matrix, and Einstein's Notation Change of Reference Frame, Transformations, Tensors Some Useful Relations Summary Kinematics of Motion, Deformation and Their Measures Description of Motion Lagrangian and Eulerian Descriptions Material Particle Displacements Continuous Deformation and Restrictions on the Motion Material Derivative Acceleration of a Material Particles Coordinate Systems and Bases Covariant Basis Contravariant Basis Alternate Way to Visualize Co- and Contra-Variant Bases Jacobian of Deformation Change of Description, Co- and Contra-Variant Measures Notations For Covariant and Contravariant Measures Deformation, Measures of Length and Change in Length Covariant and Contravariant Measures of Strain Changes in Strain Measures Due To Rigid Rotation of Frames Invariants of Strain Tensors Expanded Form of Strain Tensors Physical Meaning of Strains Polar Decomposition: Rotation and Stretch Tensors Deformation of Areas and Volumes Summary Definitions and Measures of Stresses Cauchy Stress Tensor Contravariant and Covariant Stress Tensors General Remarks Summary of Stresses and Considerations in Their Derivations General Considerations Summary of Stress Measures Conjugate Strain Measures Relations between Stress Measures and Useful Relations Summary Rate of Deformation, Strain Rate, and Spin Tensors Rate of Deformation Decomposition of [ L], the Spatial Velocity Gradient Tensor Interpretation of the Components of [D] Rate of Change or Material Derivative of Strain Tensors Physical Meaning of Spin Tensor [ W ] Vorticity Vector and Vorticity Material Derivative of Determinant of J Material Derivative of Volume Rate of Change of Area: Material Derivative of Area Stress And Strain Measures for Convected Time Derivatives Convected Time Derivatives Conjugate Convected Time Derivatives of Stress And Strain Tensors Summary Conservation and Balance Laws in Eulerian Description Introduction Mass Density Conservation Of Mass: Continuity Equation Transport Theorem Conservation Of Mass: Continuity Equation Balance of Linear Momenta Kinetics of Continuous Media: Balance of Angular Momenta First Law of Thermodynamics Second Law of Thermodynamics A Summary of Mathematical Models Summary Conservation and Balance Laws In Lagrangian Description Introduction Mathematical Model for Deforming Matter in Lagrangian Description Conservation Of Mass: Continuity Equation Balance of Linear Momenta Balance of Angular Momenta First Law of Thermodynamics Second law of thermodynamics in terms of PHI Second law of thermodynamics in terms of PSI Summary of Mathematical Models First and Second Laws for Thermoelastic Solids Summary General Considerations in the Constitutive Theories Introduction Axioms of Constitutive Theory Objective Solid Matter Fluids Preliminary Considerations in the Constitutive Theories General Approach of Deriving Constitutive Theories Summary Ordered Rate Constitutive Theories for Thermoelastic Solids Introduction Entropy inequality in PHI: Lagrangian description Constitutive Theories for Thermoelastic Solids Constitutive Theories Using Generators and Invariants Strain energy density pi: Lagrangian description Stress in terms of Green strain based on pi: Lagrangian Stress in terms of Cauchy strain based on pi: Lagrangian Constitutive Theories for the Heat Vector: Lagrangian Alternate Derivations: Strain In Terms Of Stress Alternate Derivations: Heat Vector In Terms Of Stress Summary Thermoviscoelastic Solids without Memory Introduction Constitutive Theories Using Helmholtz Free Energy Density Constitutive Theories Using Gibbs Potential Comparisons of constitutive theories using PHI and PSI Thermoviscoelastic Solids with Memory Introduction Constitutive Theories Using Helmholtz Free Energy Density Constitutive Theories Using Gibbs Potential Comparisons of constitutive theories using PHI and PSI Ordered Rate Constitutive Theories for Thermofluids Introduction Second Law of Thermodynamics: Entropy Inequality Dependent Variables and Their Arguments Development of Constitutive Theory for Thermo Fluids Rate Constitutive Theory of Order N Rate Constitutive Theory of Order Two Rate Constitutive Theory of Order One Generalized Newtonian and Newtonian Fluids Incompressible Ordered Thermo Fluids of Orders N, 2 And 1 Incompressible Generalized Newtonian, Newtonian Fluids Conjugate Measures, Validity of Rate Constitutive Theories Summary Ordered Rate Constitutive Theories for Polymers Introduction Second Law of Thermodynamics: Entropy Inequality Dependent Variables and Their Arguments Development of Constitutive Theory for Polymers Rate Constitutive Theory of Orders 'M' and 'N' Rate Constitutive Theory of Orders M=1 and N=1 Rate Constitutive Theory of Orders M=1 and N=2 Constitutive Theories for Incompressible Polymers Numerical Studies Using Giesekus Constitutive Model Ordered Rate Constitutive Theories for Hypoelastic Solids Introduction Second Law of Thermodynamics: Entropy Inequality Dependent Variables and Their Arguments Development of Constitutive Theory for Hypo-Elastic Solids Rate Constitutive Theory of Order 'N' Rate Constitutive Theory of Order Two Rate Constitutive Theory of Order One Compressible Generalized Hypo-Elastic Solids of Order One Incompressible Ordered Hypo-Elastic Solids Incompressible Generalized Hypo-Elastic Solids: Order One Summary Mathematical Models with Thermodynamic Relations Introduction Thermodynamic Pressure: Compressible Matter Mechanical Pressure: Incompressible Matter Specific Internal Energy Variable Transport Properties or Material Coefficients Final Form of the Mathematical Models Summary Principle of Virtual Work Introduction Hamilton's Principle in Continuum Mechanics Euler-Lagrange Equation: Lagrangian Description Euler-Lagrange Equation: Eulerian Description Summary and Remarks Appendices

Szczegóły: Advanced Mechanics of Continua - Karan Surana

Tytuł: Advanced Mechanics of Continua
Autor: Karan Surana
Wydawnictwo: Productivity Press Inc
ISBN: 9781498708104
Rok wydania: 2014
Ilość stron: 786
Oprawa: Twarda
Waga: 1.52 kg

Recenzje: Advanced Mechanics of Continua - Karan Surana