Continuum Mechanics Modeling of Material Behavior
- 1st Edition - March 28, 2018
- Author: Martin H. Sadd
- Language: English
- Paperback ISBN:9 7 8 - 0 - 1 2 - 8 1 1 4 7 4 - 2
- eBook ISBN:9 7 8 - 0 - 1 2 - 8 1 1 6 4 9 - 4
Continuum Mechanics Modeling of Material Behavior offers a uniquely comprehensive introduction to topics like RVE theory, fabric tensor models, micropolar elasticity, elasticit… Read more
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Request a sales quoteContinuum Mechanics Modeling of Material Behavior offers a uniquely comprehensive introduction to topics like RVE theory, fabric tensor models, micropolar elasticity, elasticity with voids, nonlocal higher gradient elasticity and damage mechanics. Contemporary continuum mechanics research has been moving into areas of complex material microstructural behavior. Graduate students who are expected to do this type of research need a fundamental background beyond classical continuum theories. The book begins with several chapters that carefully and rigorously present mathematical preliminaries: kinematics of motion and deformation; force and stress measures; and general principles of mass, momentum and energy balance.
The book then moves beyond other books by dedicating several chapters to constitutive equation development, exploring a wide collection of constitutive relations and developing the corresponding material model formulations. Such material behavior models include classical linear theories of elasticity, fluid mechanics, viscoelasticity and plasticity. Linear multiple field problems of thermoelasticity, poroelasticity and electoelasticity are also presented. Discussion of nonlinear theories of solids and fluids, including finite elasticity, nonlinear/non-Newtonian viscous fluids, and nonlinear viscoelastic materials are also given. Finally, several relatively new continuum theories based on incorporation of material microstructure are presented including: fabric tensor theories, micropolar elasticity, elasticity with voids, nonlocal higher gradient elasticity and damage mechanics.
- Offers a thorough, concise and organized presentation of continuum mechanics formulation
- Covers numerous applications in areas of contemporary continuum mechanics modeling, including micromechanical and multi-scale problems
- Integration and use of MATLAB software gives students more tools to solve, evaluate and plot problems under study
- Features extensive use of exercises, providing more material for student engagement and instructor presentation
Graduate students majoring in several different technology disciplines including engineering science, mechanics, and mechanical, civil, aerospace and materials engineering
- Cover
- Title page
- Table of Contents
- Copyright
- Preface
- Chapter 1: Introduction
- Abstract
- 1.1. Materials and the Continuum Hypothesis
- 1.2. Need for Tensors
- 1.3. Structure of the Study
- 1.4. A Little History
- Chapter 2: Mathematical Preliminaries
- Abstract
- 2.1. Index and Direct Notation
- 2.2. Summation Convention
- 2.3. Symmetric and Antisymmetric Symbols
- 2.4. Kronecker Delta and Alternating Symbol
- 2.5. Determinants
- 2.6. Vectors and Coordinate Frames
- 2.7. Changes in Coordinate Frames: Orthogonal Transformations
- 2.8. Cartesian Tensors and Transformation Laws
- 2.9. Objectivity between Different Reference Frames
- 2.10. Vector and Matrix Algebra
- 2.11. Principal Values, Directions, and Invariants of Symmetric Second-Order Tensors
- 2.12. Spherical and Deviatoric Second-Order Tensors
- 2.13. Cayley–Hamilton Theorem and Matrix Polynomials
- 2.14. Representation Theorems
- 2.15. Isotropic Tensors
- 2.16. Polar Decomposition Theorem
- 2.17. Calculus of Cartesian Field Tensors
- 2.18. Orthogonal Curvilinear Coordinate Systems
- 2.19. General Tensors
- Chapter 3: Kinematics of Motion and Deformation Measures
- Abstract
- 3.1. Material Body and Motion
- 3.2. Lagrangian and Eulerian Descriptions
- 3.3. Material Time Derivative
- 3.4. Velocity and Acceleration
- 3.5. Displacement and Deformation Gradient Tensors
- 3.6. Lagrangian and Eulerian Strain Tensors
- 3.7. Changes in Line, Area, and Volume Elements
- 3.8. Small Deformation Kinematics and Strain Tensors
- 3.9. Principal Axes for Strain Tensors
- 3.10. Spherical and Deviatoric Strain Tensors
- 3.11. Strain Compatibility
- 3.12. Rotation Tensor
- 3.13. Rate of Strain Tensors
- 3.14. Objective Time Derivatives
- 3.15. Current Configuration as Reference Configuration
- 3.16. Rivlin–Ericksen Tensors
- 3.17. Curvilinear Cylindrical and Spherical Coordinate Relations
- Chapter 4: Force and Stress
- Abstract
- 4.1. Body and Surface Forces
- 4.2. Cauchy Stress Principle: Stress Vector
- 4.3. Cauchy Stress Tensor
- 4.4. Principal Stresses and Axes for Cauchy Stress Tensor
- 4.5. Spherical, Deviatoric, Octahedral, and von Mises Stress
- 4.6. Stress Distributions and Contour Lines
- 4.7. Reference Configuration Piola–Kirchhoff Stress Tensors
- 4.8. Other Stress Tensors
- 4.9. Objectivity of Stress Tensors
- 4.10. Cylindrical and Spherical Coordinate Cauchy Stress Forms
- Chapter 5: General Conservation or Balance Laws
- Abstract
- 5.1. General Conservation Principles and the Reynolds Transport Theorem
- 5.2. Conservation of Mass
- 5.3. Conservation of Linear Momentum
- 5.4. Conservation of Moment of Momentum
- 5.5. Conservation of Linear Momentum Equations in Cylindrical and Spherical Coordinates
- 5.6. Conservation of Energy
- 5.7. Second Law of Thermodynamics—Entropy Inequality
- 5.8. Summary of Conservation Laws, General Principles, and Unknowns
- Chapter 6: Constitutive relations and formulation of classical linear theories of solids and fluids
- Abstract
- 6.1. Introduction to Constitutive Equations
- 6.2. Linear Elastic Solids
- 6.3. Ideal Nonviscous Fluids
- 6.4. Linear Viscous Fluids
- 6.5. Linear Viscoelastic Materials
- 6.6. Classical Plastic Materials
- Chapter 7: Constitutive relations and formulation of theories involving multiple constitutive fields
- Abstract
- 7.1. Introduction
- 7.2. Thermoelastic Solids
- 7.3. Poroelasticity
- 7.4. Electroelasticity
- Chapter 8: General Constitutive Relations and Formulation of Nonlinear Theories of Solids and Fluids
- Abstract
- 8.1. Introduction and General Constitutive Axioms
- 8.2. General Simple Materials
- 8.3. Nonlinear Finite Elasticity
- 8.4. Nonlinear Viscous Fluids
- 8.5. Nonlinear Integral Viscoelastic Constitutive Models
- Chapter 9: Constitutive relations and formulation of theories incorporating material microstructure
- Abstract
- 9.1. Introduction to Micromechanics Material Modeling
- 9.2. Micropolar Elasticity
- 9.3. Elasticity Theory with Voids
- 9.4. Doublet Mechanics
- 9.5. Higher Gradient Elasticity Theories
- 9.6. Fabric Theories for Granular Materials
- 9.7. Continuum Damage Mechanics
- Appendix A: Basic Field Equations in Cartesian, Cylindrical, and Spherical Coordinates
- Appendix B: Transformation of Field Variables Between Cartesian, Cylindrical, and Spherical Components
- Appendix C: MATLAB Primer and Code Listings
- Appendix D: Poem
- Index
- No. of pages: 432
- Language: English
- Edition: 1
- Published: March 28, 2018
- Imprint: Academic Press
- Paperback ISBN: 9780128114742
- eBook ISBN: 9780128116494
MS
Martin H. Sadd
Martin H. Sadd is Professor Emeritus of Mechanical Engineering at the University of Rhode Island. He received his Ph.D. in mechanics from the Illinois Institute of Technology and began his academic career at Mississippi State University. In 1979 he joined the faculty at Rhode Island and served as department chair from 1991 to 2000. Professor Sadd’s teaching background is in the area of solid mechanics with emphasis in elasticity, continuum mechanics, wave propagation, and computational methods. He has taught elasticity at two academic institutions, in several industries, and at a government laboratory. Professor Sadd’s research has been in computational modeling of materials under static and dynamic loading conditions using finite, boundary, and discrete element methods. Much of his work has involved micromechanical modeling of geomaterials including granular soil, rock, and concretes. He has authored more than 75 publications and has given numerous presentations at national and international meetings.