General Continuum Mechanics and Constitutive Modeling
- 1st Edition - November 19, 2024
- Imprint: Elsevier
- Author: Niels Saabye Ottosen
- Language: English
- Paperback ISBN:9 7 8 - 0 - 4 4 3 - 3 3 8 4 3 - 4
- eBook ISBN:9 7 8 - 0 - 4 4 3 - 3 3 8 4 4 - 1
General Continuum Mechanics and Constitutive Modeling starts with a comprehensive treatment of tensor algebra that is followed by coverage of strains, stresses, and thermo… Read more
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Request a sales quoteGeneral Continuum Mechanics and Constitutive Modeling starts with a comprehensive treatment of tensor algebra that is followed by coverage of strains, stresses, and thermodynamics. General principles for constitutive modeling are presented, including objectivity, Lie-derivative, and covariance, as are issues central to configurational mechanics, such as polyconvexity and invariance principles used to establish balance equations. The book includes a chapter on hyperelasticity which analyzes isotropic and anisotropic materials, and also discusses the distinction between energetic and entropic material response.
The finite element method and classic plasticity based on hypoelasticity are each covered, and the book concludes with a chapter covering plasticity based on hyperplasticity, including isotropy, anisotropy, thermoplasticity, and crystal plasticity.
The finite element method and classic plasticity based on hypoelasticity are each covered, and the book concludes with a chapter covering plasticity based on hyperplasticity, including isotropy, anisotropy, thermoplasticity, and crystal plasticity.
- Covers the fundamental concepts of polyconvexity, invariance principles, configurational mechanics, and hyperelasticity and plasticity in a clear and concise manner
- Describes general continuum mechanics and constitutive modeling for large deformations and rotations, with all tensor expressions written in direct notation and component and base vectors referring to arbitrary curvilinear coordinate systems
- Presents general principles for constitutive modeling, including topics such as objectivity, Lie-derivative, covariance, thermoelasticity, the differences between energetic and entropic material response, and more
Researchers, academics, and advanced undergrad and grad students within the field of solid mechanics
- Title of Book
- Cover image
- Title page
- Table of Contents
- Copyright
- Preface
- 1: Tensor algebra in general coordinates
- 1.1. Vector space, vectors, and inner product
- 1.2. Euclidean vector space, base vectors, and metric tensor
- 1.3. Vector cross product
- 1.4. Change of coordinate system
- 1.5. Second-order tensors
- 1.6. Validity of a tensor expression
- 1.7. Symmetric and antisymmetric tensors
- 1.8. Determinant and inverse of a tensor
- 1.9. Eigenvalue problem
- 1.10. Orthogonal tensors – rigid body rotations
- 1.11. Fourth-order tensors
- 1.12. Representation theorems
- 1.13. Isotropic tensors
- 1.14. Differentiation with respect to a tensor
- 1.15. Spatial differentiations – gradient, divergence, and curl
- 1.16. Derivatives ∂u/∂θi and ∂A/∂θi – covariant differentiation
- 1.17. Exercises
- 2: Kinematics
- 2.1. Configurations and motions
- 2.2. Deformation gradient F
- 2.3. The most general form of the deformation gradient F
- 2.4. Identity and metric tensors
- 2.5. Material time derivation
- 2.6. Compatibility equations for the deformation gradient F
- 2.7. Deformation of volume, surface, and line element
- 2.8. Mass conservation and Reynolds' transport theorem
- 2.9. Deformation and strain tensors
- 2.10. Polar decomposition theorem
- 2.11. Rate of deformation tensor
- 2.12. Exercises
- 3: Stresses and balance equations
- 3.1. Forces and global balance equations
- 3.2. Cauchy's stress tensor
- 3.3. Local form of balance equations
- 3.4. Other stress measures
- 3.5. Principle of virtual power
- 3.6. Exercises
- 4: Thermodynamics
- 4.1. Temperature and heat flow
- 4.2. State variables and state functions
- 4.3. The first law of thermodynamics
- 4.4. The second law of thermodynamics
- 4.5. Heat equation
- 4.6. Exercises
- 5: General principles for constitutive modeling
- 5.1. Superimposed rigid-body motion – active transformation
- 5.2. Passive transformation – change of observer
- 5.3. Transformation properties of some quantities
- 5.4. Balance of linear momentum in a noninertial frame
- 5.5. Principle of material frame-indifference
- 5.6. Objective rates. Lie derivative
- 5.7. Material isotropy
- 5.8. Classifications of constitutive modeling
- 5.9. Covariance
- 5.10. Exercises
- 6: Configurational mechanics
- 6.1. The Eshelby stress tensor
- 6.2. Application to fracture mechanics
- 6.3. Dislocation mechanics
- 6.4. Exercises
- 7: Balance equations established using invariance principles
- 7.1. Green–Naghdi–Rivlin theorem
- 7.2. Noll's theorem
- 7.3. Revised Green–Naghdi–Rivlin theorem
- 7.4. Principle of virtual power
- 7.5. Second-order gradient elasticity
- 7.6. Exercises
- 8: Convexity of strain energy function
- 8.1. Stationarity of potential energy
- 8.2. Strain energy being convex in F
- 8.3. Quasiconvexity
- 8.4. Polyconvexity
- 8.5. Rank-one convexity
- 8.6. Existence of weak solution – a sketch
- 8.7. Exercises
- 9: Hyperelasticity
- 9.1. Isotropic and isothermal elasticity
- 9.2. Anisotropic and isothermal elasticity
- Anisotropy based on C
- Anisotropy based on b
- 9.3. Decomposition into isochoric and volumetric deformation
- 9.4. Incompressibility
- 9.5. Energetic versus entropic materials
- 9.6. Thermoelasticity
- 9.7. Use of principal stretches
- 9.8. Specific models
- 9.9. Exercises
- 10: Finite element formulation of hyperelasticity
- 10.1. From tensor equations to matrix equations
- 10.2. Total Lagrangian formulation
- Linearization – tangent stiffness
- 10.3. Exercises
- 11: Plasticity based on hypoelasticity
- 11.1. Issues of hypoelasticity
- 11.2. Isotropic hardening of von Mises material
- 11.3. von Mises material with kinematic hardening
- 11.4. Exercises
- 12: Plasticity based on hyperelasticity
- 12.1. Some basic relations
- 12.2. Isotropic and isothermal elasto-plasticity
- Isotropy based on Ce
- Isotropy based on be
- 12.3. A prototype model: von Mises plasticity
- 12.4. Anisotropic isothermal elasto-plasticity
- Anisotropy based on Ce
- Anisotropy based on be
- 12.5. Thermoelasto-plasticity
- 12.6. Crystal plasticity
- 12.7. Exercises
- Bibliography
- Index
- Edition: 1
- Published: November 19, 2024
- Imprint: Elsevier
- No. of pages: 398
- Language: English
- Paperback ISBN: 9780443338434
- eBook ISBN: 9780443338441
NO
Niels Saabye Ottosen
has been a Professor in the Solid Mechanics Division, Lund University, Sweden since 1991. His research is focused in continuum mechanics, material modeling, and finite element method.
Affiliations and expertise
Solid Mechanics Division, Lund University, SwedenRead General Continuum Mechanics and Constitutive Modeling on ScienceDirect