This volume studies the behavior of solid materials under deformation.
This volume studies the behavior of solid materials under deformation. It develops continuum mechanics, elasticity, plasticity, and modern computational methods.
Part I. Foundations of Continuum Mechanics
Chapter 1. Continuum Description
1.1 Material points and bodies 1.2 Reference and current configurations 1.3 Deformation maps 1.4 Kinematics of motion 1.5 Examples
Chapter 2. Stress and Strain
2.1 Strain measures 2.2 Stress tensors 2.3 Cauchy stress 2.4 Balance laws 2.5 Examples
Chapter 3. Conservation Laws
3.1 Mass conservation 3.2 Linear momentum 3.3 Angular momentum 3.4 Energy balance 3.5 Applications
Part II. Elasticity
Chapter 4. Linear Elasticity
4.1 Hooke’s law 4.2 Isotropic materials 4.3 Stress-strain relations 4.4 Boundary value problems 4.5 Examples
Chapter 5. Elastic Equilibrium
5.1 Equilibrium equations 5.2 Compatibility conditions 5.3 Energy methods 5.4 Applications 5.5 Examples
Chapter 6. Elastic Waves
6.1 Wave propagation 6.2 Longitudinal and transverse waves 6.3 Applications 6.4 Examples 6.5 Connections
Part III. Nonlinear Elasticity
Chapter 7. Finite Deformations
7.1 Large strain theory 7.2 Deformation gradient 7.3 Constitutive laws 7.4 Applications 7.5 Examples
Chapter 8. Hyperelastic Materials
8.1 Strain energy functions 8.2 Material models 8.3 Stability 8.4 Applications 8.5 Examples
Chapter 9. Instability and Buckling
9.1 Stability criteria 9.2 Buckling phenomena 9.3 Applications 9.4 Examples 9.5 Connections
Part IV. Plasticity and Viscoelasticity
Chapter 10. Plastic Deformation
10.1 Yield criteria 10.2 Flow rules 10.3 Hardening 10.4 Applications 10.5 Examples
Chapter 11. Viscoelastic Materials
11.1 Time-dependent behavior 11.2 Constitutive models 11.3 Relaxation and creep 11.4 Applications 11.5 Examples
Chapter 12. Damage and Fracture
12.1 Crack formation 12.2 Fracture mechanics 12.3 Energy release rate 12.4 Applications 12.5 Examples
Part V. Mathematical Methods
Chapter 13. PDE Formulations
13.1 Governing equations 13.2 Boundary conditions 13.3 Weak formulations 13.4 Applications 13.5 Examples
Chapter 14. Variational Methods
14.1 Energy minimization 14.2 Euler–Lagrange equations 14.3 Stability 14.4 Applications 14.5 Examples
Chapter 15. Numerical Methods
15.1 Finite element method 15.2 Discretization 15.3 Convergence 15.4 Applications 15.5 Examples
Part VI. Advanced Topics
Chapter 16. Anisotropic Materials
16.1 Material symmetry 16.2 Constitutive laws 16.3 Applications 16.4 Examples 16.5 Connections
Chapter 17. Multiscale Modeling
17.1 Microstructure 17.2 Homogenization 17.3 Applications 17.4 Examples 17.5 Connections
Chapter 18. Nonlinear Dynamics of Solids
18.1 Large deformation dynamics 18.2 Wave interactions 18.3 Applications 18.4 Examples 18.5 Connections
Part VII. Applications
Chapter 19. Structural Engineering
19.1 Beams and plates 19.2 Stability analysis 19.3 Load-bearing structures 19.4 Applications 19.5 Examples
Chapter 20. Materials Science
20.1 Material behavior 20.2 Composite materials 20.3 Failure analysis 20.4 Applications 20.5 Examples
Chapter 21. Computational Mechanics
21.1 Simulation tools 21.2 High-performance computing 21.3 Visualization 21.4 Applications 21.5 Examples
Part VIII. Research Directions
Chapter 22. Advanced Topics
22.1 Nonlinear material models 22.2 Fracture and damage theory 22.3 Soft matter mechanics 22.4 Modern developments 22.5 Emerging areas
Chapter 23. Open Problems
23.1 Multiscale challenges 23.2 Stability and failure 23.3 Computational limits 23.4 Material modeling gaps 23.5 Future directions
Chapter 24. Historical and Conceptual Notes
24.1 Development of solid mechanics 24.2 Key contributors 24.3 Evolution of continuum theory 24.4 Cross-disciplinary impact 24.5 Summary
Appendix
A. Stress and strain formulas B. Material model reference C. Proof techniques checklist D. Numerical method tables E. Cross-reference to other MSC branches