Chapter 2. Linear Elasticity and Viscoelasticity
2.1. Elastic Isotropy and Anisotropy 43
2.1.1. Isotropic material 43
2.1.2. Anisotropic Material and Crystal Symmetry Classes 46
2.2. Variational Principles, and Work Identities 53
2.2.1. Minimum energy principles 54
2.2.2. Work identities 57
2.2.3. Haminton's principle 58
2.3. Boundary Valued Problem 59
2.4. Green Functions and Boundary Integral Equations 61
2.5. Anti-Plane Strain and Torsion 62
2.5.1. Anti-Plane Strain 62
2.5.2. Torsion of prismatic bar 63
2.6. Plane Strain and Plane Stress 63
2.6.1. General formulation 63
2.6.2. Presentation of the problems through analytic functions 65
2.7. Initial Valued Problem and Wave propagation 66
2.7.1. Plane waves in infinite isotropic medium 66
2.7.2. Waves' scattering 67
2.7.3. Surface waves 68
2.8. Viscoelasticity 69
2.8.1. Simple models 70
2.8.2. General linear models 72
2.8.3. Non-linear models 74