1. Elasticity in three dimensions
1.1 Deformation map and deformation gradient
1.2 Strain energy and hyperelasticity
1.3 Force and traction
1.4 The first Piola-Kirchhoff stress tensor


2. Constitutive models of materials
2.1 Strain measures
2.2 Linear elasticity
2.3 St. Venant-Kirchhoff model
2.4 Corotated linear elasticity
2.5 Isotropic materials and invariants
2.6 Neohookean elasticity


3. Discretization and time integration
3.1 Energy and force discretization
3.2 Linear tetrahedral elements
3.3 Force differentials
3.4 An implicit time integration scheme


4. Model reduction
4.1 Introduction
4.1.1 Survey of POD-based model reduction in computer graphics
4.2 Linear modal analysis
4.2.1 Small deformation simulation using linear modal analysis
4.2.2 Application to sound simulation
4.3 Model reduction of nonlinear deformations
4.3.1 Timestepping the reduced nonlinear equations of motion
4.3.2 Choice of basis
4.4 Model reduction and domain decomposition
4.5 Model reduction and control
4.6 Free software for model reduction
4.7 Deformation warping
4.7.1 Rotation-strain coordinate warping
4.7.2 Warping for triangle meshes
4.8 Acknowledgments
Bibliography
Authors' biographies.