Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

Part of: Synthesis digital library of engineering and computer science.

Includes bibliographical references (pages 53-56).

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.

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This book serves as a practical guide to simulation of 3D deformable solids using the Finite Element Method (FEM). It reviews a number of topics related to the theory and implementation of FEM approaches: measures of deformation, constitutive laws of nonlinear materials, tetrahedral discretizations, and model reduction techniques for real-time simulation. Simulations of deformable solids are important in many applications in computer graphics, including film special effects, computer games, and virtual surgery. The Finite Element Method has become a popular tool in many such applications. Variants of FEM catering to both offline and real-time simulation have had a mature presence in computer graphics literature. This book is designed for readers familiar with numerical simulation in computer graphics, who would like to obtain a cohesive picture of the various FEM simulation methods available, their strengths and weaknesses, and their applicability in various simulation scenarios. The book is also a practical implementation guide for the visual effects developer, offering a lean yet adequate synopsis of the underlying mathematical theory. Chapter 1 introduces the quantitative descriptions used to capture the deformation of elastic solids, the concept of strain energy, and discusses how force and stress result as a response to deformation. Chapter 2 reviews a number of constitutive models, i.e., analytical laws linking deformation to the resulting force that has successfully been used in various graphics-oriented simulation tasks. Chapter 3 summarizes how deformation and force can be computed discretely on a tetrahedral mesh, and how an implicit integrator can be structured around this discretization. Finally, chapter 4 presents the state of the art in model reduction techniques for real-time FEM solid simulation and discusses which techniques are suitable for which applications. Topics discussed in this chapter include linear modal analysis, modal warping, subspace simulation, and domain decomposition.

Also available in print.

Title from PDF title page (viewed on November 24, 2015).