Guido Dhondt obtained his civil engineering degree at the Catholic University of Leuven, Belgium (1983), going on to undertake a Ph.D. in Civil Engineering at Princeton University, USA (1987). Presently, he works in the field of fracture mechanics and finite element analysis at MTU Aero Engines, Germany. He is one of the authors of the free software finite element program CalculiX.

Preface.

Nomenclature.

1 Displacements, Strain, Stress and Energy.

1.1 The Reference State.

1.2 The Spatial State.

1.3 Strain Measures.

1.4 Principal Strains.

1.5 Velocity.

1.6 Objective Tensors.

1.7 Balance Laws.

1.8 Localization of the Balance Laws.

1.9 The Stress Tensor.

1.10 The Balance Laws in Material Coordinates.

1.11 The Weak Form of the Balance of Momentum.

1.12 The Weak Form of the Energy Balance.

1.13 Constitutive Equations.

1.14 Elastic Materials.

1.15 Fluids.

2 Linear Mechanical Applications.

2.1 General Equations.

2.2 The Shape Functions.

2.3 Numerical Integration.

2.4 Extrapolation of Integration Point Values to the Nodes.

2.5 Problematic Element Behavior.

2.6 Linear Constraints.

2.7 Transformations.

2.8 Loading.

2.9 Modal Analysis.

2.10 Cyclic Symmetry.

2.11 Dynamics: The ±-Method.

3 Geometric Nonlinear Effects.

3.1 General Equations.

3.2 Application to a Snapping-through Plate.

3.3 Solution-dependent Loading.

3.4 Nonlinear Multiple Point Constraints.

3.5 Rigid Body Motion.

3.6 Mean Rotation.

3.7 Kinematic Constraints.

3.8 Incompressibility Constraint.

4 Hyperelastic Materials.

4.1 Polyconvexity of the Stored-energy Function.

4.2 Isotropic Hyperelastic Materials.

4.3 Nonhomogeneous Shear Experiment.

4.4 Derivatives of Invariants and Principal Stretches.

4.5 Tangent Stiffness Matrix at Zero Deformation.

4.6 Inflation of a Balloon.

4.7 Anisotropic Hyperelasticity.

5 Infinitesimal Strain Plasticity.

5.1 Introduction.

5.2 The General Framework of Plasticity.

5.3 Three-dimensional Single Surface Viscoplasticity.

5.4 Three-dimensional Multisurface Viscoplasticity: the Cailletaud Single Crystal Model.

5.5 Anisotropic Elasticity with a von Mises-type Yield Surface.

6 Finite Strain Elastoplasticity.

6.1 Multiplicative Decomposition of the Deformation Gradient.

6.2 Deriving the Flow Rule.

6.3 Isotropic Hyperelasticity with a von Mises-type Yield Surface.

6.4 Extensions.

6.5 Summary of the Equations.

6.6 Stress Update Algorithm.

6.7 Derivation of Consistent Elastoplastic Moduli.

6.8 Isochoric Plastic Deformation.

6.9 Burst Calculation of a Compressor.

7 Heat Transfer.

7.1 Introduction.

7.2 The Governing Equations.

7.3 Weak Form of the Energy Equation.

7.4 Finite Element Procedure.

7.5 Time Discretization and Linearization of the Governing Equation.

7.6 Forced Fluid Convection.

7.7 Cavity Radiation.

References.

Index.