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| Preface | |
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| List of Boxes | |
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| Introduction | |
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| Nonlinear finite elements in design | |
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| Related books and a brief history of nonlinear finite elements | |
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| Notation | |
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| Mesh descriptions | |
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| Classification of partial differential equations | |
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| Exercises | |
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| Lagrangian and Eulerian finite elements in one dimension | |
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| Introduction | |
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| Governing equations for total Lagrangian formulation | |
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| Weak form for total Lagrangian formulation | |
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| Finite element discretization in total Lagrangian formulation | |
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| Element and global matrices | |
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| Governing equations for updated Lagrangian formulation | |
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| Weak form for updated Lagrangian formulation | |
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| Element equations for updated Lagrangian formulation | |
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| Governing equations for Eulerian formulation | |
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| Weak forms for Eulerian mesh equations | |
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| Finite element equations | |
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| Solution methods | |
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| Summary | |
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| Exercises | |
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| Continuum mechanics | |
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| Introduction | |
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| Deformation and motion | |
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| Strain measures | |
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| Stress measures | |
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| Conservation equations | |
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| Lagrangian conservation equations | |
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| Polar decomposition and frame-invariance | |
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| Exercises | |
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| Lagrangian meshes | |
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| Introduction | |
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| Governing equations | |
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| Weak form: principle of virtual power | |
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| Updated Lagrangian finite element discretization | |
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| Implementation | |
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| Corotational formulations | |
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| Total Lagrangian formulation | |
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| Total Lagrangian weak form | |
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| Finite element semidiscretization | |
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| Exercise | |
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| Constitutive models | |
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| Introduction | |
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| The stress-strain curve | |
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| One-dimensional elasticity | |
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| Nonlinear elasticity | |
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| One-dimensional plasticity | |
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| Multiaxial plasticity | |
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| Hyperelastic-plastic models | |
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| Viscoelasticity | |
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| Stress update algorithms | |
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| Continuum mechanics and constitutive models | |
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| Exercises | |
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| Solution methods and stability | |
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| Introduction | |
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| Explicit methods | |
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| Equilibrium solutions and implicit time integration | |
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| Linearization | |
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| Stability and continuation methods | |
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| Numerical stability | |
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| Material stability | |
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| Exercises | |
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| Arbitrary Lagrangian Eulerian formulations | |
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| Introduction | |
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| ALE continuum mechanics | |
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| Conservation laws in ALE description | |
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| ALE governing equations | |
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| Weak forms | |
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| Introduction to the Petrov-Galerkin method | |
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| Petrov-Galerkin formulation of momentum equation | |
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| Path-dependent materials | |
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| Linearization of the discrete equations | |
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| Mesh update equations | |
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| Numerical example: an elastic-plastic wave propagation problem | |
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| Total ALE formulations | |
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| Element technology | |
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| Introduction | |
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| Element performance | |
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| Element properties and patch tests | |
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| Q4 and volumetric locking | |
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| Multi-field weak forms and elements | |
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| Multi-field quadrilaterals | |
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| One-point quadrature elements | |
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| Examples | |
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| Stability | |
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| Exercises | |
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| Beams and shells | |
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| Introduction | |
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| Beam theories | |
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| Continuum-based beam | |
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| Analysis of CB beam | |
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| Continuum-based shell implementation | |
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| CB shell theory | |
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| Shear and membrane locking | |
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| Assumed strain elements | |
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| One-point quadrature elements | |
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| Exercises | |
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| Contact-impact | |
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| Introduction | |
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| Contact interface equations | |
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| Friction models | |
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| Weak forms | |
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| Finite element discretization | |
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| On explicit methods | |
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| Voigt notation | |
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| Norms | |
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| Element shape functions | |
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| Glossary | |
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| References | |
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| Index | |