**Introduction to Computational Plasticity 1st Edition by Fionn Dunne, ISBN-13: 978-0198568261**

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- Publisher: Oxford University Press; 1st edition (August 18, 2005)
- Language: English
- 241 pages
- ISBN-10: 0198568266
- ISBN-13: 978-0198568261

This book gives an introduction to computational plasticity and includes the kinematics of large deformations, together with relevant continuum mechanics. Central to the book is its focus on computational plasticity, and we cover an introduction to the finite element method which includes both quasi-static and dynamic problems. We then go on to describe explicit and implicit implementations of plasticity models in to finite element software. Throughout the book, we describe the general, multiaxial form of the theory but uniquely, wherever possible, reduce the equations to their simplest, uniaxial form to develop understanding of the general theory and we hope * physical* insight. We provide several examples of implicit and explicit implementations of von Mises time-independent and visco-plasticity in to the commercial code ABAQUS (including the fortran coding), which should prove invaluable to research students and practicing engineers developing ABAQUS ‘UMATs’. The book bridges the gap between undergraduate material on plasticity and existing advanced texts on nonlinear computational mechanics, which makes it ideal for students and practicing engineers alike. It introduces a range of engineering applications, including superplasticity, porous plasticity, cyclic plasticity and thermo-mechanical fatigue, to emphasize the subject’s relevance and importance.

**Table of Contents:**

Contents

Acknowledgements

Notation

Part I. Microplasticity and continuum plasticity

1. Microplasticity

1.1 Introduction

1.2 Crystal slip

1.3 Critical resolved shear stress

1.4 Dislocations

Further reading

2. Continuum plasticity

2.1 Introduction

2.2 Some preliminaries

2.3 Yield criterion

2.4 Isotropic hardening

2.5 Kinematic hardening

2.6 Combined isotropic and kinematic hardening

2.7 Viscoplasticity and creep

Further reading

3. Kinematics of large deformations and continuum mechanics

3.1 Introduction

3.2 The deformation gradient

3.3 Measures of strain

3.4 Interpretation of strain measures

3.5 Polar decomposition

3.6 Velocity gradient, rate of deformation, and continuum spin

3.7 Elastic–plastic coupling

3.8 Objective stress rates

3.9 Summary

Further reading

4. The finite element method for static and dynamic plasticity

4.1 Introduction

4.2 Hamilton’s principle

4.3 Introduction to the finite element method

4.4 Finite element equilibrium equations

4.5 Integration of momentum balance and equilibrium equations

Further reading

5. Implicit and explicit integration of von Mises plasticity

5.1 Introduction

5.2 Implicit and explicit integration of constitutive equations

5.3 Material Jacobian

5.4 Kinematic hardening

5.5 Implicit integration in viscoplasticity

5.6 Incrementally objective integration for large deformations

Further reading

6. Implementation of plasticity models into finite element code

6.1 Introduction

6.2 Elasticity implementation

6.3 Verification of implementations

6.4 Isotropic hardening plasticity implementation

6.5 Large deformation implementations

6.6 Elasto-viscoplasticity implementation

Part II: Plasticity models

7. Superplasticity

7.1 Introduction

7.2 Some properties of superplastic alloys

7.3 Constitutive equations for superplasticity

7.4 Multiaxial constitutive equations and applications

References

8. Porous plasticity

8.1 Introduction

8.2 Finite element implementation of the porous material constitutive equations

8.3 Application to consolidation of Ti–MMCs

References

9. Creep in an aero-engine combustor material

9.1 Introduction

9.2 Physically based constitutive equations

9.3 Multiaxial implementation into ABAQUS

References

Appendix 9.1

10. Cyclic plasticity, creep, and TMF

10.1 Introduction

10.2 Constitutive equations for cyclic plasticity

10.3 Constitutive equations for C263 undergoing TMF

References

Appendix A: Elements of tensor algebra

Differentiation

The chain rule

Rotation

Appendix B: Fortran coding available via the OUP website

Index

* Dr. Fionn Dunne* is Reader in Engineering Science at the University of Oxford.

* Dr. Nik Petrinic *is Lecturer in Engineering Science at the University of Oxford.

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