Tangent Matrice, Numerical Integration

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Table of contents

FOREWORD
TABLE OF CONTENTS
LIST OF FIGURES
SUMMARY
ÖZET
RESUME
1. INTRODUCTION
1.1 Problem Statement
1.2 Background and Literature Review
1.3 Scope and Objectives
1.4 Outline
2. FUNDAMENTAL CONCEPTS
2.1 Observations Elastic Limit
2.2 Materials and Behavior Models
2.3 Control of Plasticity
2.4 The Criterion of Plasticity
3. COUPLED DAMAGE-PLASTICITY MODEL : THEORY
3.1 Introduction
3.2 Continuum Mechanics and Thermodynamics
3.2.1 Equations of states
3.2.2 Dissipation potential
3.2.2.1 Plasticity model: yield criterion and consistency condition
3.2.2.2 Damage model: damage criterion and consistency condition
3.2.2.3 Coupling model: elasto-plastic-damage tangent modulus
3.2.3 Hardening models
3.2.4 Flow rule
3.3 Conclusion
4. COUPLED DAMAGE-PLASTICITY MODEL : NUMERICAL ASPECTS
4.1 Integration Algorithm
4.2 Tangent Matrice, Numerical Integration
4.3 Numerical Implementation and Operator Split Method for Coupled Damage-Plasticity Model
4.3.1 Discretization of the problem
4.3.2 Global computation
4.3.3 Element computation
4.3.4 Local computation and implicit backward Euler scheme
4.3.4.1 Plasticity computation
4.3.4.2 Damage computation
4.4 Numerical Examples
4.4.1 Steel sheet in simple tension test under cycling loading
4.4.2 Steel sheet in bending and shear tests under cyclic loading
4.4.2.1 Bending test
4.4.2.2 Shear test
5. CONCLUSIONS
REFERENCES