Damage Mechanics

2.04 Damage Mechanics J. L. CHABOCHE O⁄ce National d’Etudes et de Recherches AeŁrospatiales, Chatillon Cedex, France and

UniversiteŁ deTechnologie deTroyes, France 2.04.1 INTRODUCTION

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2.04.2 GENERAL NOTIONS AND CONCEPTS

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2.04.2.1 Deformation, Damage, and Crack Propagation 2.04.2.2 Damage Measurements and Definitions 2.04.2.3 Basic Thermodynamic Concepts 2.04.2.3.1 State equations 2.04.2.3.2 Complementary dissipative laws 2.04.2.3.3 Energy dissipated as heat and stored energy 2.04.2.3.4 Energy dissipated by damage 2.04.3 THEORETICAL ASPECTS OF CDM: STATE EQUATIONS 2.04.3.1 Tensorial Nature of the Damage Variables 2.04.3.2 Effective Stress Concepts 2.04.3.2.1 Net stress tensor 2.04.3.2.2 Effective stress tensor based on strain equivalence 2.04.3.2.3 Effective stress and strain tensors based on energy equivalence 2.04.3.3 Various Forms for the Damaged Elasticity Law 2.04.3.4 Different Forms of State Couplings 2.04.4 THEORETICAL ASPECTS OF CDM: EVOLUTION EQUATIONS 2.04.4.1 Coupling of Dissipations 2.04.4.2 Possible Choices for the Plastic Yield Surface 2.04.4.3 A General Approach for Plasticity/Damage Coupling 2.04.4.3.1 State equations 2.04.4.3.2 Plasticity evolution equations 2.04.4.4 Some Remarks and Exercises 2.04.4.4.1 Drawbacks and benefits of the two types of equivalence principles 2.04.4.4.2 Asymptotic behavior on approaching fracture 2.04.4.5 Damage Evolution for Rate-independent Conditions 2.04.4.5.1 Normality rules 2.04.4.5.2 The nondamage criteria 2.04.4.5.3 Consistency condition 2.04.4.5.4 Tangent operator 2.04.4.6 Damage Evolution Equations for Rate-dependent Conditions 2.04.4.6.1 Standard approach 2.04.4.6.2 Quasistandard approach 2.04.5.6.3 Damage as a fourth-rank tensor 2.04.5 COHESIVE MODELS

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2.04.5.1 Development of Cohesive Models 2.04.5.2 Review of Some Interface Debonding Models 2.04.5.2.1 Tvergaard model

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