Before a structure or component can be completed, before any analytical model can be constructed, and even before the design can be formulated, you must have a fundamental understanding of damage behavior in order to produce a safe and effective design. Damage Mechanics presents the underlying principles of continuum damage mechanics along with the latest research. The authors consider both isotropic and anisotropic theories as well as elastic and elasto-plastic damage analyses using a self-contained, easily understood approach.Beginning with the requisite mathematics, Damage Mechanics guides you from the very basic concepts to advanced mathematical and mechanical models. The first chapter offers a brief MAPLE® tutorial and supplies all of the MAPLE commands needed to solve the various problems throughout the chapter. The authors then discuss the basics of elasticity theory within the continuum mechanics framework, the simple case of isotropic damage, effective stress, damage evolution, kinematic description of damage, and the general case of anisotropic damage. The remainder of the book includes a review of plasticity theory, formulation of a coupled elasto-plastic damage theory developed by the authors, and the kinematics of damage for finite-strain elasto-plastic solids.From fundamental concepts to the latest advances, this book contains everything that you need to study the damage mechanics of metals and homogeneous materials.
Author(s): George Z. Voyiadjis, Peter I. Kattan
Edition: 1
Publisher: CRC Press
Year: 2005
Language: English
Pages: 270
Damage Mechanics......Page 9
Dedication......Page 11
Preface......Page 12
Authors......Page 14
Contents......Page 16
1.1 Maple Tutorial......Page 19
Problems......Page 21
1.2 Vectors......Page 23
Solution......Page 30
Problems......Page 31
1.3 Matrices......Page 35
Example 1.2......Page 44
Solution......Page 45
Solution......Page 46
Problems......Page 47
1.4 Indicial Notation......Page 53
Solution......Page 57
Solution......Page 58
Problems......Page 59
1.5 Transformation of Vectors......Page 62
Example 1.9......Page 65
Solution......Page 66
Problems......Page 67
1.6 Cartesian Tensors......Page 68
Solution......Page 71
Example 1.13......Page 72
Solution......Page 73
Solution......Page 74
Problems......Page 75
Example 1.15......Page 78
Example 1.16......Page 79
Solution......Page 80
Solution......Page 81
Problems......Page 82
1.8 Tensor Calculus......Page 83
Solution......Page 87
Solution......Page 88
Problems......Page 89
1.9 Maple Tensor Commands......Page 91
Problems......Page 93
2.1 Motion of a Continuum......Page 94
Solution......Page 97
Solution......Page 98
Problems......Page 99
2.2 Deformation and Strain......Page 100
Solution......Page 104
Problems......Page 105
2.3 Stress......Page 111
Example 2.6......Page 117
Solution......Page 118
Problems......Page 119
2.4 Linear Elastic Relation......Page 124
Solution......Page 126
Problems......Page 127
3.1 Introduction......Page 130
3.2 Damage Variables......Page 132
3.3 Effective Stress......Page 134
Solution......Page 137
Solution......Page 138
Problems......Page 139
3.4 Damage Evolution......Page 141
Problems......Page 143
4.1 Introduction......Page 145
4.2 Theoretical Preliminaries......Page 146
4.3 Description of Damage State......Page 147
4.4 Fourth-Order Anisotropic Damage Effect Tensor......Page 149
4.5 Kinematic Description of Elastic-Damage Deformation......Page 151
4.6 Constitutive Equation of Elastic-Damage Behavior......Page 156
4.7 Conclusion......Page 157
5.1 Introduction......Page 159
5.2 Anisotropic Damage Criterion......Page 160
5.3 Damage Tensor......Page 162
5.4 Damage Evolution......Page 165
5.5 Constitutive Model......Page 168
5.6 Uniaxial Tension Analysis......Page 170
5.7 Finite Element Implementation......Page 171
5.8 Center-Cracked Thin Plate Under In-Plane Tensile Forces......Page 173
5.9 Conclusion......Page 182
6.1 Introduction......Page 183
6.2 Theoretical Formulation......Page 184
6.3 Monotonic and Cyclic Tension Loadings on 316 Stainless Steel......Page 191
6.4 Modifcation of the Kinematic Hardening Model for Non-Proportional Loading......Page 197
6.5 Model Predictions and Comparisons with Experimental Data for Non-Proportional Loadings......Page 198
6.6 Ratchetting......Page 201
6.7 Conclusions......Page 203
7.1 Stress Transformation between Damaged and Undamaged States......Page 205
7.1.1 Effective Stress Tensor......Page 206
7.1.2 Effective Backstress Tensor......Page 208
7.2 Strain Rate Transformation between Damaged and Undamaged States......Page 209
7.2.1 Effective Elastic Strain......Page 210
7.2.2 Effective Plastic Strain Rate......Page 211
7.3.1 Damage Evolution......Page 216
7.3.2 Plastic Deformation......Page 218
7.3.3 Coupling of Damage and Plastic Deformation......Page 219
7.4 Application to Void Growth: Gurson’s Model......Page 222
7.5 Effective Spin Tensor......Page 225
Problems......Page 226
8.1 Theoretical Preliminaries......Page 229
8.2 Description of Damage State......Page 230
8.3 Fourth-Order Anisotropic Damage Effect Tensor......Page 232
8.4 The Kinematics of Damage for Elasto-Plastic Behavior with Finite Strains......Page 234
8.4.1 A Multiplicative Decomposition......Page 236
8.4.2 Fictitious Damage Deformation Gradients......Page 244
8.4.3 An Additive Decomposition......Page 245
8.5 Irreversible Thermodynamics......Page 248
8.6 Constitutive Equation for Finite Elasto-Plastic Deformation with Damage Behavior......Page 254
Problems......Page 256
References......Page 257
