## Modeling of Creep for Structural Analysis"Creep Modeling for Structural Analysis" develops methods to simulate and analyze the time-dependent changes of stress and strain states in engineering structures up to the critical stage of creep rupture. The principal subjects of creep mechanics are the formulation of constitutive equations for creep in structural materials under multi-axial stress states; the application of structural mechanics models of beams, plates, shells and three-dimensional solids and the utilization of procedures for the solution of non-linear initial-boundary value problems. The objective of this book is to review some of the classical and recently proposed approaches to the modeling of creep for structural analysis applications as well as to extend the collection of available solutions of creep problems by new, more sophisticated examples. In Chapter 1, the book discusses basic features of the creep behavior in materials and structures and presents an overview of various approaches to the modeling of creep. Chapter 2 collects constitutive models that describe creep and damage processes under multi-axial stress states. Chapter 3 deals with the application of constitutive models to the description of creep for several structural materials. Constitutive and evolution equations, response functions and material constants are presented according to recently published experimental data. In Chapter 4 the authors discuss structural mechanics problems. Governing equations of creep in three-dimensional solids, direct variational methods and time step algorithms are reviewed. Examples are presented to illustrate the application of advanced numerical methods to the structural analysis. An emphasis is placed on the development and verification of creep-damage material subroutines inside the general purpose finite element codes. |

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### Contents

1 | |

112 MultiAxial Creep and Stress State Effects | 7 |

12 Creep in Engineering Structures | 11 |

13 Basic Approaches to Creep Modeling | 15 |

Constitutive Models of Creep | 17 |

22 Secondary Creep | 22 |

221 Isotropic Creep | 23 |

2212 Creep Potentials with Three Invariants of the Stress Tensor | 25 |

43 Beams | 122 |

432 Closed Form Solution | 124 |

433 Variational Formulation and the Ritz Method | 126 |

434 Examples | 128 |

4342 Finite Element Solutions | 132 |

435 Stress State Effects and Cross Section Assumptions | 138 |

Reﬁned vs Classical Beam Theory | 144 |

44 Plates and Shells | 148 |

222 Creep of Initially Anisotropic Materials | 28 |

2221 Classical Creep Equations | 30 |

2222 NonClassical Creep Equations | 38 |

223 Functions of Stress and Temperature | 44 |

23 Primary Creep and Creep Transients | 48 |

231 Time and Strain Hardening | 50 |

232 Kinematic Hardening | 53 |

24 Tertiary Creep and Creep Damage | 60 |

241 ScalarValued Damage Variables | 62 |

2412 MicromechanicallyConsistent Models | 72 |

2413 MechanismBased Models | 75 |

2414 Models Based on Dissipation | 77 |

242 DamageInduced Anisotropy | 78 |

Examples of Constitutive Equations for Various Materials | 85 |

31 Models of Isotropic Creep for Several Alloys | 86 |

312 Steel 13CrMo45 | 87 |

32 Model for Anisotropic Creep in a MultiPass Weld Metal | 92 |

321 Origins of Anisotropic Creep | 93 |

322 Modeling of Secondary Creep | 99 |

323 Identiﬁcation of Material Constants | 100 |

Modeling of Creep in Structures | 103 |

42 InitialBoundary Value Problems and General Solution Procedures | 106 |

422 VectorMatrix Representation | 108 |

423 Numerical Solution Techniques | 111 |

4231 Time Integration Methods | 113 |

4232 Solution of Boundary Value Problems | 117 |

4233 Variational Formulations and Procedures | 118 |

442 Examples | 151 |

4422 Long Term Strength Analysis of a Steam Transfer Line From the | 161 |

Basic Operations of Tensor Algebra | 167 |

A1 Polar and Axial Vectors | 168 |

A2 Operations with Vectors | 169 |

A23 Scalar Dot Product of Two Vectors | 170 |

A3 Bases | 171 |

A4 Operations with Second Rank Tensors | 172 |

A42 Multiplication by a Scalar | 173 |

A46 Dot Products of a Second Rank Tensor and a Vector | 174 |

A48 Trace | 175 |

A410 SkewSymmetric Tensors | 176 |

A413 Determinant and Inverse of a Second Rank Tensor | 177 |

A415 CayleyHamilton Theorem | 178 |

A417 Orthogonal Tensors | 179 |

Elements of Tensor Analysis | 181 |

B2 Hamilton Nabla Operator | 182 |

B3 Integral Theorems | 184 |

B4 ScalarValued Functions of Vectors and Second Rank Tensors | 185 |

Orthogonal Transformations and Orthogonal Invariants | 187 |

C2 Invariants for the Full Orthogonal Group | 188 |

C31 Invariants for a Single Second Rank Symmetric Tensor | 189 |

C32 Invariants for a Set of Vectors and Second Rank Tensors | 194 |

C4 Invariants for the Orthotropic Symmetry Group | 196 |

199 | |

215 | |

### Other editions - View all

Modeling of Creep for Structural Analysis Konstantin Naumenko,Holm Altenbach No preview available - 2007 |

Modeling of Creep for Structural Analysis Konstantin Naumenko,Holm Altenbach No preview available - 2010 |