This monograph provides a compact introduction into the classical, i.e. rate-independent, plasticity theory. Starting from the engineering stress-strain diagram, the concept of elastic and elasto-plastic material behavior is introduced, as well as the concept of uniaxial and multiaxial stress states. Continuum mechanical modeling in the elasto-plastic range requires, in regards to the constitutive equation, in addition to the elastic law (e.g. Hooke’s law), a yield condition, a flow rule and a hardening rule. These basic equations are thoroughly introduced and explained for one-dimensional stress states. Considering three-dimensional plasticity, different sets of stress invariants to characterize the stress matrix and the decomposition of the stress matrix in its hydrostatic and deviatoric part are introduced. Furthermore, the concept of the yield condition, flow rule and hardening rule is generalized for multiaxial stress states. Some typical yield conditions are introduced and their graphical representation in different stress spaces is discussed in detail. The book concludes with an introduction in the elasto-plastic finite element simulation of mechanical structures. In the context of numerical approximation methods, the so-called predictor-corrector methods are used to integrate the constitutive equations. This is again introduced in detail based on one-dimensional stress states and afterwards generalized to the three-dimensional case. Test your knowledge with questions and answers about the book in the Springer Nature Flashcards app.
Author(s): Andreas Öchsner
Publisher: Springer
Year: 2022
Language: English
Pages: 115
City: Cham
Preface
Contents
Symbols and Abbreviations
Latin Symbols (Capital Letters)
Latin Symbols (Small Letters)
Greek Symbols (Capital Letters)
Greek Symbols (Small Letters)
Mathematical Symbols
Special Matrices
Indices, Superscripted
Indices, Subscripted
Abbreviations
1 Introduction
1.1 Uniaxial Tensile Testing
1.2 Continuum Mechanical Modelling
References
2 Theory of One-Dimensional Plasticity
2.1 Initial Remarks
2.2 Yield Condition
2.3 Flow Rule
2.4 Hardening Rule
2.4.1 Isotropic Hardening
2.4.2 Kinematic Hardening
2.4.3 Combined Hardening
2.5 Elasto-plastic Modulus
2.6 Consideration of Unloading, Reversed Loading and Cyclic Loading
References
3 Theory of Three-Dimensional Plasticity
3.1 Comments on the Stress Matrix
3.2 Graphical Representation of Yield Conditions
3.3 Yield Conditions
3.3.1 Mises Yield Condition
3.3.2 Tresca Yield Condition
3.3.3 Drucker-Prager Yield Condition
3.3.4 Sayir Yield Condition
3.4 Flow Rule
3.5 Hardening Rule
3.5.1 Isotropic Hardening
3.5.2 Kinematic Hardening
References
4 Elasto-plastic Finite Element Simulations
4.1 Approach for One-Dimensional Problems
4.1.1 Integration of the Material Equations
4.1.2 Derivation of the Fully Implicit Backward-Euler Algorithm for Isotropic Hardening
4.1.3 Derivation of the Fully Implicit Backward-Euler Algorithm for Kinematic Hardening
4.1.4 Derivation of the Fully Implicit Backward-Euler Algorithm for Combined Hardening
4.1.5 Derivation of the Semi-implicit Backward-Euler Algorithm for Isotropic Hardening
4.1.6 Sample Problems and Supplementary Problems
4.2 Approach for Three-Dimensinal Problems
4.2.1 Differentiation of the Yield Conditions
4.2.2 Derivation of the Fully Implicit Backward Euler Algorithm for Isotropic Hardening
References
Index
