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Analysis and Computation of Microstructure in Finite Plasticity 2015 ed. [Kõva köide]

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  • Formaat: Hardback, 257 pages, kõrgus x laius: 235x155 mm, kaal: 5325 g, 78 Illustrations, black and white; XII, 257 p. 78 illus., 1 Hardback
  • Sari: Lecture Notes in Applied and Computational Mechanics 78
  • Ilmumisaeg: 11-May-2015
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319182412
  • ISBN-13: 9783319182414
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Analysis and Computation of Microstructure in Finite Plasticity 2015 ed.Suurem pilt
  • Formaat: Hardback, 257 pages, kõrgus x laius: 235x155 mm, kaal: 5325 g, 78 Illustrations, black and white; XII, 257 p. 78 illus., 1 Hardback
  • Sari: Lecture Notes in Applied and Computational Mechanics 78
  • Ilmumisaeg: 11-May-2015
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319182412
  • ISBN-13: 9783319182414
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783319182414.html
Märksõnad:
This book addresses the need for a fundamental understanding of the physical origin, the mathematical behavior and the numerical treatment of models which include microstructure. Leading scientists present their efforts involving mathematical analysis, numerical analysis, computational mechanics, material modelling and experiment. The mathematical analyses are based on methods from the calculus of variations, while in the numerical implementation global optimization algorithms play a central role. The modeling covers all length scales, from the atomic structure up to macroscopic samples. The development of the models ware guided by experiments on single and polycrystals and results will be checked against experimental data.
1 Numerical Algorithms for the Simulation of Finite Plasticity with Microstructures
1(30)
Carsten Carstensen
Dietmar Gallistl
Boris Kramer
1.1 Introduction
1(2)
1.2 Preliminaries and Notation
3(1)
1.3 Convergent Adaptive Finite Element Method for the Two-Well Problem in Elasticity
4(6)
1.3.1 Review of the Model Problem
5(1)
1.3.2 Adaptive Algorithm
6(3)
1.3.3 Convergence for the Deformation Gradient
9(1)
1.4 Guaranteed Lower Energy Bounds for the Two-Well Problem
10(7)
1.4.1 Nonconforming FEM and Discrete Energy Functional
10(2)
1.4.2 Lower Energy Bounds
12(3)
1.4.3 Guaranteed Error Control for the Pseudo-stress
15(1)
1.4.4 Numerical Experiments
16(1)
1.5 Discontinuous Galerkin Method for Degenerate Convex Minimization Problems
17(8)
1.5.1 Optimal Design Benchmark
18(2)
1.5.2 Discontinuous Galerkin Methods
20(1)
1.5.3 Lifting Operator R
20(1)
1.5.4 Connection with the Nonconforming Method
21(1)
1.5.5 Adaptive Finite Element Method
22(1)
1.5.6 Computational Experiments
22(1)
1.5.7 Γ-shaped Domain
23(1)
1.5.8 Slit Domain
24(1)
1.6 Conclusions and Outlook
25(6)
2 Variational Modeling of Slip: From Crystal Plasticity to Geological Strata
31(32)
Sergio Conti
Georg Dolzmann
Carolin Kreisbeck
2.1 Introduction
31(2)
2.2 Experimental Observation of Slip Microstructures in Nature
33(4)
2.2.1 Chevron Folds in Rocks
34(1)
2.2.2 Kink Bands in Stacks of Paper under Compression
34(2)
2.2.3 Simple Laminates in Shear Experiments in Crystal Plasticity
36(1)
2.3 The Hunt-Peletier-Wadee Model for Kink Bands
37(1)
2.4 Variational Modeling of Microstructure
38(3)
2.5 Models in Crystal Plasticity with One Active Slip System
41(12)
2.5.1 Variational Formulation of Crystal Plasticity
42(2)
2.5.2 Relaxation Results in Crystal Plasticity with One Slip System
44(2)
2.5.3 Heuristic Origin of the Laminates
46(3)
2.5.4 Relation to Kink Bands in Rocks
49(2)
2.5.5 Elastic Approximation
51(1)
2.5.6 Higher-Order Regularizations
52(1)
2.6 Beyond One Slip-System
53(10)
2.6.1 Two Slip Systems in a Plane
53(1)
2.6.2 Three Slip Systems in a Plane
54(9)
3 Rate-Independent versus Viscous Evolution of Laminate Microstructures in Finite Crystal Plasticity
63(26)
Christina Gunther
Dennis M. Kochmann
Klaus Hackl
3.1 Introduction
63(1)
3.2 Variational Modeling of Microstructures
64(3)
3.3 Single Slip Crystal Plasticity
67(1)
3.4 Partial Analytical Relaxation via Lamination
67(3)
3.5 Rate-Independent Evolution
70(3)
3.5.1 Evolution Equations
70(1)
3.5.2 Laminate Rotation
71(1)
3.5.3 Laminate Initiation
72(1)
3.5.4 Numerical Scheme
72(1)
3.6 Simulation of Rotating Laminates
73(2)
3.7 Viscous Evolution
75(3)
3.7.1 Evolution Equations
76(1)
3.7.2 Laminate Rotation
77(1)
3.7.3 Laminate Initiation
77(1)
3.8 Comparison of the Laminate Evolution for the Rate-Independent Case and the Viscosity Limit
78(7)
3.9 Conclusion and Discussion
85(4)
4 Variational Gradient Plasticity: Local-Global Updates, Regularization and Laminate Microstructures in Single Crystals
89(36)
Steffen Mauthe
Christian Miehe
4.1 Introduction
90(3)
4.2 A Multifield Formulation of Gradient Crystal Plasticity
93(10)
4.2.1 Introduction of Long-Range Field Variables
93(3)
4.2.2 Introduction of Short-Range Field Variables
96(3)
4.2.3 Energy Storage, Dissipation Potential and Load Functionals
99(3)
4.2.4 Rate-Type Variational Principle and Euler Equations
102(1)
4.2.5 Explicit Form of the Micro-force Balance Equations
103(1)
4.3 Algorithmic Formulation of Gradient Crystal Plasticity
103(5)
4.3.1 Time-Discrete Field Variables in Incremental Setting
103(1)
4.3.2 Update Algorithms for the Short-Range Field Variables
104(1)
4.3.3 Time-Discrete Incremental Variational Principle
105(1)
4.3.4 Space-Time-Discrete Incremental Variational Principle
106(2)
4.4 Example 1: Analysis of an F.C.C. Crystal Grain Aggregate
108(2)
4.4.1 Slip Systems and Euler Angles
108(1)
4.4.2 Voronoi-Tessellated Unit Cell under Shear
109(1)
4.5 Example 2: Laminate Microstructure in Single Crystals
110(8)
4.5.1 Double Slip Systems
111(1)
4.5.2 Implications of Same Plane Double Slip
112(2)
4.5.3 Laminate Deformation Microstructure in Single Crystal Copper
114(4)
4.6 Conclusion
118(7)
5 Variational Approaches and Methods for Dissipative Material Models with Multiple Scales
125(32)
Alexander Mielke
5.1 Introduction
125(2)
5.2 Variational Formulations for Evolution
127(7)
5.2.1 Generalized Gradient Systems and the Energy-Dissipation Principle
128(4)
5.2.2 Rate-Independent Systems and Energetic Solutions
132(2)
5.3 Evolutionary Γ-Convergence
134(4)
5.3.1 pE-convergence for Generalized Gradient Systems
134(3)
5.3.2 pE-convergence for Rate-Independent Systems
137(1)
5.4 Justification of Rate-Independent Models
138(9)
5.4.1 Wiggly Energies Give Rise to Rate-Independent Friction
139(2)
5.4.2 1D Elastoplasticity as Limit of a Chain of Bistable Springs
141(2)
5.4.3 Balanced-Viscosity Solutions as Vanishing-Viscosity Limits
143(4)
5.5 Rate-Independent Evolution of Microstructures
147(10)
5.5.1 Laminate Evolution in Finite-Strain Plasticity
148(1)
5.5.2 A Two-Phase Shape-Memory Model for Small Strains
149(8)
6 Energy Estimates, Relaxation, and Existence for Strain-Gradient Plasticity with Cross-Hardening
157(18)
Keith Anguige
Patrick W. Dondl
6.1 Introduction
158(1)
6.2 A Continuum Model for Strain-Gradient Plasticity with Cross Hardening
159(5)
6.2.1 Plastic Shear
160(1)
6.2.2 Locks and Cross-Hardening
161(1)
6.2.3 Geometrically Necessary Dislocations
162(1)
6.2.4 The Model
163(1)
6.3 Relaxation of the Single-Slip Condition
164(4)
6.4 Some Remarks about Existence of Minimizers
168(1)
6.5 Energy Estimates for a Shear Experiment
168(3)
6.6 Conclusions
171(4)
7 Gradient Theory for Geometrically Nonlinear Plasticity via the Homogenization of Dislocations
175(30)
Stefan Muller
Lucia Scardia
Caterina Ida Zeppieri
7.1 Introduction
175(8)
7.2 Key Mathematical Challenges
183(1)
7.3 Heuristics for Scaling Regimes
184(5)
7.3.1 The Core Energy of a Single Dislocation
184(2)
7.3.2 The Core Energy of Many Dislocations
186(1)
7.3.3 The Interaction Energy
187(2)
7.4 Main Result
189(4)
7.4.1 Set-Up
189(2)
7.4.2 Results
191(2)
7.5 Ideas of Proof
193(12)
8 Microstructure in Plasticity, a Comparison between Theory and Experiment
205(14)
Olga Dmitrieva
Dierk Raabe
Stefan Muller
Patrick W. Dondl
8.1 Introduction
205(2)
8.2 Modeling Continuum Plasticity
207(1)
8.3 A Single-Pass Shear Deformation Experiment and the Resulting Microstructure
208(8)
8.3.1 Sample Preparation and Shear Deformation Experiments
208(1)
8.3.2 Digital Image Correlation for Strain Mapping and EBSD for Texture Mapping
209(1)
8.3.3 Outcome of the Single Crystal Shear Deformation Experiments
210(2)
8.3.4 Energy Minimizing Microstructure
212(3)
8.3.5 An Analysis of the Substructure Within the Lamination Bands
215(1)
8.4 Conclusions
216(3)
9 Construction of Statistically Similar RVEs
219(38)
Lisa Scheunemann
Daniel Balzani
Dominik Brands
Jorg Schroder
9.1 Introduction
220(2)
9.2 Statistically Similar RVEs
222(11)
9.2.1 Method
223(1)
9.2.2 Lower and Upper Bounds of RVEs
224(1)
9.2.3 Statistical Measures
225(8)
9.3 Construction and Analysis of SSRVEs
233(17)
9.3.1 Objective Functions
235(5)
9.3.2 Coupled Micro-macro Simulations
240(1)
9.3.3 SSRVEs Based on Different Sets of Statistical Measures
241(3)
9.3.4 Comparison of Stress on Microscale
244(4)
9.3.5 Analysis of Bounds
248(2)
9.4 Conclusion
250(7)
Author Index 257