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题名 Analysis and Computation of Microstructure in Finite Plasticity / Sergio Conti, Klaus Hackl, editors.

出版资料	Cham : Springer Verlag, c2015.

目录
1.	Numerical Algorithms for the Simulation of Finite Plasticity with Microstructures / Boris Kramer	1
1.1.	Introduction	1
1.2.	Preliminaries and Notation	3
1.3.	Convergent Adaptive Finite Element Method for the Two-Well Problem in Elasticity	4
1.3.1.	Review of the Model Problem	5
1.3.2.	Adaptive Algorithm	6
1.3.3.	Convergence for the Deformation Gradient	9
1.4.	Guaranteed Lower Energy Bounds for the Two-Well Problem	10
1.4.1.	Nonconforming FEM and Discrete Energy Functional	10
1.4.2.	Lower Energy Bounds	12
1.4.3.	Guaranteed Error Control for the Pseudo-stress	15
1.4.4.	Numerical Experiments	16
1.5.	Discontinuous Galerkin Method for Degenerate Convex Minimization Problems	17
1.5.1.	Optimal Design Benchmark	18
1.5.2.	Discontinuous Galerkin Methods	20
1.5.3.	Lifting Operator R	20
1.5.4.	Connection with the Nonconforming Method	21
1.5.5.	Adaptive Finite Element Method	22
1.5.6.	Computational Experiments	22
1.5.7.	₀أ-shaped Domain	23
1.5.8.	Slit Domain	24
1.6.	Conclusions and Outlook	25
2.	Variational Modeling of Slip: From Crystal Plasticity to Geological Strata / Carolin Kreisbeck	31
2.1.	Introduction	31
2.2.	Experimental Observation of Slip Microstructures in Nature	33
2.2.1.	Chevron Folds in Rocks	34
2.2.2.	Kink Bands in Stacks of Paper under Compression	34
2.2.3.	Simple Laminates in Shear Experiments in Crystal Plasticity	36
2.3.	The Hunt-Peletier-Wadee Model for Kink Bands	37
2.4.	Variational Modeling of Microstructure	38
2.5.	Models in Crystal Plasticity with One Active Slip System	41
2.5.1.	Variational Formulation of Crystal Plasticity	42
2.5.2.	Relaxation Results in Crystal Plasticity with One Slip System	44
2.5.3.	Heuristic Origin of the Laminates	46
2.5.4.	Relation to Kink Bands in Rocks	49
2.5.5.	Elastic Approximation	51
2.5.6.	Higher-Order Regularizations	52
2.6.	Beyond One Slip-System	53
2.6.1.	Two Slip Systems in a Plane	53
2.6.2.	Three Slip Systems in a Plane	54
3.	Rate-Independent versus Viscous Evolution of Laminate Microstructures in Finite Crystal Plasticity / Klaus Hackl	63
3.1.	Introduction	63
3.2.	Variational Modeling of Microstructures	64
3.3.	Single Slip Crystal Plasticity	67
3.4.	Partial Analytical Relaxation via Lamination	67
3.5.	Rate-Independent Evolution	70
3.5.1.	Evolution Equations	70
3.5.2.	Laminate Rotation	71
3.5.3.	Laminate Initiation	72
3.5.4.	Numerical Scheme	72
3.6.	Simulation of Rotating Laminates	73
3.7.	Viscous Evolution	75
3.7.1.	Evolution Equations	76
3.7.2.	Laminate Rotation	77
3.7.3.	Laminate Initiation	77
3.8.	Comparison of the Laminate Evolution for the Rate-Independent Case and the Viscosity Limit	78
3.9.	Conclusion and Discussion	85
4.	Variational Gradient Plasticity: Local-Global Updates, Regularization and Laminate Microstructures in Single Crystals / Christian Miehe	89
4.1.	Introduction	90
4.2.	A Multifield Formulation of Gradient Crystal Plasticity	93
4.2.1.	Introduction of Long-Range Field Variables	93
4.2.2.	Introduction of Short-Range Field Variables	96
4.2.3.	Energy Storage, Dissipation Potential and Load Functionals	99
4.2.4.	Rate-Type Variational Principle and Euler Equations	102
4.2.5.	Explicit Form of the Micro-force Balance Equations	103
4.3.	Algorithmic Formulation of Gradient Crystal Plasticity	103
4.3.1.	Time-Discrete Field Variables in Incremental Setting	103
4.3.2.	Update Algorithms for the Short-Range Field Variables	104
4.3.3.	Time-Discrete Incremental Variational Principle	105
4.3.4.	Space-Time-Discrete Incremental Variational Principle	106
4.4.	Example 1: Analysis of an F.C.C. Crystal Grain Aggregate	108
4.4.1.	Slip Systems and Euler Angles	108
4.4.2.	Voronoi-Tessellated Unit Cell under Shear	109
4.5.	Example 2: Laminate Microstructure in Single Crystals	110
4.5.1.	Double Slip Systems	111
4.5.2.	Implications of Same Plane Double Slip	112
4.5.3.	Laminate Deformation Microstructure in Single Crystal Copper	114
4.6.	Conclusion	118
5.	Variational Approaches and Methods for Dissipative Material Models with Multiple Scales / Alexander Mielke	125
5.1.	Introduction	125
5.2.	Variational Formulations for Evolution	127
5.2.1.	Generalized Gradient Systems and the Energy-Dissipation Principle	128
5.2.2.	Rate-Independent Systems and Energetic Solutions	132
5.3.	Evolutionary ₀أ-Convergence	134
5.3.1.	pE-convergence for Generalized Gradient Systems	134
5.3.2.	pE-convergence for Rate-Independent Systems	137
5.4.	Justification of Rate-Independent Models	138
5.4.1.	Wiggly Energies Give Rise to Rate-Independent Friction	139
5.4.2.	1D Elastoplasticity as Limit of a Chain of Bistable Springs	141
5.4.3.	Balanced-Viscosity Solutions as Vanishing-Viscosity Limits	143
5.5.	Rate-Independent Evolution of Microstructures	147
5.5.1.	Laminate Evolution in Finite-Strain Plasticity	148
5.5.2.	A Two-Phase Shape-Memory Model for Small Strains	149
6.	Energy Estimates, Relaxation, and Existence for Strain-Gradient Plasticity with Cross-Hardening / Patrick W. Dondl	157
6.1.	Introduction	158
6.2.	A Continuum Model for Strain-Gradient Plasticity with Cross Hardening	159
6.2.1.	Plastic Shear	160
6.2.2.	Locks and Cross-Hardening	161
6.2.3.	Geometrically Necessary Dislocations	162
6.2.4.	The Model	163
6.3.	Relaxation of the Single-Slip Condition	164
6.4.	Some Remarks about Existence of Minimizers	168
6.5.	Energy Estimates for a Shear Experiment	168
6.6.	Conclusions	171
7.	Gradient Theory for Geometrically Nonlinear Plasticity via the Homogenization of Dislocations / Caterina Ida Zeppieri	175
7.1.	Introduction	175
7.2.	Key Mathematical Challenges	183
7.3.	Heuristics for Scaling Regimes	184
7.3.1.	The Core Energy of a Single Dislocation	184
7.3.2.	The Core Energy of Many Dislocations	186
7.3.3.	The Interaction Energy	187
7.4.	Main Result	189
7.4.1.	Set-Up	189
7.4.2.	Results	191
7.5.	Ideas of Proof	193
8.	Microstructure in Plasticity, a Comparison between Theory and Experiment / Patrick W. Dondl	205
8.1.	Introduction	205
8.2.	Modeling Continuum Plasticity	207
8.3.	A Single-Pass Shear Deformation Experiment and the Resulting Microstructure	208
8.3.1.	Sample Preparation and Shear Deformation Experiments	208
8.3.2.	Digital Image Correlation for Strain Mapping and EBSD for Texture Mapping	209
8.3.3.	Outcome of the Single Crystal Shear Deformation Experiments	210
8.3.4.	Energy Minimizing Microstructure	212
8.3.5.	An Analysis of the Substructure Within the Lamination Bands	215
8.4.	Conclusions	216
9.	Construction of Statistically Similar RVEs / Jorg Schroder	219
9.1.	Introduction	220
9.2.	Statistically Similar RVEs	222
9.2.1.	Method	223
9.2.2.	Lower and Upper Bounds of RVEs	224
9.2.3.	Statistical Measures	225
9.3.	Construction and Analysis of SSRVEs	233
9.3.1.	Objective Functions	235
9.3.2.	Coupled Micro-macro Simulations	240
9.3.3.	SSRVEs Based on Different Sets of Statistical Measures	241
9.3.4.	Comparison of Stress on Microscale	244
9.3.5.	Analysis of Bounds	248
9.4.	Conclusion	250
	Author Index	257

复本

馆藏地	索书号	处理状态
Innovative Univ. Library	QA931 .A46 2015	AVAILABLE

载体形态	xi, 256 p. : ill. ; 25 cm.
Content Type	text txt rdacontent.
载体类型	unmediated n rdamedia.
Carrier Type	volume nc rdacarrier.
丛编	Lecture notes in applied and computational mechanics, 1613-7736 ; v. 78.
	Lecture notes in applied and computational mechanics ; v. 78. 1613-7736.
主题	Plasticity -- Mathematical models.
	Microstructure -- Mathematical models.
其它责任者	Hackl, K. (Klaus), editor.
	Conti, Sergio, 1971- editor.
国际标准书号	9783319182414
	3319182412

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