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Advances in Extended and Multifield Theories for Continua 2011 ed. [Kõva köide]

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  • Formaat: Hardback, 221 pages, kõrgus x laius: 235x155 mm, kaal: 635 g, XIX, 221 p., 1 Hardback
  • Sari: Lecture Notes in Applied and Computational Mechanics 59
  • Ilmumisaeg: 15-Jul-2011
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3642227376
  • ISBN-13: 9783642227370
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Advances in Extended and Multifield Theories for Continua 2011 ed.Suurem pilt
  • Formaat: Hardback, 221 pages, kõrgus x laius: 235x155 mm, kaal: 635 g, XIX, 221 p., 1 Hardback
  • Sari: Lecture Notes in Applied and Computational Mechanics 59
  • Ilmumisaeg: 15-Jul-2011
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3642227376
  • ISBN-13: 9783642227370
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783642227370.html
Märksõnad:
Modern computational techniques, such as the Finite Element Method, have, since their development several decades ago, successfully exploited continuum theories for numerous applications in science and technology. Although standard continuum methods based upon the Cauchy-Boltzmann continuum are still of great importance and are widely used, it increasingly appears that material properties stemming from microstructural phenomena have to be considered. This is particularly true for inhomogeneous load and deformation states, where lower-scale size effects begin to affect the macroscopic material response; something standard continuum theories fail to account for. Following this idea, it is evident that standard continuum mechanics has to be augmented to capture lower-scale structural and compositional phenomena, and to make this information accessible to macroscopic numerical simulations.



Continuum Thermodynamic and Rate Variational Formulation of Models for Extended Continua
1(18)
Bob Svendsen
1 Introduction
1(2)
2 Energy Balance and Basic Constitutive Assumptions
3(2)
3 Euclidean Frame-Indifference of the Energy Balance
5(2)
4 Material Frame-Indifference of the Free Energy Density
7(1)
5 Dissipation Principle and Reduced Evolution-Field Relations
8(2)
6 Variational Formulation
10(3)
7 Discussion
13(6)
References
15(4)
From Lattice Models to Extended Continua
19(28)
Stefan Diehels
Daniel Scharding
1 Introduction
19(2)
2 Lattice Models
21(5)
2.1 Honeycomb Structure
21(2)
2.2 Effective Shear Modulus
23(2)
2.3 Reference Data
25(1)
3 Extended Continuum Theories
26(4)
3.1 The Linear Cosserat Theory
27(1)
3.2 Analytical Solution for Shear
28(2)
4 Parameter Identification
30(4)
4.1 Gradient-Based Methods
30(2)
4.2 Evolution Strategies
32(2)
5 Conclusions and Outlook
34(13)
References
35(3)
Appendix
38(9)
Rotational Degrees of Freedom in Modeling Materials with Intrinsic Length Scale
47(22)
Elena Pasternak
Hans-Bernd Muhlhaus
Arcady V. Dyskin
1 Introduction
47(1)
2 Non-standard Continua for Modeling Materials with Microstructure
48(4)
3 Homogenization of ID Structures
52(6)
3.1 Homogenization by Differential Expansion
53(1)
3.2 Homogenization by Integral Transformation (Non-local Cosserat Continuum)
54(3)
3.3 Harmonic Waves in ID Structures
57(1)
4 Homogenization by Differential Expansions in 3D
58(1)
5 Cosserat Model of Layered Materials with Sliding Layers and Stress Concentrations
59(2)
6 Path-Independent Integrals in Cosserat Continuum
61(3)
7 Conclusions
64(5)
References
65(4)
Micromorphic vs. Phase-Field Approaches for Gradient Viscoplasticity and Phase Transformations
69(20)
Samuel Forest
Kais Ammar
Benoit Appolaire
1 Introduction
69(2)
2 Thermomechanics with Additional Degrees of Freedom
71(4)
2.1 General Setting
71(2)
2.2 Micromorphic Model as a Special Case
73(1)
2.3 Phase-Field Model as a Special Case
74(1)
3 Constitutive Framework for Gradient and Micromorphic Viscoplasticity
75(3)
3.1 Introduction of Viscous Generalized Stresses
75(2)
3.2 Decomposition of the Generalized Strain Measures
77(1)
4 Phase-Field Models for Elastoviscoplastic Materials
78(8)
4.1 Coupling with Diffusion
80(1)
4.2 Partition of Free Energy and Dissipation Potential
81(2)
4.3 Multi-phase Approach for the Mechanical Contribution
83(2)
4.4 Voigt/Taylor Model Coupled Phase-Field Mechanical Theory
85(1)
5 Conclusion
86(3)
References
86(3)
Geometrically Nonlinear Continuum Thermomechanics Coupled to Diffusion: A Framework for Case II Diffusion
89(20)
Andrew T. McBride
Swantje Bargmann
Paul Steinmann
1 Introduction
89(2)
2 Preliminaries: Notation and Key Concepts
91(3)
3 Governing Equations
94(8)
3.1 Conservation of Solid Mass
94(1)
3.2 Conservation of Diffusing Species Mass
94(2)
3.3 Balance of Linear and Angular Momentum
96(1)
3.4 Balance of Internal Energy
96(1)
3.5 Balance of Entropy
97(2)
3.6 Constitutive Relations
99(2)
3.7 Temperature Evolution Equation
101(1)
4 Key Features of the Helmholtz Energy Required to Reproduce Case II Diffusion
102(2)
4.1 Energy Associated with Viscoelastic Effects
103(1)
4.2 Energy Associated with Mixing
104(1)
5 Discussion and Conclusions
104(5)
References
106(3)
Effective Electromechanical Properties of Heterogeneous Piezoelectrics
109(20)
Marc-Andre Keip
Jorg Schroder
1 Introduction
109(3)
2 Boundary Value Problems on the Macro- and the Mesoscale
112(4)
2.1 Macroscopic Electro-Mechanically Coupled BVP
112(2)
2.2 Mesoscopic Electro-Mechanically Coupled BVP
114(2)
3 Effective Properties of Piezoelectric Materials
116(4)
4 Numerical Example
120(4)
4.1 Invariant Formulation and Material Parameters
121(1)
4.2 Investigation of the "Wolfgang Ehlers 60" Mesostructure
122(2)
5 Conclusion
124(5)
References
125(4)
Coupled Thermo-and Electrodynamics of Multiphasic Continua
129(24)
Bernd Markert
1 Mixture and Porous Media Theories
129(3)
1.1 The Macroscopic Mixture Approach
130(1)
1.2 Volume Fractions, Saturation and Density
130(2)
2 Kinemalical Relations
132(6)
2.1 Mixture Kinematics
132(2)
2.2 Deformation and Strain Measures
134(4)
3 Some Aspects of Electrodynamics
138(4)
3.1 Preliminaries
138(1)
3.2 The Macroscopic Maxwell Equations
139(2)
3.3 Fusion of Electrodynamics and Thermodynamics
141(1)
4 Balance Relations
142(8)
4.1 Stress Concept and Dual Variables
142(2)
4.2 Master Balance Principle for Mixtures
144(6)
5 Conclusion
150(3)
References
151(2)
Ice Formation in Porous Media
153(22)
Joachim Bluhm
Tim Ricken
Moritz Bloßfeld
1 Introduction
153(2)
2 Basics
155(2)
3 Simplified Quadruple Model
157(9)
3.1 Field Equations
157(1)
3.2 Constitutive Theory
158(8)
4 Examples
166(1)
4.1 Example 1: Capillary Suction during Freezing
167(3)
4.2 Example 2: Heat of Fusion during Phase Transition
170(1)
5 Conclusion
171(4)
References
172(3)
Optical Measurements for a Cold-Box Sand and Aspects of Direct and Inverse Problems for Micropolar Elasto-Plasticity
175(22)
Rolf Mahnken
Ismail Caylak
1 Introduction
175(3)
2 Specimens and Testing Equipment
178(2)
2.1 Materials and Specimen Preparation
178(1)
2.2 Experimental Equipment
178(2)
3 Uniaxial Compression and Tension Tests
180(4)
3.1 SD-Effect and Optical Measurements
180(3)
3.2 Rate Dependency and Reproducibility
183(1)
3.3 Influence of Storage Time
183(1)
4 Thermo-Mechanical Characterization
184(3)
4.1 Heat Exchanger Variation for Thermal Loading
184(2)
4.2 Mechanical Loading for Different Isothermal Conditions
186(1)
5 Triaxial Characterization
187(1)
6 Modeling of Micropolar Continua
188(3)
6.1 Basic Equations
188(1)
6.2 Yield Function and Plastic Potential
189(2)
7 Direct and Inverse Problems for Micropolar Solids
191(3)
7.1 Direct Problem: Weak Formulation
191(1)
7.2 Inverse Problem: Constrained Least Squares Problem
192(2)
8 Summary and Outlook
194(3)
References
195(2)
Model Reduction for Complex Continua - At the Example of Modeling Soft Tissue in the Nasal Area
197(22)
Annika Radermacher
Stefanie Reese
1 Indroduction
197(3)
2 Model Reduction for Non-linear Structural Mechanics
200(3)
2.1 SVD-Based Reduction
200(3)
2.2 Error Definition
203(1)
3 Biomechanical Structural Applications
203(12)
3.1 Examples
203(2)
3.2 Study of Convergence
205(1)
3.3 Study of Parameters
205(8)
3.4 Human Nose Model
213(2)
4 Conclusion
215(4)
References
215(4)
Author Index 219