Buryachenko Micromechanics of Heterogeneous Materials

1. Auflage 2007
ISBN: 978-0-387-68485-7
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 687 Seiten

Here is an accurate and timely account of micromechanics, which spans materials science, mechanical engineering, applied mathematics, technical physics, geophysics, and biology. The book features rigorous and unified theoretical methods of applied mathematics and statistical physics in the material science of microheterogeneous media. Uniquely, it offers a useful demonstration of the systematic and fundamental research of the microstructure of the wide class of heterogeneous materials of natural and synthetic nature.

Autoren/Hrsg.

Buryachenko, Valeriy

Inhaltsverzeichnis

1;Preface;6
2;Contents;10
3;1 Introduction;20
3.1;1.1 Classification of Composites and Nanocomposites;20
3.2;1.2 Effective Material and Field Characteristics;27
3.3;1.3 Homogenization of Random Structure CM;31
3.4;1.4 Overview of the Book;34
4;2 Foundations of Solid Mechanics;36
4.1;2.1 Elements of Tensor Analysis;36
4.2;2.2 The Theory of Strains and Stresses;39
4.3;2.3 Basic Equations of Solid Mechanics;43
4.4;2.4 Basic Equations of Thermoelasticity and Electroelasticity;50
4.5;2.5 Symmetry of Elastic Properties;59
4.6;2.6 Basic Equations of Thermoelastoplastic Deformations;66
5;3 Green’s Functions, Eshelby and Related Tensors;70
5.1;3.1 Static Green’s Function;70
5.2;3.2 The Second Derivative of Green’s Function and Related Problems;73
5.3;3.3 Dynamic Green’s and Related Functions;77
5.4;3.4 Inhomogeneity in an Elastic Medium;81
5.5;3.5 Ellipsoidal Inhomogeneity in the Elastic Medium;86
5.6;3.6 Eshelby Tensor;90
5.7;3.7 Coated Ellipsoidal Inclusion;97
5.8;3.8 Related Problems for Ellipsoidal Inhomogeneity in an Infinite Medium;104
6;4 Multiscale Analysis of the Multiple Interacting Inclusions Problem: Finite Number of Interacting Inclusions;114
6.1;4.1 Description of Numerical Approaches Used for Analyses of Multiple Interacting Heterogeneities;114
6.2;4.2 Basic Equations for Multiple Heterogeneities and Numerical Solution for One Inclusion;117
6.3;4.3 Volume Integral Equation Method;128
6.4;4.4 Hybrid VEE and BIE Method for Multiscale Analysis of Interacting Inclusions ( Macro Problem);139
6.5;4.5 Complex Potentials Method for 2-D Problems;149
7;5 Statistical Description of Composite Materials;156
7.1;5.1 Basic Terminology and Properties of Random Variables and Random Point Fields;157
7.2;5.2 Some Random Point Field Distributions;167
7.3;5.3 Ensemble Averaging of Random Structures;177
7.4;5.4 Numerical Simulation of Random Structures;195
8;6 Effective Properties and Energy Methods in Thermoelasticity of Composite Materials;204
8.1;6.1 Effective Thermoelastic Properties;204
8.2;6.2 Effective Energy Functions;213
8.3;6.3 Some General Exact Results;218
8.4;6.4 Variational Principle of Hashin and Shtrikman;228
8.5;6.5 Bounds of Effective Elastic Moduli;231
8.6;6.6 Bounds of Effective Conductivity;245
8.7;6.7 Bounds of Effective Eigenstrain;247
9;7 General Integral Equations of Micromechanics of Composite Materials;250
9.1;7.1 General Integral Equations for Matrix Composites of Any Structure;251
9.2;7.2 Random Structure Composites;253
9.3;7.3 Doubly and Triply Periodical Structure Composites;260
9.4;7.4 Random Structure Composites with Long-Range Order;263
9.5;7.5 Triply Periodic Particulate Matrix Composites with Imperfect Unit Cells;265
9.6;7.6 Conclusion;267
10;8 Multiparticle Effective Field and Related Methods in Micromechanics of Random Structure Composites;268
10.1;8.1 Definitions of Effective Fields and Effective Field Hypotheses;269
10.2;8.2 Analytical Representation of Effective Thermoelastic Properties;277
10.3;8.3 One-Particle Approximation of the MEFM and Mori- Tanaka Approach;283
11;9 Some Related Methods in Micromechanics of Random Structure Composites;302
11.1;9.1 Related Perturbation Methods;302
11.2;9.2 Effective Medium Methods;310
11.3;9.3 Differential Methods;317
11.4;9.4 Estimation of Effective Properties of Composites with Nonellipsoidal Inclusions;322
11.5;9.5 Numerical Results;325
11.6;9.6 Discussion;333
12;10 Generalization of the MEFM in Random Structure Matrix Composites;334
12.1;10.1 Two Inclusions in an Infinite Matrix;335
12.2;10.2 Composite Material;338
12.3;10.3 First-order Approximation of the Closing Assumption and Effective Elastic Moduli;343
12.4;10.4 Abandonment from the Approximative Hypothesis ( 10.26);351
12.5;10.5 Some Particular Cases;353
12.6;10.6 Some Particular Numerical Results;361
13;11 Periodic Structures and Periodic Structures with Random Imperfections;366
13.1;11.1 General Analysis of Periodic Structures and Periodic Structures with Random Imperfections;366
13.2;11.2 Triply Periodical Particular Matrix Composites in Varying External Stress Field;370
13.3;11.3 Graded Doubly Periodical Particular Matrix Composites in Varying External Stress Field;380
13.4;11.4 Triply Periodic Particulate Matrix Composites with Imperfect Unit Cells;390
14;12 Nonlocal Effects in Statistically Homogeneous and Inhomogeneous Random Structure composites;404
14.1;12.1 General Analysis of Approaches in Nonlocal Micromechanics of Random Structure Composites;404
14.2;12.2 The Nonlocal Integral Equation;409
14.3;12.3 Methods for the Solution of the Nonlocal Integral Equation;411
14.4;12.4 Average Stresses in the Components and Effective Properties for Statistically Homogeneous Media;415
14.5;12.5 Effective Properties of Statistically Inhomogeneous Media;422
14.6;12.6 Concluding Remarks;433
15;13 Stress Fluctuations in Random Structure Composites;436
15.1;13.1 Perturbation Method;438
15.2;13.2 Method of Integral Equations;446
15.3;13.3 Elastically Homogeneous Composites with Randomly Distributed Residual Microstresses;453
15.4;13.4 Stress Fluctuations Near a Crack Tip in Elastically Homogeneous Materials with Randomly Distributed Residual Microstresses;459
15.5;13.5 Concluding Remarks;468
16;14 Random Structure Matrix Composites in a Half- Space;470
16.1;14.1 General Analysis of Approaches in Micromechanics of Random Structure Composites in a Half- space;470
16.2;14.2 General Integral Equation, Definitions of the Nonlocal Effective Properties, and Averaging Operations;474
16.3;14.3 Finite Number of Inclusions in a Half-Space;477
16.4;14.4 Nonlocal Effective Operators of Thermoelastic Properties of Microinhomogeneous Half- Space;481
16.5;14.5 Statistical Properties of Local Residual Microstresses in Elastically Homogeneous Half- Space;488
16.6;14.6 Numerical Results;493
17;15 Effective Limiting Surfaces in the Theory of Nonlinear Composites;500
17.1;15.1 Local Limiting Surface;501
17.2;15.2 Effective Limiting Surface;504
17.3;15.3 Numerical Results;511
17.4;15.4 Concluding Remarks;522
18;16 Nonlinear Composites;524
18.1;16.1 Nonlinear Elastic Composites;525
18.2;16.2 Deformation Plasticity Theory of Composite Materials;532
18.3;16.3 Power-Law Creep;536
18.4;16.4 Elastic–Plastic Behavior of Elastically Homogeneous Materials with Random Residual Microstresses;540
18.5;16.5 A Local Theory of Elastoplastic Deformations of Metal Matrix Composites;546
19;17 Some related problems;556
19.1;17.1 Conductivity;556
19.2;17.2 Thermoelectroelasticity of Composites;568
19.3;17.3 Wave Propagation in a Composite Material;580
20;18 Multiscale Mechanics of Nanocomposites;590
20.1;18.1 Elements of Molecular Dynamic (MD) Simulation;590
20.2;18.2 Bridging Nanomechanics to Micromechanics in Nanocomposites;597
20.3;18.3 Modeling of Nanofiber NCs in the Framework of Continuum Mechanics;601
20.4;18.4 Modeling of Clay NCs in the Framework of Continuum Mechanics;609
20.5;18.5 Some Related Problems in Modeling of NCs Reinforced with NFs and Nanoplates;621
21;19 Conclusion. Critical Analysis of Some Basic Concepts of Micromechanics;626
22;A Appendix;630
22.1;A.1 Parametric Representation of Rotation Matrix;630
22.2;A.2 Second and Fourth-Order Tensors of Special Structures;632
22.3;A.3 Analytical Representation of Some Tensors;638
23;References;642
24;Index;698