Micromechanics of heterogeneous materials:
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| Format: | Book |
| Language: | English |
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New York, NY
Springer
2007
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| Subjects: | |
| Online Access: | Beschreibung für Leser Inhaltsverzeichnis |
| Physical Description: | XX, 686 S. Ill., graph. Darst. |
| ISBN: | 9780387368276 |
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MICROMECHANICS OF HETEROGENEOUS MATERIALS VALERIY A. BURYACHENKO
UNVIERSITY OF DAYTON RESEARCH INSTITUTE }SP NNGER CONTENTS 1
INTRODUCTION 1 1.1 CLASSIFICATION OF COMPOSITES AND NANOCOMPOSITES 1
1.1.1 GEOMETRICAL CLASSIFICATION OF COMPOSITE MATERIALS (CM) . 2 1.1.2
CLASSIFICATION OF MECHANICAL PROPERTIES OF CM CONSTITUENTS 5 1.1.3
CLASSIFICATION OF CM MANUFACTURING 8 1.2 EFFECTIVE MATERIAL AND FIELD
CHARACTERISTICS.: 8 1.3 HOMOGENIZATION OF RANDOM STRUCTURE CM 12 1.4
OVERVIEW OF THE BOOK 15 2 FOUNDATIONS OF SOLID MECHANICS 17 2.1 ELEMENTS
OF TENSOR ANALYSIS 17 2.2 THE THEORY OF STRAINS AND STRESSES 20 2.3
BASIC EQUATIONS OF SOLID MECHANICS 24 2.3.1 CONSERVATION LAWS, BOUNDARY
CONDITIONS, AND CONSTITUTIVE EQUATION 24 2.3.2 THE EQUATIONS OF LINEAR
ELASTICITY 28 2.3.3 EXTREMUM PRINCIPLES OF ELASTOSTATIC 29 2.4 BASIC
EQUATIONS OF THERMOELASTICITY AND ELECTROELASTICITY 31 2.4.1
THERMOELASTICITY EQUATIONS 31 2.4.2 ELECTROELASTIC EQUATIONS 35 2.4.3
MATRIX REPRESENTATION OF SOME SYMMETRIE TENSORS 38 2.5 SYMMETRY OF
ELASTIC PROPERTIES 40 2.6 BASIC EQUATIONS OF THERMOELASTOPLASTIC
DEFORMATIONS 47 2.6.1 INCREMENTAL THEORY OF PLASTICITY 47 2.6.2
DEFORMATION THEORY OF PLASTICITY 49 3 GREEN'S FUNCTIONS, ESHELBY AND
RELATED TENSORS 51 3.1 STATIC GREEN'S FUNCTION 51 3.2 THE SECOND
DERIVATIVE OF GREEN'S FUNCTION AND RELATED PROBLEMS 54 3.2.1 THE SECOND
DERIVATIVE OF GREEN'S FUNCTION 54 3.2.2 THE TENSORS RELATED TO THE
GREEN'S FUNCTION 57 3.3 DYNAMIC GREEN'S AND RELATED FUNCTIONS 58 3.4
INHOMOGENEITY IN AN ELASTIC MEDIUM 62 XII CONTENTS 3.4.1 GENERAL CASE OF
INHOMOGENEITY IN AN ELASTIC MEDIUM . 62 3.4.2 INTERFACE BOUNDARY
OPERATORS 65 3.5 ELLIPSOIDAL INHOMOGENEITY IN THE ELASTIC MEDIUM 67 3.6
ESHELBY TENSOR 71 3.6.1 TENSOR REPRESENTATION OF ESHELBY TENSOR 71 3.6.2
ESHELBY AND RELATED TENSORS IN A SPECIAL BASIS 75 3.7 COATED ELLIPSOIDAL
INCLUSION 78 3.7.1 GENERAL REPRESENTATION FOR THE CONCENTRATOR FACTORS
FOR COATED HETEROGENEITY 79 3.7.2 SINGLE ELLIPSOIDAL INCLUSION WITH THIN
COATING 81 3.7.3 NUMERICAL ASSESSMENT OF THIN-LAYER HYPOTHESIS 84 3.8
RELATED PROBLEMS FOR ELLIPSOIDAL INHOMOGENEITY IN AN INFINITE MEDIUM 85
3.8.1 CONDUCTIVITY PROBLEM 85 3.8.2 SCATTERING OF ELASTIC WAVES BY
ELLIPSOIDAL INCLUSION IN A HOMOGENEOUS MEDIUM 90 3.8.3 PIEZOELECTRIC
PROBLEM 93 MULTISCALE ANALYSIS OF THE MULTIPLE INTERACTING INCLUSIONS
PROBLEM: FINITE NUMBER OF INTERACTING INCLUSIONS 95 4.1 DESCRIPTION OF
NUMERICAL APPROACHES USED FOR ANALYSES OF MULTIPLE INTERACTING
HETEROGENEITIES 95 4.2 BASIC EQUATIONS FOR MULTIPLE HETEROGENEITIES AND
NUMERICAL SOLUTION FOR ONE INCLUSION 98 4.2.1 BASIC EQUATIONS FOR
MULTIPLE HETEROGENEITIES 98 4.2.2 THE HETEROGENEITY VI INSIDE AN
IMAGINARY ELLIPSOID VF . 101 4.2.3 THE HETEROGENEITY UJ INSIDE A
NONELLIPSOIDAL IMAGINARY DOMAIN VF 104 4.2.4 ESTIMATION OF CONCENTRATOR
FACTOR TENSORS BY FEA 105 4.3 VOLUME INTEGRAL EQUATION METHOD 109 4.3.1
REGULARIZED REPRESENTATION OF INTEGRAL EQUATIONS 109 4.3.2 THE ITERATION
METHOD 111 4.3.3 INITIAL APPROXIMATION FOR INTERACTING INCLUSIONS IN AN
INFINITE MEDIUM 113 4.3.4 FIRST-ORDER AND SUBSEQUENT APPROXIMATIONS 117
4.3.5 NUMERICAL RESULTS FOR TWO CYLINDRICAL INCLUSIONS IN AN INFINITE
MATRIX 119 4.4 HYBRID VEE AND BIE METHOD FOR MULTISCALE ANALYSIS OF
INTERACTING INCLUSIONS (MACRO PROBLEM) 120 4.4.1 INITIAL APPROXIMATION
FOR THE FIELDS INDUCED BY A MACROINCLUSION 120 4.4.2 INITIAL
APPROXIMATION IN THE MICRO PROBLEM 122 4.4.3 THE SUBSEQUENT
APPROXIMATIONS 123 4.4.4 SOME DETAILS OF THE ITERATION SCHEME IN
MULTISCALE ANALYSIS 124 4.4.5 NUMERICAL RESULT FOR A SMALL INCLUSION
NEAR A LARGE ONE. 126 4.4.6 DISCUSSION 129 ^ H P W CONTENTS XIII 4.5
COMPLEX POTENTIALS METHOD FOR 2-D PROBLEMS 130 5 STATISTICAL DESCRIPTION
OF COMPOSITE MATERIALS 137 5.1 BASIC TERMINOLOGY AND PROPERTIES OF
RANDOM VARIABLES AND RANDOM POINT FIELDS 138 5.1.1 RANDOM VARIABLES 138
5.1.2 RANDOM POINT FIELDS 141 5.1.3 BASIC DESCRIPTORS OF RANDOM POINT
FIELDS 144 5.2 SOME RANDOM POINT FIELD DISTRIBUTIONS 148 5.2.1 POISSON
DISTRIBUTION 148 5.2.2 STATISTICALLY HOMOGENEOUS CLUSTERED POINT FIELDS
150 5.2.3 INHOMOGENEOUS POISSON FIELDS 152 5.2.4 GIBBS POINT FIELDS 154
5.3 ENSEMBLE AVERAGING OF RANDOM STRUCTURES 158 5.3.1 ENSEMBLE
DISTRIBUTION FUNCTIONS 159 5.3.2 STATISTICAL AVERAGES OF FUNCTIONS 164
5.3.3 STATISTICAL DESCRIPTION OF INDICATOR FUNCTIONS 165 5.3.4
GEOMETRICAL DESCRIPTION AND AVERAGING OF DOUBLY AND TRIPLY PERIODIC
STRUCTURES . 171 5.3.5 REPRESENTATIONS OF ODF 173 5.4 NUMERICAL
SIMULATION OF RANDOM STRUCTURES 176 5.4.1 MATERIALS AND IMAGE ANALYSIS
PROCEDURES 178 5.4.2 HARD-CORE MODEL 179 5.4.3 HARD-CORE SHAKING MODEL
(HCSM) 180 5.4.4 COLLECTIVE REARRANGEMENT MODEL (CRM) 181 6 EFFECTIVE
PROPERTIES AND ENERGY METHODS IN THERMOELASTICITY OF COMPOSITE MATERIALS
185 6.1 EFFECTIVE THERMOELASTIC PROPERTIES 185 6.1.1 HILL'S CONDITION
AND REPRESENTATIVE VOLUME ELEMENT 185 6.1.2 EFFECTIVE ELASTIC MODULI 188
6.1.3 OVERALL THERMOELASTIC PROPERTIES 191 6.2 EFFECTIVE ENERGY
FUNCTIONS 194 6.3 SOME GENERAL EXACT RESULTS 199 6.3.1 TWO-PHASE
COMPOSITES 199 6.3.2 POLYCRYSTALS COMPOSED OF TRANSVERSALLY ISOTROPIE
CRYSTALS 207 6.4 VARIATIONAL PRINCIPLE OF HASHIN AND SHTRIKMAN 209 6.5
BOUNDS OF EFFECTIVE ELASTIC MODULI 212 6.5.1 HILL'S BOUNDS 212 6.5.2
HASHIN-SHTRIKMAN BOUNDS 217 6.5.3 BOUNDS OF HIGHER ORDER 222 6.6 BOUNDS
OF EFFECTIVE CONDUCTIVITY 226 6.7 BOUNDS OF EFFECTIVE EIGENSTRAIN 228
CONTENTS GENERAL INTEGRAL EQUATIONS OF MICROMECHANICS OF COMPOSITE
MATERIALS 231 7.1 GENERAL INTEGRAL EQUATIONS FOR MATRIX COMPOSITES OF
ANY STRUCTURE 232 7.2 RANDOM STRUCTURE COMPOSITES 234 7.2.1 GENERAL
INTEGRAL EQUATION FOR RANDOM STRUCTURE COMPOSITES 234 7.2.2 SOME
PARTICULAR CASES 237 7.2.3 COMPARISON WITH RELATED EQUATIONS 239 7.3
DOUBLY AND TRIPLY PERIODICAL STRUCTURE COMPOSITES 241 7.4 RANDOM
STRUCTURE COMPOSITES WITH LONG-RANGE ORDER 244 7.5 TRIPLY PERIODIC
PARTICULATE MATRIX COMPOSITES WITH IMPERFECT UNIT CELLS 246 7.6
CONCLUSION 248 MULTIPARTICLE EFFECTIVE FIELD AND RELATED METHODS IN
MICROMECHANICS OF RANDOM STRUCTURE COMPOSITES 249 8.1 DEFINITIONS OF
EFFECTIVE FIELDS AND EFFECTIVE FIELD HYPOTHESES . 250 8.1.1 EFFECTIVE
FIELDS 250 8.1.2 APPROXIMATE EFFECTIVE FIELD HYPOTHESIS 253 8.1.3
CLOSING EFFECTIVE FIELD HYPOTHESIS 255 8.1.4 EFFECTIVE FIELD HYPOTHESIS
AND COMPOSITES WITH ONE SORT OF INHOMOGENEITIES 255 8.2 ANALYTICAL
REPRESENTATION OF EFFECTIVE THERMOELASTIC PROPERTIES . 258 8.2.1 AVERAGE
STRESSES IN THE COMPONENTS 258 8.2.2 EFFECTIVE PROPERTIES OF THE
COMPOSITE 260 8.2.3 SOME RELATED MULTIPARTICLE METHODS 262 8.3
ONE-PARTICLE APPROXIMATION OF THE MEFM AND MORI-TANAKA APPROACH 264
8.3.1 ONE-PARTICLE ("QUASI-CRYSTALLINE") APPROXIMATION OF MEFM 264 8.3.2
MORI-TANAKA APPROACH 269 8.3.3 EFFECTIVE PROPERTIES ESTIMATED VIA THE
MEF AND MTM AT QI = Q 272 8.3.4 SOME METHODS RELATED TO THE
ONE-PARTICLE APPROXIMATION OF THE MEFM 277 8.3.5 SOME ANALYTICAL
REPRESENTATIONS FOR EFFECTIVE MODULI . 280 SOME RELATED METHODS IN
MICROMECHANICS OF RANDOM STRUCTURE COMPOSITES 283 9.1 RELATED
PERTURBATION METHODS 283 9.1.1 COMBINED MEFM-PERTURBATION METHOD 283
9.1.2 PERTURBATION METHOD FOR SMALL CONCENTRATIONS OF INCLUSIONS 286
9.1.3 PERTURBATION METHOD FOR WEAKLY INHOMOGENEOUS MEDIA . 287 9.1.4
ELASTICALLY HOMOGENEOUS MEDIA WITH RANDOM FIELD OF RESIDUAL
MICROSTRESSES 290 CONTENTS XV 9.2 EFFECTIVE MEDIUM METHODS 291 9.2.1
APPLICATION TO COMPOSITE MATERIALS 291 9.2.2 ANALYSIS OF POLYCRYSTAL
MATERIALS 296 9.3 DIFFERENTIAL METHODS 298 9.3.1 SCHEME OF THE
DIFFERENTIAL METHOD 298 9.3.2 ONE-PARTICLE DIFFERENTIAL METHOD 300 9.3.3
MULTIPARTICLE DIFFERENTIAL METHOD (COMBINATION WITH EMM AND WITH MEFM)
301 9.4 ESTIMATION OF EFFECTIVE PROPERTIES OF COMPOSITES WITH
NONELLIPSOIDAL INCLUSIONS 303 9.5 NUMERICAL RESULTS 306 9.5.1 COMPOSITES
WITH SPHEROIDAL INHOMOGENEITIES 306 9.5.2 COMPOSITES REINFORCED BY
NONELLIPSOIDAL INHOMOGENEITIES WITH ELLIPSOIDAL VF 311 9.6 DISCUSSION
314 10 GENERAIIZATION OF THE MEFM IN RANDOM STRUCTURE MATRIX COMPOSITES
315 10.1 TWO INCLUSIONS IN AN INFINITE MATRIX 316 10.2 COMPOSITE
MATERIAL 319 10.2.1 GENERAL REPRESENTATIONS 319 10.2.2 SOME RELATED
INTEGRAL EQUATIONS 321 10.2.3 CLOSING ASSUMPTION AND THE EFFECTIVE
PROPERTIES 322 10.2.4 CONDITIONAL MEAN VALUE OF STRESSES IN THE
INCLUSIONS 323 10.3 FIRST-ORDER APPROXIMATION OF THE CLOSING ASSUMPTION
AND EFFECTIVE ELASTIC MODULI 324 10.3.1 GENERAL EQUATION FOR THE
EFFECTIVE FIELDS I&IJ) 324 10.3.2 CLOSING ASSUMPTIONS FOR THE STRAIN
POLARIZATION TENSOR (T7(Y)|;^,X I ;W J -,X J )(Y) 326 10.3.3 EFFECTIVE
ELASTIC PROPERTIES AND STRESS CONCENTRATOR FACTORS 329 10.3.4 SYMMETRIE
CLOSING ASSUMPTION 329 10.3.5 CLOSING ASSUMPTIONS FOR THE EFFECTIVE
FIELDS (JTI,J,K) 330 10.4 ABANDONMENT FROM THE APPROXIMATIVE HYPOTHESIS
(10.26) 332 10.5 SOME PARTICULAR CASES 334 10.5.1 IDENTICAL ALIGNED
INCLUSIONS 334 10.5.2 IMPROVED ANALYSIS OF COMPOSITES WITH IDENTICAL
ALIGNED FIBERS 337 10.5.3 EFFECTIVE FIELD HYPOTHESIS 339 10.5.4
QUASI-CRYSTALLINE APPROXIMATION 341 10.6 SOME PARTICULAR NUMERICAL
RESULTS 342 11 PERIODIC STRUCTURES AND PERIODIC STRUCTURES WITH RANDOM
IMPERFECTIONS 347 11.1 GENERAL ANALYSIS OF PERIODIC STRUCTURES AND
PERIODIC STRUCTURES WITH RANDOM IMPERFECTIONS 347 CONTENTS 11.2 TRIPLY
PERIODICAL PARTICULAR MATRIX COMPOSITES IN VARYING EXTERNAL STRESS FIELD
351 11.2.1 BASIC EQUATION AND APPROXIMATIVE EFFECTIVE FIELD HYPOTHESIS
351 11.2.2 THE FOURIER TRANSFORM METHOD 352 11.2.3 ITERATION METHOD 353
11.2.4 AVERAGE STRAINS IN THE COMPONENTS 354 11.2.5 EFFECTIVE PROPERTIES
OF COMPOSITES 355 11.2.6 NUMERICAL RESULTS 356 11.3 GRADED DOUBLY
PERIODICAL PARTICULAR MATRIX COMPOSITES IN VARYING EXTERNAL STRESS FIELD
361 11.3.1 LOCAL APPROXIMATION OF EFFECTIVE STRESSES 361 11.3.2
ESTIMATION OF THE NONLOCAL OPERATOR VIA THE ITERATION METHOD 363 11.3.3
GENERAL RELATIONS FOR AVERAGE STRESSES AND EFFECTIVE THERMOELASTIC
PROPERTIES 364 11.3.4 SOME PARTICULAR CASES FOR EFFECTIVE PROPERTIES
REPRESENTATIONS 364 11.3.5 DOUBLY PERIODIC INCLUSION FIELD IN A FINITE
STRINGER 365 11.3.6 NUMERICAL RESULTS FOR THREE-DIMENSIONAL FIELDS 367
11.3.7 NUMERICAL RESULTS FOR TWO-DIMENSIONAL FIELDS 369 11.3.8
CONCLUSION 370 11.4 TRIPLY PERIODIC PARTICULATE MATRIX COMPOSITES WITH
IMPERFECT UNIT CELLS 371 11.4.1 CHOICE OF THE HOMOGENEOUS COMPARISON
MEDIUM 371 11.4.2 MEFM ACCOMPANIED BY MONTE CARLO SIMULATION 374 11.4.3
CHOICE OF THE PERIODIC COMPARISON MEDIUM. GENERAL SCHEME 376 11.4.4 THE
VERSION OF MEFM USING THE PERIODIC COMPARISON MEDIUM 380 11.4.5
CONCLUDING REMARKS 383 NONLOCAL EFFECTS IN STATISTICALLY HOMOGENEOUS AND
INHOMOGENEOUS RANDOM STRUCTURE COMPOSITES 385 12.1 GENERAL ANALYSIS OF
APPROACHES IN NONLOCAL MICROMECHANICS OF RANDOM STRUCTURE COMPOSITES 385
12.2 THE NONLOCAL INTEGRAL EQUATION 390 12.3 METHODS FOR THE SOLUTION OF
THE NONLOCAL INTEGRAL EQUATION . 392 12.3.1 DIRECT QUADRATURE METHOD
392 12.3.2 THE ITERATION METHOD 392 12.3.3 THE FOURIER TRANSFORM METHOD
FOR STATISTICALLY HOMOGENEOUS MEDIA 393 12.4 AVERAGE STRESSES IN THE
COMPONENTS AND EFFECTIVE PROPERTIES FOR STATISTICALLY HOMOGENEOUS MEDIA
396 12.4.1 DIFFERENTIAL REPRESENTATIONS 396 12.4.2 THE REDUCTION OF
INTEGRAL OVERALL CONSTITUTIVE EQUATIONS TO DIFFERENTIAL ONES 397
CONTENTS XVII 12.4.3 "QUASI-CRYSTALLINE" APPROXIMATION 398 12.4.4
NUMERICAL ANALYSIS OF NONLOCAL EFFECTS FOR STATISTICALLY HOMOGENEOUS
COMPOSITES 399 12.5 EFFECTIVE PROPERTIES OF STATISTICALLY INHOMOGENEOUS
MEDIA 403 12.5.1 LOCAL EFFECTIVE PROPERTIES OF FGMS 403 12.5.2
ELASTICALLY HOMOGENEOUS COMPOSITES 406 12.5.3 NUMERICAL RESULTS OF
ESTIMATION OF EFFECTIVE PROPERTIES OF FGMS 407 12.5.4 PERTURBATION
METHOD 412 12.5.5 COMBINED MEFM-PERTURBATION METHOD 413 12.5.6 THE MEF
METHOD 413 12.6 CONCLUDING REMARKS 414 STRESS FLUCTUATIONS IN RANDOM
STRUCTURE COMPOSITES 417 13.1 PERTURBATION METHOD 419 13.1.1 EXACT
REPRESENTATION FOR FIRST AND SECOND MOMENTS OF STRESSES AVERAGED OVER
THE PHASE VOLUMES 419 13.1.2 LOCAL FLUCTUATION OF STRESSES 423 13.1.3
CORRELATION FUNCTION OF STRESSES 423 13.1.4 NUMERICAL RESULTS AND
DISCUSSIONS 425 13.2 METHOD OF INTEGRAL EQUATIONS 427 13.2.1 ESTIMATION
OF THE SECOND MOMENT OF EFFECTIVE STRESSES . 427 13.2.2 IMPLICIT
REPRESENTATIONS FOR THE SECOND MOMENT OF STRESSES 428 13.2.3 EXPLICIT
ESTIMATION OF SECOND MOMENTS OF STRESSES INSIDE THE PHASES 430 13.2.4
NUMERICAL ESTIMATION OF THE SECOND MOMENTS OF STRESSES IN THE PHASES 431
13.2.5 RELATED METHOD OF ESTIMATIONS OF THE SECOND MOMENTS OF STRESSES
433 13.3 ELASTICALLY HOMOGENEOUS COMPOSITES WITH RANDOMLY DISTRIBUTED
RESIDUAL MICROSTRESSES 434 13.3.1 THE CONDITIONAL AVERAGE OF THE
STRESSES INSIDE THE COMPONENTS 435 13.3.2 THE SECOND MOMENT STRESSES
INSIDE THE PHASES 435 13.3.3 NUMERICAL EVALUATION OF STATISTICAL
RESIDUAL STRESS DISTRIBUTION IN ELASTICALLY HOMOGENEOUS MEDIA 438 13.4
STRESS FLUCTUATIONS NEAR A CRACK TIP IN ELASTICALLY HOMOGENEOUS
MATERIALS WITH RANDOMLY DISTRIBUTED RESIDUAL MICROSTRESSES 440 13.4.1
THE AVERAGE AND CONDITIONAL MEAN VALUES OF SIF FOR ISOLATED CRACK IN A
COMPOSITE MATERIAL 441 13.4.2 CONDITIONAL DISPERSION OF SIF FOR A CRACK
IN THE COMPOSITE MEDIUM 444 13.4.3 CRACK IN A FINITE INCLUSION CLOUD 445
13.4.4 NUMERICAL ESTIMATION OF THE FIRST AND SECOND STATISTICAL MOMENTS
OF STRESS INTENSITY FACTORS 447 XVIII CONTENTS 13.5 CONCLUDING REMARKS
449 14 RANDOM STRUCTURE MATRIX COMPOSITES IN A HALF-SPACE 451 14.1
GENERAL ANALYSIS OF APPROACHES IN MICROMECHANICS OF RANDOM STRUCTURE
COMPOSITES IN A HALF-SPACE 451 14.2 GENERAL INTEGRAL EQUATION,
DEFINITIONS OF THE NONLOCAL EFFECTIVE PROPERTIES, AND AVERAGING
OPERATIONS 455 14.3 FINITE NUMBER OF INCLUSIONS IN A HALF-SPACE 458
14.3.1 A SINGLE INCLUSION SUBJECTED TO INHOMOGENEOUS EFFECTIVE STRESS
458 14.3.2 TWO INCLUSIONS 459 14.4 NONLOCAL EFFECTIVE OPERATORS OF
THERMOELASTIC PROPERTIES OF MICROINHOMOGENEOUS HALF-SPACE 462 14.4.1
DILUTE CONCENTRATION OF INCLUSIONS 462 14.4.2 C 2 ORDER ACCURATE
ESTIMATION OF EFFECTIVE THERMOELASTIC PROPERTIES 463 14.4.3
QUASI-CRYSTALLINE APPROXIMATION 465 14.4.4 INFLUENCE OF A CORRELATION
HOLE V% 468 14.5 STATISTICAL PROPERTIES OF LOCAL RESIDUAL MICROSTRESSES
IN ELASTICALLY HOMOGENEOUS HALF-SPACE 469 14.5.1 FIRST MOMENT OF
STRESSES IN THE INCLUSIONS 469 14.5.2 LIMITING CASE FOR A STATISTICALLY
HOMOGENEOUS MEDIUM . 471 14.5.3 STRESS FLUCTUATIONS INSIDE THE
INCLUSIONS 472 14.6 NUMERICAL RESULTS 474 15 EFFECTIVE LIMITING SURFACES
IN THE THEORY OF NONLINEAR COMPOSITES 481 15.1 LOCAL LIMITING SURFACE
482 15.1.1 LOCAL LIMITING SURFACE FOR BULK STRESSES 482 15.1.2 LOCAL
LIMITING SURFACE FOR INTERFACE STRESSES 483 15.1.3 FRACTURE CRITERION
FOR AN ISOLATED CRACK 485 15.2 EFFECTIVE LIMITING SURFACE 485 15.2.1
UTILIZING FLUCTUATIONS OF BULK STRESSES INSIDE THE PHASES . 485 15.2.2
UTILIZING INTERFACE STRESS FLUCTUATIONS 487 15.2.3 EFFECTIVE FRACTURE
SURFACE FOR AN ISOLATED CRACK IN THE ELASTICALLY HOMOGENEOUS MEDIUM WITH
RANDOM RESIDUAL MICROSTRESSES 489 15.2.4 SCHEME OF SIMPLE PROBABILITY
MODEL OF COMPOSITE FRACTURE 490 15.3 NUMERICAL RESULTS 492 15.3.1
UTILIZING FLUCTUATIONS OF BULK STRESSES INSIDE THE PHASES . 492 15.3.2
UTILIZING INTERFACE STRESS FLUCTUATIONS 499 15.3.3 EFFECTIVE ENERGY
RELEASE RATE AND FRACTURE PROBABILITY . 501 15.4 CONCLUDING REMARKS 503
CONTENTS XIX NONLINEAR COMPOSITES 505 16.1 NONLINEAR ELASTIC COMPOSITES
506 16.1.1 POPULAER LINEARIZATION SCHEINE 506 16.1.2 MODIFIED
LINEARIZATION SCHEINE 510 16.2 DEFORMATION PLASTICITY THEORY OF
COMPOSITE MATERIALS 513 16.2.1 GENERAL SCHEINE 513 16.2.2 ELASTOPLASTIC
DEFORMATION OF COMPOSITES WITH AN INCOMPRESSIBLE MATRIX 516 16.2.3
GENERAL CASE OF ELASTOPLASTIC DEFORMATION 517 16.3 POWER-LAW CREEP 517
16.4 ELASTIC-PLASTIC BEHAVIOR OF ELASTICALLY HOMOGENEOUS MATERIALS WITH
RANDOM RESIDUAL MICROSTRESSES 521 16.4.1 LEADING EQUATIONS AND
ELASTOPLASTIC DEFORMATIONS 521 16.4.2 NUMERICAL RESULTS FOR
TEMPERATURE-INDEPENDENT PROPERTIES 525 16.5 A LOCAL THEORY OF
ELASTOPLASTIC DEFORMATIONS OF METAL MATRIX COMPOSITES 527 16.5.1
GEOMETRICAL STRUCTURE OF THE COMPONENTS 527 16.5.2 AVERAGE STRESSES
INSIDE THE COMPONENTS AND OVERALL ELASTIC MODULI 529 16.5.3
ELASTOPLASTIC DEFORMATION 530 16.5.4 NUMERICAL RESULTS 532 SOME RELATED
PROBLEMS 537 17.1 CONDUCTIVITY 537 17.1.1 BASIC EQUATIONS AND GENERAL
ANALYSIS 537 17.1.2 PERTURBATION METHODS 539 17.1.3 SELF-CONSISTENT
METHODS 543 17.1.4 NONLINEAR AND NONLOCAL PROPERTIES 548 17.2
THERMOELECTROELASTICITY OF COMPOSITES 549 17.2.1 GENERAL ANALYSIS 549
17.2.2 GENERALIZED HILL'S CONDITIONS AND EFFECTIVE PROPERTIES. 553
17.2.3 EFFECTIVE ENERGY FUNCTIONS 555 17.2.4 TWO-PHASE COMPOSITES 556
17.2.5 DISCONTINUITIES OF GENERALIZED FIELDS AT THE INTERFACE BETWEEN
COMPONENTS 557 17.2.6 PHASE-AVERAGED FIRST AND SECOND MOMENTS OF THE
FIELD S 558 17.3 WAVE PROPAGATION IN A COMPOSITE MATERIAL 561 17.3.1
GENERAL INTEGRAL EQUATIONS AND EFFECTIVE FIELDS 561 17.3.2 FOURIER
TRANSFORM OF EFFECTIVE WAVE OPERATOR 564 17.3.3 EFFECTIVE WAVE OPERATOR
FOR COMPOSITES WITH SPHERICAL ISOTROPIE INCLUSIONS 568 XX CONTENTS 18
MULTISCALE MECHANICS OF NANOCOMPOSITES 571 18.1 ELEMENTS OF MOLECULAR
DYNAMIC (MD) SIMULATION 571 18.1.1 GENERAL ANALYSIS OF MD SIMULATION OF
NANOCOMPOSITES. 571 18.1.2 FOUNDATIONS OF MD SIMULATION AND THEIR USE
IN ESTIMATION OF ELASTIC MODULI 574 18.1.3 INTERFACE MODELING OF NC 576
18.2 BRIDGING NANOMECHANICS TO MICROMECHANICS IN NANOCOMPOSITES . 578
18.2.1 GENERAL REPRESENTATIONS FOR THE LOCAL EFFECTIVE MODULI. 579
18.2.2 GENERALIZATION OF POPULAER MICROMECHANICAL METHODS TO THE
ESTIMATIONS OF EFFECTIVE MODULI OF NCS 580 18.3 MODELING OF NANOFIBER
NCS IN THE FRAMEWORK OF CONTINUUM MECHANICS 582 18.3.1 STATISTICAL
DESCRIPTION OF NCS WITH PRESCRIBED RANDOM ORIENTATION OF NTS 582 18.3.2
ONE NANOFIBER INSIDE AN INFINITE MATRIX 583 18.3.3 NUMERICAL RESULTS FOR
NCS REINFORCED WITH NANOFIBERS . 586 18.4 MODELING OF CLAY NCS IN THE
FRAMEWORK OF CONTINUUM MECHANICS 590 18.4.1 EXISTING MODELING OF
CLUSTERED MATERIALS AND CLAY NCS . 590 18.4.2 ESTIMATIONS OF EFFECTIVE
THERMOELASTIC PROPERTIES AND STRESS CONCENTRATOR FACTORS OF CLAY NCS VIA
THE MEF . 593 18.4.3 NUMERICAL SOLUTION FOR A SINGLE CLUSTER IN AN
INFINITE MEDIUM 596 18.4.4 NUMERICAL ESTIMATIONS OF EFFECTIVE PROPERTIES
OF CLAY NCS 598 18.5 SOME RELATED PROBLEMS IN MODELING OF NCS REINFORCED
WITH NFS AND NANOPLATES 602 19 CONCLUSION. CRITICAL ANALYSIS OF SOME
BASIC CONCEPTS OF MICROMECHANICS 607 A APPENDIX 611 A.L PARAMETRIC
REPRESENTATION OF ROTATION MATRIX 611 A.2 SECOND AND FOURTH-ORDER
TENSORS OF SPECIAL STRUCTURES 613 A.2.1 E-BASIS 613 A.2.2 P-BASIS !.
614 A.2.3 B-BASIS 617 A.3 ANALYTICAL REPRESENTATION OF SOME TENSORS 619
A.3.1 EXTERIOR-POINT ESHELBY TENSOR 619 A.3.2 SOME TENSORS DESCRIBING
FLUCTUATIONS OF RESIDUAL STRESSES 621 A.3.3 INTEGRAL REPRESENTATIONS FOR
STRESS INTENSITY FACTORS 622 REFERENCES 623 INDEX 679 |
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| author | Buryachenko, Valeriy A. |
| author_facet | Buryachenko, Valeriy A. |
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| building | Verbundindex |
| bvnumber | BV023802078 |
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| discipline | Physik Elektrotechnik / Elektronik / Nachrichtentechnik |
| format | Book |
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| id | DE-604.BV023802078 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T10:09:48Z |
| institution | BVB |
| isbn | 9780387368276 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017444277 |
| oclc_num | 254325536 |
| open_access_boolean | |
| owner | DE-634 DE-11 |
| owner_facet | DE-634 DE-11 |
| physical | XX, 686 S. Ill., graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Springer |
| record_format | marc |
| spelling | Buryachenko, Valeriy A. Verfasser aut Micromechanics of heterogeneous materials Valeriy A. Buryachenko New York, NY Springer 2007 XX, 686 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mechanische Eigenschaft (DE-588)4217961-0 gnd rswk-swf Festkörpermechanik (DE-588)4129367-8 gnd rswk-swf Mikromechanik (DE-588)4205811-9 gnd rswk-swf Verbundwerkstoff (DE-588)4062670-2 gnd rswk-swf Verbundwerkstoff (DE-588)4062670-2 s Mikromechanik (DE-588)4205811-9 s Mechanische Eigenschaft (DE-588)4217961-0 s Festkörpermechanik (DE-588)4129367-8 s DE-604 http://deposit.dnb.de/cgi-bin/dokserv?id=2840728&prov=M&dok_var=1&dok_ext=htm Beschreibung für Leser GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017444277&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Buryachenko, Valeriy A. Micromechanics of heterogeneous materials Mechanische Eigenschaft (DE-588)4217961-0 gnd Festkörpermechanik (DE-588)4129367-8 gnd Mikromechanik (DE-588)4205811-9 gnd Verbundwerkstoff (DE-588)4062670-2 gnd |
| subject_GND | (DE-588)4217961-0 (DE-588)4129367-8 (DE-588)4205811-9 (DE-588)4062670-2 |
| title | Micromechanics of heterogeneous materials |
| title_auth | Micromechanics of heterogeneous materials |
| title_exact_search | Micromechanics of heterogeneous materials |
| title_full | Micromechanics of heterogeneous materials Valeriy A. Buryachenko |
| title_fullStr | Micromechanics of heterogeneous materials Valeriy A. Buryachenko |
| title_full_unstemmed | Micromechanics of heterogeneous materials Valeriy A. Buryachenko |
| title_short | Micromechanics of heterogeneous materials |
| title_sort | micromechanics of heterogeneous materials |
| topic | Mechanische Eigenschaft (DE-588)4217961-0 gnd Festkörpermechanik (DE-588)4129367-8 gnd Mikromechanik (DE-588)4205811-9 gnd Verbundwerkstoff (DE-588)4062670-2 gnd |
| topic_facet | Mechanische Eigenschaft Festkörpermechanik Mikromechanik Verbundwerkstoff |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2840728&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017444277&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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