Random Heterogeneous Materials: Microstructure and Macroscopic PropertiesThe interdisciplinary subject of random heterogeneous materials has experienced remarkable growth since the publication of the well-known monograph Statistical Con tinuum Theories by Beran ( 1968). Many of these advances, especially those concerning the statistical characterization of the microstructure and its effect on the physical prop erties of the material, have not been treated fully in any book. One of the intents of the present book is to fill this gap. This book also distinguishes itself in that it provides a unified rigorous framework to characterize the microstructures and macroscopic properties of the widely diverse types of heterogeneous materials found in nature and synthetic products. Emphasis is placed on providing foundational theoretical methods that can simultaneously yield results of practical utility. This book treats a wide breadth of topics, but the choice of subjects naturally reflects my own interests. The sheer enormity of the field has prevented me from covering many important topics. I apologize to those colleagues, known and unknown, who may not find enough of their own work cited in the ensuing pages. |
Contents
I | 1 |
II | 3 |
III | 6 |
IV | 7 |
V | 8 |
VII | 9 |
IX | 10 |
X | 12 |
CLXXVIII | 306 |
CLXXIX | 308 |
CLXXXI | 311 |
CLXXXII | 313 |
CLXXXIII | 315 |
CLXXXIV | 318 |
CLXXXV | 321 |
CLXXXVIII | 324 |
XII | 14 |
XIII | 17 |
XV | 18 |
XVI | 19 |
XVII | 21 |
XVIII | 23 |
XIX | 24 |
XX | 25 |
XXI | 28 |
XXII | 32 |
XXIII | 33 |
XXIV | 34 |
XXV | 43 |
XXVI | 44 |
XXVII | 45 |
XXVIII | 48 |
XXIX | 50 |
XXXI | 57 |
XXXII | 58 |
XXXIII | 59 |
XXXIV | 60 |
XXXVI | 65 |
XXXVII | 72 |
XXXVIII | 75 |
XXXIX | 79 |
XL | 81 |
XLI | 83 |
XLII | 85 |
XLIII | 87 |
XLIV | 88 |
XLVI | 89 |
XLVII | 90 |
XLVIII | 92 |
XLIX | 93 |
L | 95 |
LI | 96 |
LII | 97 |
LIII | 100 |
LIV | 102 |
LV | 104 |
LVI | 105 |
LVII | 109 |
LIX | 110 |
LX | 111 |
LXI | 112 |
LXII | 114 |
LXIII | 116 |
LXIV | 118 |
LXV | 119 |
LXVI | 120 |
LXVII | 122 |
LXVIII | 124 |
LXIX | 125 |
LXX | 127 |
LXXI | 128 |
LXXIII | 129 |
LXXV | 130 |
LXXVI | 134 |
LXXVII | 136 |
LXXVIII | 137 |
LXXIX | 139 |
LXXX | 151 |
LXXXI | 152 |
LXXXII | 153 |
LXXXIII | 154 |
LXXXIV | 155 |
LXXXVI | 157 |
LXXXVIII | 158 |
LXXXIX | 160 |
XC | 161 |
XCI | 163 |
XCII | 164 |
XCIII | 165 |
XCIV | 166 |
XCVI | 167 |
XCIX | 169 |
C | 170 |
CI | 171 |
CIII | 172 |
CIV | 176 |
CVI | 177 |
CVII | 179 |
CVIII | 181 |
CIX | 183 |
CX | 188 |
CXI | 189 |
CXII | 192 |
CXIII | 194 |
CXIV | 199 |
CXV | 201 |
CXVI | 203 |
CXVIII | 207 |
CXIX | 210 |
CXX | 211 |
CXXI | 215 |
CXXII | 217 |
CXXIII | 222 |
CXXIV | 223 |
CXXV | 224 |
CXXVI | 227 |
CXXVII | 230 |
CXXVIII | 231 |
CXXIX | 234 |
CXXX | 235 |
CXXXI | 240 |
CXXXII | 242 |
CXXXIII | 243 |
CXXXIV | 245 |
CXXXV | 246 |
CXXXVI | 248 |
CXXXVII | 249 |
CXXXVIII | 250 |
CXL | 251 |
CXLI | 252 |
CXLII | 254 |
CXLIII | 255 |
CXLIV | 257 |
CXLV | 258 |
CXLVI | 260 |
CXLVII | 261 |
CXLVIII | 262 |
CXLIX | 264 |
CL | 265 |
CLI | 269 |
CLII | 270 |
CLIII | 271 |
CLIV | 273 |
CLV | 275 |
CLVII | 277 |
CLVIII | 278 |
CLIX | 279 |
CLXI | 281 |
CLXIII | 283 |
CLXIV | 285 |
CLXVI | 286 |
CLXVII | 287 |
CLXVIII | 289 |
CLXIX | 291 |
CLXX | 292 |
CLXXII | 293 |
CLXXIII | 294 |
CLXXIV | 295 |
CLXXV | 297 |
CLXXVI | 303 |
CLXXVII | 305 |
CLXXXIX | 332 |
CXC | 334 |
CXCI | 337 |
CXCII | 338 |
CXCIII | 339 |
CXCV | 341 |
CXCVII | 344 |
CXCVIII | 345 |
CXCIX | 346 |
CC | 348 |
CCI | 349 |
CCII | 350 |
CCIV | 353 |
CCV | 354 |
CCVII | 356 |
CCVIII | 357 |
CCIX | 359 |
CCXI | 361 |
CCXII | 363 |
CCXIII | 367 |
CCXIV | 368 |
CCXV | 369 |
CCXVI | 370 |
CCXVII | 373 |
CCXVIII | 377 |
CCXIX | 379 |
CCXXI | 380 |
CCXXII | 383 |
CCXXIV | 385 |
CCXXV | 390 |
CCXXVI | 397 |
CCXXVII | 398 |
CCXXIX | 401 |
CCXXX | 402 |
CCXXXI | 403 |
CCXXXII | 404 |
CCXXXIII | 407 |
CCXXXIV | 410 |
CCXXXV | 413 |
CCXXXVII | 415 |
CCXXXVIII | 416 |
CCXXXIX | 417 |
CCXL | 419 |
CCXLI | 424 |
CCXLII | 426 |
CCXLIII | 428 |
CCXLIV | 429 |
CCXLVIII | 430 |
CCL | 431 |
CCLI | 432 |
CCLIII | 433 |
CCLIV | 434 |
CCLVI | 436 |
CCLVII | 437 |
CCLVIII | 441 |
CCLIX | 442 |
CCLX | 448 |
CCLXI | 451 |
CCLXII | 453 |
CCLXIII | 455 |
CCLXIV | 457 |
CCLXV | 459 |
CCLXVI | 460 |
CCLXVII | 462 |
CCLXVIII | 467 |
CCLXIX | 470 |
CCLXXI | 474 |
CCLXXII | 477 |
CCLXXIII | 479 |
CCLXXIV | 481 |
CCLXXV | 485 |
CCLXXVI | 486 |
CCLXXVII | 488 |
CCLXXVIII | 490 |
CCLXXIX | 491 |
CCLXXX | 496 |
CCLXXXI | 497 |
CCLXXXII | 500 |
CCLXXXIII | 501 |
CCLXXXIV | 502 |
CCLXXXVI | 503 |
CCLXXXVII | 504 |
CCLXXXVIII | 505 |
CCXC | 506 |
CCXCI | 507 |
CCXCII | 509 |
CCXCIII | 510 |
CCXCIV | 511 |
CCXCV | 514 |
CCXCVI | 519 |
CCXCVII | 520 |
CCXCVIII | 521 |
CCC | 530 |
CCCII | 534 |
CCCIII | 539 |
CCCIV | 540 |
CCCV | 541 |
CCCVI | 552 |
CCCVII | 554 |
CCCIX | 555 |
CCCX | 563 |
CCCXI | 564 |
CCCXII | 566 |
CCCXIV | 568 |
CCCXV | 576 |
CCCXVI | 577 |
CCCXVII | 578 |
CCCXVIII | 579 |
CCCXIX | 580 |
CCCXX | 581 |
CCCXXI | 582 |
CCCXXII | 584 |
CCCXXIII | 585 |
CCCXXV | 586 |
CCCXXVI | 587 |
CCCXXVII | 589 |
CCCXXVIII | 590 |
CCCXXIX | 592 |
CCCXXX | 593 |
CCCXXXI | 594 |
CCCXXXIII | 609 |
CCCXXXIV | 610 |
CCCXXXV | 611 |
CCCXXXVII | 620 |
CCCXXXIX | 621 |
CCCXLI | 623 |
CCCXLII | 624 |
CCCXLIII | 625 |
CCCXLV | 627 |
CCCXLVII | 629 |
CCCXLVIII | 630 |
CCCXLIX | 631 |
CCCL | 632 |
CCCLI | 633 |
CCCLIII | 636 |
CCCLIV | 642 |
CCCLV | 647 |
CCCLVII | 650 |
CCCLVIII | 654 |
CCCLIX | 656 |
CCCLXI | 661 |
663 | |
693 | |
Other editions - View all
Random Heterogeneous Materials: Microstructure and Macroscopic Properties Salvatore Torquato No preview available - 2013 |
Common terms and phrases
anisotropic approximation arbitrary arrays asymptotic average bulk modulus cells Chapter cluster coefficients computed correlation functions corresponding critical exponents cross-property defined denote derived dimensionless disks dispersions effective bulk modulus effective properties effective stiffness tensor elastic moduli ellipsoidal ensemble equation equilibrium ergodic evaluated exact expansion expression Figure fluid permeability formula fully penetrable G₂ given hard spheres heterogeneous materials impenetrable spheres inclusions indicator function integral interface isotropic isotropic composites isotropic media k-mer K₁ laminate lattice limit lower bound macroscopically isotropic matrix medium microstructure Milton nearest-neighbor obtained overlapping spheres parameter particles percolation threshold phase Phys Poisson ratio polydisperse porous media probability density function problem quantities r₁ radial distribution function random media relation Section shear modulus simulation spheres of radius spherical spheroids statistically homogeneous Stell surface symmetry Theorem three-dimensional Torquato trapping constant trial fields two-dimensional two-phase two-point probability function upper bound V₁ vector yields zero Φι