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Subject Index

3D-p-finite element method 392

abrasion 1, 162abstract multi field problem 372abutment of a bridge 649accumulation 111, 160, 198, 313, 626acid attack 152acidic fluids 152acoustic emissions 169, 204across-wind force 26

dimensionless lift coefficient, 26Strouhal-number, 26

across-wind vibrations 29action 4adaptive

method, 368, 372, 424, 425time

step control, 594stepping procedure, 446stepping scheme, 369, 412, 443

adaptivityerror-controlled temporal, 443in space and time, 425

advanced directional factors 23aerodynamic admittance, 24applicable characteristic suction

force, 25directional wind effect, 24iteration, 24suction force on the facade element,

24ageing 3

chemically caused, 367aggregate 189, 302, 307

algebraic equation 369algorithmic balance equation 415alkali-aggregate reaction 158alkali-carbonate reaction 160alkali-silica reaction 158, 302, 305,

311, 359amplitude counting 574analytical counting method 578anchor pull-out test 495angular frequency 115anisotropic

shape function, 380softening law, 478

apodization 120approximation of state variable 381,

414approximativ solution 368arbitrary order of accuracy 410arbitrary polynomial degree 380arc-length controlled iteration method

407arched steel bridge 512, 607assembling 384assumed natural strain 362, 380asymptotic displacement 469asymptotic state 112

Babuska-Brezzi-condition 398, 585back polarization 315back stress tensor 246, 256balance equation 373–375balance of linear momentum 296,

426, 427band-pass 120

712 Subject Index

Bauschinger effect 255, 256beam finite elements 369beat 118Bernoulli formulation 397biaxial strength 126Biot

coefficients, 286, 288modulus, 286

Biot-Coussy theory 285black-box modelling 635blending function method 402BMW 3-serie 572Bossak-α method 411boundary condition 373brittle failure 307Bubnov-Galerkin

discontinuous method, 412, 421building class 4, 659

C0-continous 476C0-discontinuous 476calcium

diffusion, 296dissolution, 295, 296, 300, 356ion concentration, 297, 298, 300, 354leaching, 107, 150, 152, 297, 591, 592

cantilever beam 563capillary

pressure, 285, 289, 292, 307tension, 143

carbonation 1Cauchy-Green tensor 437cementitious

beam, 601material, 124, 236, 591

cement paste 124centrifuge model test 646change of position 367chaos theory 370chemical

dissolution, 354equilibrium, 295expansive process, 359loading, 592

range, 600porosity, 300

chemo-mechanicaldamage model, 374tangent coupling tensor, 386

chloride 1CMDSS device 200coalescence 256coaxial states 116complementary

energy, 238strain energy, 271

compliance tensor 238, 269, 278composite structure 207compressive strength 246, 262, 265,

270, 290, 622, 629computational durability mechanics

285computer-aided design 372concrete 180, 237, 244, 265

corrosion, 95cover, 625high strength, 187permeability, 590properties, 618shell structure, 583strength, 628

conductivity tensor 297connection plate 613consistent linearization 367, 369, 377,

415constitutive

equation, 373, 427law, 374

continuity 412condition, 409, 418

continuum damage theory 307continuum mechanics 294control cycle 519controllable numerical dissipation

409–411convection 37convergence 422convex modelling 370cooling 351

rate, 101coordinate modal assurance criterion

569corrector iteration 405, 408correlation length 631corrosion 1

attack, 625rate, 625reinforcement, 625

Subject Index 713

COSSAN 538coupled balance equation 377coupled field problem 372, 376covariance analysis 520crack

band, 625elliptical, 270, 272, 274, 278, 280extension, 492formation, 190growth, 489growth criteria, 488initiation, 207kinked, 274, 276kinking, 453microcrack, 190

elliptical, 284mixed mode, 272, 274, 278propagation, 174, 225, 369, 474simulation, 493surface, 476tip, 454, 469topology, 493

cracking strains 244Craig-Bampton approach 499creep 143, 285, 291

effects, 133long-term, 286strain, 265–267

critical degree of saturation 95crown cracks 351crushing energy 246CSH 293, 300, 356cumulative distribution function 531cycle

amplitudedouble amplitude, 120scalar amplitude, 118tensorial amplitude, 114, 316

average, 114circulation, 117counting, 575in-phase (=IP) cycles, 114irregular cycle, 116, 198, 518multiaxial, 115out-of-phase (=OOP) cycles, 115ovality, 114packages of cycles, 205polarization, 114, 202, 315polarization changes, 203

regular cycles, 198shape, 203span, 117strain cycles, 114uniaxial, 115

cyclicflow rule, 161, 201loading, 123, 129, 256, 519, 623, 647,

650mobility, 113, 162, 206multidimensional simple shear tests,

198preloading, 112, 203, 315tensile and flexural load, 136test, 180, 621triaxial tests, 198

Dahlquist theorem 411Daltons law 307damage 237, 366

accumulation, 7, 579, 581chemical, 298chemo-mechanical, 295, 367creep, 367criterion, 300, 478detection, 634, 640driving forces, 627evolution, 167, 626fatigue, 367gradient enhanced, 307hygro-mechanical, 367isotropic, 238mechanisms, 625model

anisotropic, 244anisotropic elastoplastic, 244continuum, 270, 274, 284micropore, 255, 259

parameter, 238, 295, 300, 307thermo-mechanical, 367

damage equivalent factors 69damaging process 139Darcys law 307data windowing 120Debye-Huckel-Onsager theory 298degeneration of a trajectory 118degradation 3, 262, 411, 654

macroscopic, 367process, 131, 182, 623

714 Subject Index

stiffness, 134structural, 180, 359

degraded road bridge 617deionized water 356derivative-based method 552derivative-free strategy 555design

concept, 93process, 371working life, 659

destructive test 619deterioration 1, 307, 366

brittle, 367ductile, 367mechanic, 369mechanism, 411model, 372

deterministic subspace identification527

detrended strain path 118detrending 116differential settlements 109diffusion 292direction of accumulation 161, 200,

201, 314direct search algorithm 555Dirichlet boundary condition 374,

411, 591, 598Dirlik distribution function 579discontinuous

displacement approximation, 369finite elements, 448

discrete-time system matrix 526discrete Fourier transform (DFT)

119discrete inverse Fourier transform

(DIFT) 120discretization 414

method, 294disjoining pressure 143, 291, 293dissipation potential 297dissolution 152, 305

front, 356process, 150, 152, 374

drilling core 618driving force 373Drucker-Prager

plasticity model, 290potential, 246, 269

drying 351creep, 291process, 590shrinkage, 285

ductile mode 129durability 92, 150, 294, 411, 424, 574,

659analysis, 354mechanics model, 424structural, 368

dynamicinfluence coefficient, 634load parameters, 82

distance between the pulse peaks,84

pressure coefficients, 82pulse amplitudes, 82wall distance factor, 86wall height factor, 86

response, 90critical damping ratio, 91modal decomposition, 91resonant amplification factors, 91

stiffness requirement, 572

E-Modulus 134earthquake 113, 162, 362, 649edge modes 393effective

balance equation, 415elastic properties, 271, 276linearized system of equation, 421,

422right hand side, 416stress, 244, 285, 289, 307

elastic, 289plastic, 289

tangent matrix, 416eigenfrequency 634elastoplastic models 244electrical resistance method 163electrophoretic effect 298element 379embedded

crack models, 252discontinuity approach, 369

endochronic models 518energy

complementary, 272

Subject Index 715

conserving, 369decaying method, 369

enhanced assumed strain 252, 362,380, 427, 448

enriched finite elements 372entropy 286enumeration strategy 555environmental

attack, 583humidity, 143

equivalentelliptical crack, 278elliptical microcrack, 276strain, 238, 307

errorcriterion, 431, 432estimate, 412, 444, 594

h-method, 443local, 443p-method, 444

estimator, 391, 445indicator, 391, 444

h-method, 444local, 443p-method, 444

measure, 372, 425ettringite formation 157Eurocode 659evolution

algorithm, 555long-term, 629strategy, 556

excessive displacement 367exchangeable salt 152expansion 157, 307, 311experimental results 40

macroscopic temperature behaviour,42

explicit mode 518exponential convergency 388exposure classes 93extended finite element method 369,

448external damage 95

fabric 109, 162face modes 394failure

function, 238probability, 529, 530, 534, 541, 612

Falancs 581Faraday constant 298fatigue 1, 163, 169, 180, 626, 653,

655, 659analysis of bridge hangers, 29crack, 272damage, 267, 367

process, 612failure, 262high-cycle, 262, 270high cycle, 129, 174, 207life, 627lifetime, 270load, 270low-cycle, 259, 262low cycle, 129, 255Newmark-Wilson time-step method,

31strain, 185, 266test, 259ultra low cycle, 255

Ficks law 297filtering 119finite difference method 649finite element method 367–369first-order reliability method 531first order kinetic law 305first passage 540

probability, 541flattened strain trajectory 117foundations 109, 646Fourier transform 119fracture

energy, 187, 238, 252, 290, 478approach, 625

mechanism, 124process, 369

fragmentation 162free energy 238, 286, 297freeze thaw attack 148, 293frost

attack, 194damage, 293deicing salt attack, 148suction, 95

full scale experiments 32

Galerkin 377continuous method, 369, 408, 412,

416

716 Subject Index

discontinuous method, 369, 408, 412,416

solution, 594temporal approximation, 419time integration scheme, 372, 411,

416, 594, 598, 600type finite element method, 410

Gateaux derivative 385Gauss-Legendre

integration, 421, 460quadrature, 386, 458

generalizedexternal force vector, 413internal force

tensor, 383vector, 403, 413

mid-point approximations, 414, 415tangent

damping matrix, 413damping tensor, 385mass matrix, 413stiffness matrix, 403, 413stiffness tensor, 385

genetic algorithm 556geogrids 650global balance equation 373gradient-based algorithm 561grading curve 189grain size distribution curve 205grey-box modelling 635Griffith criterion 493gust response factor 11

equivalent quasi-static load, 12fatigue analysis of gust-induced

effects, 18

h-finite element method 379, 388h-method 412Hunxer Brucke 617, 648hanging node concept 431Hankel matrix 523, 638hardening

isotropic, 256kinematic, 256modulus, 246

harmonicexcitation, 649oscillation, 115

harmony with nature 6

Hasofer-Lind-algorithm 533hazard 654headed stud 207heat

capacity, 286conduction, 36, 292of hydration, 142transmission, 39

Helmholtz energy 246Hessian matrix 568hierarchical

concept, 388polynomial interpolation, 426

high-cycle model for soils 517, 646high-speed railway lines 79

aerodynamic loads, 79critical train speed, 81noise barrier, 80prevailing frequency fp, 81wind shelter walls, 80

higher order finite elements 380Hilber-α method 411historiotropy 203, 315history

integration, 583variable, 434, 440, 478

hodograph 116hoop stress 489hourglass control 380hydration products 302hydraulic pressure 148hygral

behaviour, 143conditions, 359

hygro-mechanicalanalysis, 583, 590damage, 367

identification 637implicit

backward Euler scheme, 238mode, 518

Importance Sampling 534indicator function 533inf-sub-condition 398initial condition 412in situ test stand 39inspection 6instability 367

Subject Index 717

integration 377scheme energy conserving, 411scheme energy decaying, 411

integrity 289, 290intensity of accumulation 161, 314interaction 3interactive effect 3intermediate configuration 256internal

damage, 96modes, 394

interpolation property 390interval algebra 370intrinsic permeability 307inverse Fourier transform 120investment cost 5ion transport 295, 374isomorphic variables 198isoparametric approximation 390isotropic damage parameter 286iteration methods 403

Jacobitemporal transformer, 420tensor, 383transformation, 383

jump condition 418

kinematical relation 427kinematic hardening law 255kinking angle 272Kirchhoff-Love formulation 397Kohlrauschs law 297, 298Krylov-based model reduction methods

500, 504Kuhn-Tucker conditions 238, 300,

478

Lagrange 390multipliers, 507, 511non-hierarchical concept, 388polynomials, 369, 380shape function, 380, 381, 412

latent heat 286Latin hypercube sampling 535, 536,

617, 627, 631leaching 354leakage 356

least squares problem 567Legendre 380, 389, 390

modified polynomials, 389polynomials, 369, 389shape function, 389type, 392

Leon model 244life-cycle

design, 7investigation, 499

lifetime 207analysis of bridge hangers, 34

lock-in effect, 34stochastic excitation force, 34

assessment, 610control, 659

lifetime-orientedanalysis, 562, 583design, 1, 371, 548, 562

concept, 365, 607model, 365

limit state 367serviceability, 367ultimate, 367

linear convergence rate 388linearized

discrete balance equation, 385weak form, 419

liquefaction 113, 162, 206liquid saturation 289load

-deflection curve, 493-independent influences, 92cycles, 266, 269pattern, 87

static and dynamic designcalculations, 87

symmetric load pattern, 90scenario, 7

loadingbiaxial, 256cycles, 280cyclic, 278

local balance equation 373localization 634lock-in 25

effect, 26aerodynamic damping, 26large oscillation amplitudes, 26

718 Subject Index

Scruton number, 26range, 28

lift force, 28locking-free element formulation 430locking phenomena 379Lode angle 314long-term

calculation, 499creep, 285degradation mechanisms, 632experiments, 39

loss of equilibrium 367low-frequency vibration comfort 573low order

approximation, 379finite elements, 379

macro time 657maintenance 6Markov parameters 638, 640material

degradation, 124failure, 374model, 625

matrix dissolution 295Matsuoka and Nakai condition 313Maxwell symmetry 288mean wind speeds 15

Gumbel-distribution, 16logistic distribution, 16occurrence probability of an extreme

value, 20rosettes of 10-minutes means of wind

velocities, 18terrain factor, 21Weibull-distribution, 16wind direction, 18wind effect admittance, 22wind rosette, 18

meshdependency, 246locking, 519

metallic materials 137micro-ice-lens model 95, 148, 194micro and macro time domain 33microcrack 124, 133

formation, 194micromechanical model 293

micromechanics 271microplasticity 137microprestress 291microscopic

alteration, 367analysis, 621

microstructure 133, 150micro time 657Mindlin-Reissner

formulation, 397kinematics, 362

Miner’s rule 205minimum energy 492modal

analysis, 527, 634of wind-induced oscillations, 13

assurance criterion, 569damping, 634reduction, 503

mode-I-crack extension 490model

adaptivity, 426reduction, 498, 499, 503

mode shapes 634moisture

permeability, 147transport, 147, 285, 359, 586uptake, 194

molar conductivity 298monopile foundation 650Monte Carlo

method, 627Simulation, 533, 534, 617, 654

distance-controlled, 542strategy, 555

multi-axial stress state 269multi-dimensional multi-field element

377multi-field

numerical method, 365problem, 367, 369, 380

multi-level solution philosophy 367multi-scale 658

modeling, 616, 657multi-stage cyclic loading 136multi-surface models 518multiaxial loading 126multiphysics problems 373, 379, 380multisurface

Subject Index 719

damage-plasticity model, 290plasticity, 237

nanostructure 293natural convection 36natural resource 6Neo-Hooke model 256Nernst-Einstein relation 297Neumann boundary condition 374Newmark 377, 414

adaptive solution, 594approximations, 414generalized α method, 411integration, 598integration scheme, 594method, 369, 411, 412, 514time integration, 372, 594time integration scheme, 600type finite difference, 410

Newmark-α time intergration method408, 411, 412, 416

Newtoncorrection, 407, 416quasi Newton method, 405

Newton-Cotes integration 458–460Newton-Raphson

iteration, 368, 422method, 405, 424modified method, 405procedure, 377scheme, 378, 408

non-destructivemeasurement, 194test, 618

non-linearalgebraic equation, 415differential equations, 367first order semidiscrete initial value

problem, 416vector equation, 403

non-local equivalent strain 359normalization 117normalized cross orthogonality 570notch filter 121nucleation law 256numerical

method, 368modeling, 373

models, 39numerically dissipative integration

410NURBS 613Nyquist frequency 119

optimization 656method, 365, 551problem, 546result, 614strategy, 372

optimum design 372order of accuracy 369orthogonality check 570oscillation 115

P- and S-wave velocities 203p-finite element method 379, 387,

388, 402, 588p-method 412p-refinement 391Pade-Via-Lanczos algorithm 500Palmgren-Miner’s hypothesis 136parallel

optimization software, 561processing, 543

parallelization 542–544, 559, 615Paris law 272, 276, 280partial

density, 302differential equations, 367

partially saturated material 289, 302partition of unity 449, 471passage to a kinematic mechanism

367PC cluster 615perfomance concept 93period T 116permeability 292, 307, 590Petrov-Galerkin

continuous method, 252, 412, 422phase shift 118Pickett effect 291Piola-Kirchhoff stress tensor 427,

428, 506plastic

-damage model, 237deformation, 216stretching, 519

plasticity theorie 237

720 Subject Index

plate finite elements 369polarization 314

changes, 162polycyclic loading 198, 646population-based evolution strategy

560pore

pressure, 307size distribution, 150water pressure accumulation, 113,

205, 649porosity 289, 292, 295porous media 285post-cyclic behaviour 163, 207power spectral density function 577practical design 365predictor

iteration, 405step, 408

pressure vessel 259, 362prestressing tendon 625, 626primal method 553principle of maximum dissipation 244probabilistic lifetime analysis 611probability 657

density function, 535subjective, 370

process 543prognosis of deterioration 368, 372projection 117proper orthogonal decomposition 504pseudo

-creep, 116-relaxation, 116, 160, 519

pulse processes 34push-out test 207

quality assurance 1, 659quasi-brittle damage 131

Rackwitz-Fiessler-algorithm 533rainflow

counting, 581method, 575

randomfield, 631variable, 609

Rankinecriterion, 238, 290, 307

damage surface, 246ratcheting effect 256reaction-diffusion 297, 600reaction kinetics 359reactive

aggregates, 302porous media, 298

recycling 5reduced integration technique 430regularization 237, 307relaxation effect 298reliability 3, 4, 653, 656

analysis, 528, 529, 542, 543time-variant, 614

analysis method, 365problem, 520, 531, 541

time-invariant, 531reliability-based optimum design 529renewal processes 34

fatigue events, 34macro time domain, 34

repair 4, 6representative elementary volume

297residual

-based error criterion, 426deformation, 183strain, 116, 160, 198

resilient strain 116, 198resistance 4Response Surface Method 537, 538rest period 191restraint stresses 141return mapping algorithm 252revitalization 5right stretch tensor 114Ritz

load-dependent Ritz vectors, 500, 506road bridge 617robust structural design 607Roscoe’s invariants 198rotating crack 244rotation operator 315Russian Roulette & Splitting 542

S-N curve 626safety 1salt attack 194saturation 588, 589

Subject Index 721

scaling 293Schur complement 511second-order reliability method 531second order accuracy 409–411seepage velocity 307selective reduced integration 380semidiscrete

balance equation, 412differential equation, 369structural equation, 367

sequentialconvex programming, 553linear programming, 553quadratic programming, 533, 553

serendipity approximation 402service

-life control, 4, 7life, 1performance, 366

serviceability 1settlement 109, 646shakedown 112shaker test 574shape function

3-D, 392anisotropic, 369, 381, 395, 397hierarchical, 369isotropic, 381

shaping filter 520shell

finite elements, 369structure, 583

short term thermal impacts 40shrinkage 143, 285, 289, 351side frame 572Simpson integration 460single-field

numerical method, 365problem, 367

singular value decomposition 500,526

smeared crackapproach, 269concept, 292model, 265

softened water 152softening modulus 246soil 109, 114, 160, 198, 517, 646

-structure interaction, 109

solid discretizationshell-like, 400slab-like, 400truss-like, 400

solid formulationshell-like, 397slab-like, 397truss-like, 397

sorption behaviour 143spatial

discretization, 379method, 377, 379

finite element discretization, 377, 380scatter, 631

special eigenvalue problem 527spectral

analysis, 119moment, 577, 578

spherical cavaties 129state

spacematrix, 636model, 520, 634system, 636

variable, 413stationary problem 372, 403steel

bars, 625pipe, 641structure, 607

stiffness 216degradation, 134, 139reduction, 137

stochasticsampling method, 617void ratio, 647

strain energyfunction, 428release rate, 489

strategy for polycyclic loading of soil517

strengthening 6stress

Cauchy, 256fluctuation, 316intensity factor, 137, 272Kirchhoff, 256von Mises, 581

stress-strain

722 Subject Index

curve, 124relation, 265

strong discontinuity approach 252,448

structuralanalysis, 371degradation, 180, 359design, 365, 371failure, 356optimization, 529, 545, 546, 548, 555,

612problem, 372, 545

optimization problemimplicit nature, 548semi-infinite, 551

subsetmethod, 536simulation, 536, 537

subspaceidentification, 522, 524, 525methods, 520

substructure technique 502sulfate 107

attack, 157surface energy 143sustainability 5, 6swelling 302synthesis (composition) approach 371system identification 519

T-stress 271tangential stiffness matrix 632Taylor

expansion, 427series, 378

Taylor-Hood 400approximation, 398element, 585

temperature profile 141temporal

discretization, 380method, 408

discretization method, 377weak form, 419weak formulation, 412

test function 377thaumasite formation 157thawing rate 101theory of mixtures 294

theory of porous media 293–295, 302,307

theory of probability 370thermal

actions, 35design process, 35lifetime analysis, 35

behaviour, 140conductivity, 292cracking, 142expansion, 140

coefficient, 140incompatibility, 140loading, 141loads on structures, 42

low-cycle fatigue, 42properties, 140radiation, 36, 37transmission, 36

thermic dilatation coefficient 286thickness refinement 427tied-arch bridge 642time

derivatives, 377discretisation, 499history

calculation, 574method, 520

integration, 514, 518, 595error, 443method, 368parameter, 414scheme, 367, 369

variant formulation, 368time-invariant

behavior, 365problem, 531

time-variant fatigue processes 33rainflow cycle counting, 34

Timoshenko formulation 397traction vector 477, 478traffic load 617

fatigue load models, 62models, 46on road bridges, 46

fatigue load model 3, 69load model 1, 58load model 2, 60

transformation method 552, 553

Subject Index 723

transient vibration time 640transport-damage process 588triaxial stresses 126tuned-mass damper 573, 574tunnel lining 351

ultimate tension stress 478ultrasonic transmission time 180uncertainty 369, 370, 539, 627

categories, 370informal, 370lexical, 370stochastic, 370

uniaxialcompression, 124

cyclic load, 133elasto-plastic material law, 625stress state, 269tension, 125

unit-cell analyses 255upgrading 4

variance-reducing simulation method534

verification 634vertical tie rod 607vibration

comfort, 572measurement, 645

vibratory compaction 648viscosity 265visual degree of (external)damage

103void volume fraction 256Voigt notation 428volume fraction 295vortex

-induced across-wind vibration, 609excitation, 25

shedding, 25wind turbulence, 25

warranty 7weak

form, 372formulation, 369, 377

welding 610white-box modelling 635wind

buffeting, 10equivalent roughness length, 20gustiness, 10gust loading, 14integral length scales, 12turbulence intensity, 12

load, 27, 607ESDU model, 29Ruscheweyh-model, 27Vickery-model, 28

power plant, 650–652offshore, 650

tunnel experiment, 32windowing 120Wohler

approach, 626limit stress, 278test, 182

working-life 4

XFEM 473, 474displacement field, 452p-version, 469

yield conditionGurson, 256von Mises, 256

yield strength 137

Zienkiewicz error indicator 444, 445