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Journal of Geophysical Research 80, 752–755 (1975) Subject Index 3D-p-finite element method 392 abrasion 1, 162 abstract multi field problem 372 abutment of a bridge 649 accumulation 111, 160, 198, 313, 626 acid attack 152 acidic fluids 152 acoustic emissions 169, 204 across-wind force 26 dimensionless lift coefficient, 26 Strouhal-number, 26 across-wind vibrations 29 action 4 adaptive method, 368, 372, 424, 425 time step control, 594 stepping procedure, 446 stepping scheme, 369, 412, 443 adaptivity error-controlled temporal, 443 in space and time, 425 advanced directional factors 23 aerodynamic admittance, 24 applicable characteristic suction force, 25 directional wind effect, 24 iteration, 24 suction force on the fa¸cade element, 24 ageing 3 chemically caused, 367 aggregate 189, 302, 307 algebraic equation 369 algorithmic balance equation 415 alkali-aggregate reaction 158 alkali-carbonate reaction 160 alkali-silica reaction 158, 302, 305, 311, 359 amplitude counting 574 analytical counting method 578 anchor pull-out test 495 angular frequency 115 anisotropic shape function, 380 softening law, 478 apodization 120 approximation of state variable 381, 414 approximativ solution 368 arbitrary order of accuracy 410 arbitrary polynomial degree 380 arc-length controlled iteration method 407 arched steel bridge 512, 607 assembling 384 assumed natural strain 362, 380 asymptotic displacement 469 asymptotic state 112 Babuˇska-Brezzi-condition 398, 585 back polarization 315 back stress tensor 246, 256 balance equation 373–375 balance of linear momentum 296, 426, 427 band-pass 120 712 Subject Index Bauschinger effect 255, 256 beam finite elements 369 beat 118 Bernoulli formulation 397 biaxial strength 126 Biot coefficients, 286, 288 modulus, 286 Biot-Coussy theory 285 black-box modelling 635 blending function method 402 BMW 3-serie 572 Bossak-α method 411 boundary condition 373 brittle failure 307 Bubnov-Galerkin discontinuous method, 412, 421 building class 4, 659 C 0 -continous 476 C 0 -discontinuous 476 calcium diffusion, 296 dissolution, 295, 296, 300, 356 ion concentration, 297, 298, 300, 354 leaching, 107, 150, 152, 297, 591, 592 cantilever beam 563 capillary pressure, 285, 289, 292, 307 tension, 143 carbonation 1 Cauchy-Green tensor 437 cementitious beam, 601 material, 124, 236, 591 cement paste 124 centrifuge model test 646 change of position 367 chaos theory 370 chemical dissolution, 354 equilibrium, 295 expansive process, 359 loading, 592 range, 600 porosity, 300 chemo-mechanical damage model, 374 tangent coupling tensor, 386 chloride 1 CMDSS device 200 coalescence 256 coaxial states 116 complementary energy, 238 strain energy, 271 compliance tensor 238, 269, 278 composite structure 207 compressive strength 246, 262, 265, 270, 290, 622, 629 computational durability mechanics 285 computer-aided design 372 concrete 180, 237, 244, 265 corrosion, 95 cover, 625 high strength, 187 permeability, 590 properties, 618 shell structure, 583 strength, 628 conductivity tensor 297 connection plate 613 consistent linearization 367, 369, 377, 415 constitutive equation, 373, 427 law, 374 continuity 412 condition, 409, 418 continuum dam age theory 307 con tin uummechanics 294 control cycle 519 controllable numerical dissipation 409–411 convection 37 convergence 422 convex modelling 370 cooling 351 rate, 101 coordinate modal assurance criterion 569 corrector iteration 405, 408 correlation length 631 corrosion 1 attack, 625 rate, 625 reinforcement, 625 Subject Index 713 COSSAN 538 coupled balance equation 377 coupled field problem 372, 376 covariance analysis 520 crack band, 625 elliptical, 270, 272, 274, 278, 280 extension, 492 formation, 190 growth, 489 growth criteria, 488 initiation, 207 kinked, 274, 276 kinking, 453 microcrack, 190 elliptical, 284 mixed mode, 272, 274, 278 propagation, 174, 225, 369, 474 simulation, 493 surface, 476 tip, 454, 469 topology, 493 cracking strains 244 Craig-Bampton approach 499 creep 143, 285, 291 effects, 133 long-term, 286 strain, 265–267 critical degree of saturation 95 crown cracks 351 crushing energy 246 CSH 293, 300, 356 cumulative distribution function 531 cycle amplitude double amplitude, 120 scalar amplitude, 118 tensorial amplitude, 114, 316 average, 114 circulation, 117 counting, 575 in-phase (=IP) cycles, 114 irregular cycle, 116, 198, 518 multiaxial, 115 out-of-phase (=OOP) cycles, 115 ovality, 114 packages of cycles, 205 polarization, 114, 202, 315 polarization changes, 203 regular cycles, 198 shape, 203 span, 117 strain cycles, 114 uniaxial, 115 cyclic flow rule, 161, 201 loading, 123, 129, 256, 519, 623, 647, 650 mobility, 113, 162, 206 multidimensional simple shear tests, 198 preloading, 112, 203, 315 tensile and flexural load, 136 test, 180, 621 triaxial tests, 198 Dahlquist theorem 411 Daltons law 307 damage 237, 366 accumulation, 7, 579, 581 chem ical, 298 ch emo-m echanical, 295, 367 creep, 367 criterion, 300, 478 detection, 634, 640 driving forces, 627 evolution, 167, 626 fatigue, 367 gradient enhanced, 307 hygro-mechanical, 367 isotropic, 238 mechanisms, 625 model anisotropic, 244 anisotropic elastoplastic, 244 continuum, 270, 274, 284 micropore, 255, 259 parameter, 238, 295, 300, 307 thermo-mechanical, 367 damage equivalent factors 69 damaging process 139 Darcys law 307 data windowing 120 Debye-H¨uckel-Onsager theory 298 degeneration of a trajectory 118 degradation 3, 262, 411, 654 macroscopic, 367 process, 131, 182, 623 714 Subject Index stiffness, 134 structural, 180, 359 degraded road bridge 617 deionized water 356 derivative-based method 552 derivative-free strategy 555 design concept, 93 process, 371 working life, 659 destructive test 619 deterioration 1, 307, 366 brittle, 367 ductile, 367 mechanic, 369 mechanism, 411 model, 372 deterministic subspace identification 527 detrended strain path 118 detrending 116 differential settlements 109 diffusion 292 direction of accumulation 161, 200, 201, 314 direct search algorithm 555 Dirichlet boundary condition 374, 411, 591, 598 Dirlik distribution function 579 discontinuous displacement approximation, 369 finite elements, 448 discrete-timesystemmatrix 526 discrete Fourier transform (DFT) 119 discrete inverse Fourier transform (DIFT) 120 discretization 414 method, 294 disjoining pressure 143, 291, 293 dissipation potential 297 dissolution 152, 305 front, 356 process, 150, 152, 374 drilling core 618 driving force 373 Drucker-Prager plasticity model, 290 potential, 246, 269 drying 351 creep, 291 process, 590 shrinkage, 285 ductile mode 129 durability 92, 150, 294, 411, 424, 574, 659 analysis, 354 mechanics model, 424 structural, 368 dynamic influence coefficient, 634 load param eters, 82 d ist ance between the pulse peaks, 84 pressure coefficients, 82 pulse amplitudes, 82 wall distance factor, 86 wall height factor, 86 response, 90 critical damping ratio, 91 modal decomposition, 91 resonant amplification factors, 91 stiffness requirement, 572 E-Modulus 134 earthquake 113, 162, 362, 649 edge modes 393 effective balance equation, 415 elastic properties, 271, 276 linearized system of equation, 421, 422 right hand side, 416 stress, 244, 285, 289, 307 elastic, 289 plastic, 289 tangent matrix, 416 eigenfrequency 634 elastoplastic models 244 electrical resistance method 163 electrophoretic effect 298 element 379 embedded crack models, 252 discontinuity approach, 369 endochronic models 518 energy complementary, 272 Subject Index 715 conserving, 369 decaying method, 369 enhanced assumed strain 252, 362, 380, 427, 448 enriched finite elements 372 entropy 286 enumeration strategy 555 environmental attack, 583 humidity, 143 equivalent elliptical crack, 278 elliptical microcrack, 276 strain, 238, 307 error criterion, 431, 432 estimate, 412, 444, 594 h-method, 443 local, 443 p-method, 444 estimator, 391, 445 indicator, 391, 444 h-method, 444 local, 443 p-method, 444 measure, 372, 425 ettringite formation 157 Eurocode 659 evolution algorithm, 555 long-term, 629 strategy, 556 excessive displacement 367 exchangeable salt 152 expansion 157, 307, 311 experimental results 40 macroscopic temperature behaviour, 42 explicit mode 518 exponential convergency 388 exposure classes 93 extended finite element method 369, 448 external damage 95 fabric 109, 162 face modes 394 failure function, 238 probability, 529, 530, 534, 541, 612 Falancs 581 Faraday constant 298 fat igue 1, 163, 169, 180, 626, 653, 655, 659 analysis of bridge hangers, 29 crack, 272 damage, 267, 367 process, 612 failure, 262 high-cycle, 262, 270 high cycle, 129, 174, 207 life, 627 lifetime, 270 load, 270 low-cycle, 259, 262 low cycle, 129, 255 Newmark-Wilson time-step method, 31 strain, 185, 266 test, 259 ultra low cycle, 255 Ficks law 297 filtering 119 finite difference method 649 finite element method 367–369 first-order reliability method 531 first order kinetic law 305 first passage 540 probability, 541 flattened strain trajectory 117 foundations 109, 646 Fourier transform 119 fracture energy, 187, 238, 252, 290, 478 approach, 625 mechanism, 124 process, 369 fragmentation 162 free energy 238, 286, 297 freeze thaw attack 148, 293 frost attack, 194 damage, 293 deicing salt attack, 148 suction, 95 full scale experiments 32 Galerkin 377 continuous method, 369, 408, 412, 416 716 Subject Index discontinuous method, 369, 408, 412, 416 solution, 594 temporal approximation, 419 time integration scheme, 372, 411, 416, 594, 598, 600 type finite element method, 410 Gˆateaux derivative 385 Gauss-Legendre integration, 421, 460 quadrature, 386, 458 generalized external force vector, 413 internal force tensor, 383 vector, 403, 413 mid-point approximations, 414, 415 tangent damping matrix, 413 damping tensor, 385 mass matrix, 413 stiffness matrix, 403, 413 stiffness tensor, 385 genetic algorithm 556 geogrids 650 global balance equation 373 gradient-based algorithm 561 grading curve 189 grain size distribution curve 205 grey-box modelling 635 Griffith criterion 493 gust response factor 11 equivalent quasi-static load, 12 fatigue analysis of gust-induced effects, 18 h-finite element method 379, 388 h-method 412 H¨unxer Br¨ucke 617, 648 hanging node concept 431 Hankel matrix 523, 638 hardening isotropic, 256 kinematic, 256 modulus, 246 harmonic excitation, 649 oscillation, 115 harmony with nature 6 Hasofer-Lind-algorith m 533 h azard 654 headed stud 207 heat capacity, 286 conduction, 36, 292 of hydration, 142 transmission, 39 Helmholtz energy 246 Hessian matrix 568 hierarchical concept, 388 polynomial interpolation, 426 high-cycle model for soils 517, 646 high-speed railway lines 79 aerodynamic loads, 79 critical train speed, 81 noise barrier, 80 prevailing frequency f p ,81 wind shelter walls, 80 higher order finite elements 380 Hilber-α method 411 historiotropy 203, 315 history integration, 583 variable, 434, 440, 478 hodograph 116 hoop stress 489 hourglass control 380 hydration products 302 hydraulic pressure 148 hygral behaviour, 143 conditions, 359 hygro-mechanical analysis, 583, 590 damage, 367 identification 637 implicit backward Euler scheme, 238 mode, 518 Importance Sampling 534 indicator function 533 inf-sub-condition 398 initial condition 412 in situ test stand 39 inspection 6 instability 367 Subject Index 717 integration 377 scheme energy conserving, 411 scheme energy decaying, 411 integrity 289, 290 intensity of accumulation 161, 314 interaction 3 interactive effect 3 intermediate configuration 256 internal damage, 96 modes, 394 interpolation property 390 interval algebra 370 intrinsic permeability 307 inverse Fourier transform 120 investment cost 5 ion transport 295, 374 isomorphic variables 198 isoparametric approximation 390 isotropic damage parameter 286 iteration methods 403 Jacobi temporal transformer, 420 tensor, 383 transformation, 383 jump condition 418 kinematical relation 427 kinematic hardening law 255 kinking angle 272 Kirchhoff-Love formulation 397 Kohlrauschs law 297, 298 Krylov-based model reduction methods 500, 504 Kuhn-Tucker conditions 238, 300, 478 Lagrange 390 multipliers, 507, 511 non-hierarchical concept, 388 polynomials, 369, 380 shape function, 380, 381, 412 latent heat 286 Latin hypercube sampling 535, 536, 617, 627, 631 leaching 354 leakage 356 least squares problem 567 Legendre 380, 389, 390 m odified polynomials, 389 pol ynomials, 369, 389 shape function, 389 type, 392 Leon model 244 life-cycle design, 7 investigation, 499 lifetime 207 analysis of bridge hangers, 34 lock-in effect, 34 stochastic excitation force, 34 assessment, 610 control, 659 lifetime-oriented analysis, 562, 583 design, 1, 371, 548, 562 concept, 365, 607 model, 365 limit state 367 serviceability, 367 ultimate, 367 linear convergence rate 388 linearized discrete balance equation, 385 weak form, 419 liquefaction 113, 162, 206 liquid saturation 289 load -deflection curve, 493 -independent influences, 92 cycles, 266, 269 pattern, 87 static and dynamic design calculations, 87 symmetric load pattern, 90 scenario, 7 loading biaxial, 256 cycles, 280 cyclic, 278 local balance equation 373 localization 634 lock-in 25 effect, 26 aerodynamic damping, 26 large oscillation amplitudes, 26 718 Subject Index Scruton number, 26 range, 28 lift force, 28 locking-free element formulation 430 locking phenomena 379 Lode angle 314 long-term calculation, 499 creep, 285 degradation mechanisms, 632 experiments, 39 loss of equilibrium 367 low-frequency vibration comfort 573 low order approximation, 379 finite elements, 379 macro time 657 maintenance 6 Markov parameters 638, 640 material degradation, 124 failure, 374 model, 625 matrix dissolution 295 Matsuoka and Nakai condition 313 Maxwell symmetry 288 mean wind speeds 15 Gumbel-distribution, 16 logistic distribution, 16 occurrence probability of an extreme value, 20 rosettes of 10-minutes means of wind velocities, 18 terrain factor, 21 Weibull-distribution, 16 wind direction, 18 wind effect admittance, 22 wind rosette, 18 mesh dependency, 246 locking, 519 metallic materials 137 micro-ice-lens model 95, 148, 194 micro and macro timedom ain 33 micro crack 124, 133 formation, 194 micromechanical model 293 micromechanics 271 microplasticity 137 microprestress 291 microscopic alteration, 367 analysis, 621 microstructure 133, 150 micro time 657 Mindlin-Reissner formulation, 397 kinematics, 362 Miner’s rule 205 minimum energy 492 modal analysis, 527, 634 of wind-induced oscillations, 13 assurance criterion, 569 damping, 634 reduction, 503 mode-I-crack extension 490 model adaptivity, 426 reduction, 498, 499, 503 mode shapes 634 moisture permeability, 147 transport, 147, 285, 359, 586 uptake, 194 molar conductivity 298 monopile foundation 650 Monte Carlo method, 627 Simulation, 533, 534, 617, 654 distance-controlled, 542 strategy, 555 multi-axial stress state 269 multi-dimensional multi-field element 377 multi-field num erical method, 365 problem, 367, 369, 380 mul ti-level solution philosophy 367 mult i-scale 658 modeling, 616, 657 multi-stage cyclic loading 136 multi-surface models 518 multiaxial loading 126 multiphysics problems 373, 379, 380 multisurface [...]... 119 optimization 656 method, 365, 551 problem, 546 result, 614 strategy, 372 optimum design 372 order of accuracy 369 orthogonality check 570 oscillation 115 P- and S-wave velocities 203 p-finite element method 379, 387, 388, 402, 588 p-method 412 p-refinement 391 Pad´-Via-Lanczos algorithm 500 e Palmgren-Miner’s hypothesis 136 parallel optimization software, 561 processing, 543 parallelization 542–544,... Surface Method 537, 538 rest period 191 restraint stresses 141 return mapping algorithm 252 revitalization 5 right stretch tensor 114 Ritz load-dependent Ritz vectors, 500, 506 road bridge 617 robust structural design 607 Roscoe’s invariants 198 rotating crack 244 rotation operator 315 Russian Roulette & Splitting 542 S-N curve safety 1 salt attack saturation 626 194 588, 589 Subject Index scaling 293 Schur... Cauchy, 256 fluctuation, 316 intensity factor, 137, 272 Kirchhoff, 256 von Mises, 581 stress-strain 722 Subject Index curve, 124 relation, 265 strong discontinuity approach 252, 448 structural analysis, 371 degradation, 180, 359 design, 365, 371 failure, 356 optimization, 529, 545, 546, 548, 555, 612 problem, 372, 545 optimization problem implicit nature, 548 semi-infinite, 551 subset method, 536 simulation,... pore pressure, 307 size distribution, 150 water pressure accumulation, 113, 205, 649 porosity 289, 292, 295 porous media 285 post-cyclic behaviour 163, 207 power spectral density function 577 practical design 365 predictor iteration, 405 step, 408 pressure vessel 259, 362 prestressing tendon 625, 626 primal method 553 principle of maximum dissipation 244 probabilistic lifetime analysis 611 probability... Schur complement 511 second-order reliability method 531 second order accuracy 409–411 seepage velocity 307 selective reduced integration 380 semidiscrete balance equation, 412 differential equation, 369 structural equation, 367 sequential convex programming, 553 linear programming, 553 quadratic programming, 533, 553 serendipity approximation 402 service -life control, 4, 7 life, 1 performance, 366 serviceability... regularization 237, 307 relaxation effect 298 reliability 3, 4, 653, 656 analysis, 528, 529, 542, 543 time-variant, 614 analysis method, 365 problem, 520, 531, 541 time-invariant, 531 reliability-based optimum design 529 renewal processes 34 fatigue events, 34 macro time domain, 34 repair 4, 6 representative elementary volume 297 residual -based error criterion, 426 deformation, 183 strain, 116, 160, 198 resilient... form, 419 weak formulation, 412 test function 377 thaumasite formation 157 thawing rate 101 theory of mixtures 294 theory of porous media 293–295, 302, 307 theory of probability 370 thermal actions, 35 design process, 35 lifetime analysis, 35 behaviour, 140 conductivity, 292 cracking, 142 expansion, 140 coefficient, 140 incompatibility, 140 loading, 141 loads on structures, 42 low-cycle fatigue, 42 properties, . 244 life-cycle design, 7 investigation, 499 lifetime 207 analysis of bridge hangers, 34 lock-in effect, 34 stochastic excitation force, 34 assessment, 610 control, 659 lifetime-oriented analysis, 562, 583 design, . 623 714 Subject Index stiffness, 134 structural, 180, 359 degraded road bridge 617 deionized water 356 derivative-based method 552 derivative-free strategy 555 design concept, 93 process, 371 working. 143, 291, 293 dissipation potential 297 dissolution 152, 305 front, 356 process, 150, 152, 374 drilling core 618 driving force 373 Drucker-Prager plasticity model, 290 potential, 246, 269 drying