Preface	6
	Contents	12
	Multiscale Analysis as a Central Component of Urban Physics Modeling	14
	1 Introduction	14
	2 Urban Physics: A State of the Art	15
	2.1 From Environmental Physics	15
	2.2 From Urban Planning	16
	2.3 From Building Physics	16
	2.4 From Smart City	17
	3 Urban Physics: A New Framework	17
	3.1 The City as an Interface	17
	3.2 Multiband Aspects of the Radiation Interacting with the Cities	18
	3.3 Shortwave	20
	3.4 Long Waves	21
	4 Computational Model	22
	4.1 The Simplest Model	23
	4.2 View Factors	26
	4.3 Radiosity Equations	27
	4.4 Neumann Series	31
	5 Coupling Short and Long Waves in Transient Situations	33
	5.1 Improving the Performances of the Finite Element Solution Using Super Elements	35
	5.2 Other Aspects of the City Behavior Simulation	35
	6 Conclusion	35
	References	37
	A Path-Following Method Based on Plastic Dissipation Control	41
	1 Introduction	41
	2 Path-Following Method Framework	43
	3 Dissipation Constraint for Geometrically Nonlinear Small Strain Elasto-plasticity	44
	3.1 Explicit Formulation---Version 1	45
	3.2 Explicit Formulation---Version 2	47
	3.3 Implicit Formulations	48
	4 Dissipation Constraint for Embedded Discontinuity Finite Elements	49
	5 Numerical Examples	53
	5.1 Geometrically Nonlinear Elasto-plastic Shell Analysis	53
	5.2 Failure of Steel Frame	54
	6 Conclusions	57
	References	58
	Improved Implicit Immersed Boundary Method via Operator Splitting	60
	1 Introduction	60
	2 Methodology	62
	2.1 Overview of the Immersed Boundary Methods	63
	2.2 Moving Immersed Boundary Method	65
	3 Numerical Results	67
	3.1 Flow over a Stationary Circular Cylinder	67
	3.2 Flow over an Oscillating Circular Cylinder	71
	4 Conclusions	76
	References	76
	Modelling Wave Energy Conversion of a Semi-submerged Heaving Cylinder	78
	1 Introduction	78
	2 Problem Formulation	79
	2.1 Fluid Equations	79
	2.2 Rigid Body Equations of Motion	80
	2.3 Boundary Conditions and Wave Generation	81
	2.4 Pressure-Velocity Decoupling Algorithm	84
	2.5 Fluid-Structure Interaction	86
	3 Energy Extraction	88
	4 Conclusions	89
	References	89
	Multiscale Modeling of Imperfect Interfaces and Applications	91
	1 Introduction	92
	2 Imperfect Interface Approach	95
	2.1 Matched Asymptotic Expansion Method	95
	2.2 Homogenization in Non-interacting Approximation (NIA) for Microcracked Media	107
	3 A St. Venant-Kirchhoff Imperfect Interface Model	114
	3.1 Matched Asymptotic Expansion Method in Finite Strains	114
	3.2 Homogenization of the Microcracked Interphase	122
	4 Numerical Applications	123
	5 Conclusions	129
	References	130
	A Stochastic Multi-scale Approach for Numerical Modeling of Complex Materials---Application to Uniaxial Cyclic Response of Concrete	133
	1 Introduction	133
	2 Multi-scale Stochastic Approach for Modeling Concrete	136
	2.1 Homogenized Material Behavior at Macroscale	137
	2.2 Material Behavior Law at E-mesoscale	138
	2.3 Stochastic Modeling of Heterogeneous E-mesoscale	143
	3 Numerical Implementation	148
	3.1 Random Vector Fields Generation Using FFT	148
	3.2 Material Response at Mesoscale	149
	3.3 Material Response at Macroscale	151
	4 Numerical Applications	154
	4.1 1D Homogenized Response at Macroscale	155
	4.2 Heterogeneous Structure at E-mesoscale	156
	4.3 Concrete Response in Uniaxial Compressive Cyclic Loading	160
	5 Conclusion	164
	Appendix 1	165
	References	168
	Relating Structure and Model	171
	1 Introduction	171
	2 Scaling	173
	2.1 Scaling in Parameter Space	173
	2.2 Scaling in Measurement Space	174
	2.3 Scaling of Dynamically Loaded Structures	174
	3 Loading Reconstruction	175
	3.1 Treatment of Measurement Noise	176
	3.2 Static Loading	176
	3.3 Dynamic Loading	177
	4 Examples	178
	4.1 Scaling in Parameter Space	179
	4.2 Scaling in Measurement Space	180
	4.3 Scaling of Dynamic Properties	181
	4.4 Force Reconstruction---Static Loading	181
	4.5 Force Reconstruction---Dynamic Loading	183
	5 Discussion and Conclusion	192
	References	193
	Fat Latin Hypercube Sampling and Efficient Sparse Polynomial Chaos Expansion for Uncertainty Propagation on Finite Precision Models: Application to 2D Deep Drawing Process	194
	1 Introduction	195
	2 FEM Error Assessment Using Finite Difference Scheme	197
	3 Introduction to Polynomial Chaos Expansion	197
	4 Sampling Scheme Taking into Account Model Resolution	200
	4.1 Implementation of the Fat-LHS	201
	5 Sparse PCE Models for Restricted Training Sets	203
	5.1 Truncating Multi-variate Polynomials Expansion	203
	5.2 Combining Q-norm and LARS	205
	5.3 Error Evaluation of the Polynomial Expansion	206
	6 Results and Discussions	207
	6.1 Analytical Example	207
	6.2 2D Deep Drawing Process	210
	7 Conclusions and Prospects	219
	References	220
	Multiscale Atomistic-to-Continuum Reduced Models for Micromechanical Systems	223
	1 Introduction	223
	1.1 Models at Atomistic Scale	224
	1.2 Concurrent Atomistic-to-Continuum Methods	225
	2 Problem Definition with Multiple Scales	227
	2.1 Atomistic Model Problem	227
	2.2 QC and BD Formulations	229
	3 Comparison and Unified Formulation with Reduced Model	239
	3.1 Unified Coupling Formulation	240
	4 Numerical Example	241
	4.1 Error Convergence	245
	5 Conclusion	247
	References	247
	Inverse Problems in a Bayesian Setting	252
	1 Introduction	252
	2 Bayesian Updating	256
	2.1 Setting	256
	2.2 Recollection of Bayes's Theorem	259
	2.3 Conditional Expectation	260
	3 Characterising the Posterior	267
	3.1 The Posterior Distribution Measure	267
	3.2 A Posterior Random Variable---Filtering	268
	3.3 Approximations	273
	4 Numerical Realisation	281
	5 The Linear Bayesian Update	285
	6 The Nonlinear Bayesian Update	288
	7 Conclusion	291
	References	292
	Heterogeneous Materials Models, Coupled Mechanics-Probability Problems and Energetically Optimal Model Reduction	294
	1 Introduction	295
	2 Theoretical Formulation Heterogeneous Multiscale Method	297
	2.1 State-of-the-art Developments	297
	2.2 Meso-Scale Model of Material Heterogeneities With deterministic Material Parameters	298
	2.3 Probability Aspects of Inelastic Localized Failure for Heterogenous Materials	302
	3 Stochastic Fields Coupling	304
	3.1 Heterogeneous Multiscale Model	305
	3.2 Variational Low-Rank Approach with Successive Rank-1 Update (VLR-SR1U)	306
	3.3 Basic VLR-SR1U	307
	3.4 VLR-OPT: Optimisation of Given Low-Rank Approximation	309
	3.5 RBSSE: Adaptive Construction of the Stochastic Solution Space	311
	3.6 Numerical Experiments	313
	References	320
	Modelling of Internal Fluid Flow in Cracks with Embedded Strong Discontinuities	321
	1 Introduction	321
	2 Numerical Model Formulations	325
	2.1 Enhanced Kinematics	327
	2.2 The Enhanced Weak Form	330
	2.3 Constitutive Model	331
	2.4 The Finite Element Equations of a Coupled Poroplastic Problem	334
	2.5 The Operator Split Algorithm	336
	3 Numerical Simulations	337
	3.1 Preparation of 2D Plain Strain Rock Specimens	337
	3.2 Influence of Heterogeneity in Tension and Compression Tests	339
	3.3 Drained Compression Test of the Poro-plastic Sample with the Localized Failure	341
	4 Conclusions	345
	References	346
	Reliability Calculus on Crack Propagation Problem with a Markov Renewal Process	348
	1 Introduction and Motivation	348
	2 The Model Settings and Elements of Markov Renewal Theory	352
	2.1 Basic Definitions	352
	2.2 Markov Renewal Process and Semi-Markov Kernel	354
	2.3 Markov Renewal Equation	357
	2.4 Further Model Settings	359
	2.5 The Transition Probability Function of the PDMP and Its Markov Renewal Equation	362
	2.6 Practical Calculation of Semi-Markov Kernel	365
	3 Reliability Calculus	365
	3.1 Previous Method on Reliability Calculus	366
	3.2 A New Method on Reliability Calculus	366
	3.3 Practical Implementation	371
	4 Estimation of Reliability	373
	5 Simulation Results	376
	5.1 Simulation Results on a Given Example	376
	5.2 Simulation Results on Experimental Data	377
	6 Conclusions	380
	References	381
	Multi-scale Simulation of Newtonian and Non-Newtonian Multi-phase Flows	384
	1 Introduction	384
	2 Mathematical Background	385
	2.1 Macro-Scale Equations	386
	2.2 Micro-Scale Equations	389
	3 Numerical Methods	391
	3.1 Macro-Scale Discretization	391
	3.2 Micro-Scale Discretization	394
	3.3 Efficient Solution to the Cubic Equation in the FENE Model	395
	4 Results for Imposed and Complex Flows	397
	4.1 Newtonian Fluids	398
	4.2 Non-Newtonian Fluids	399
	5 Conclusions	401
	References	401
	Numerical Modeling of Flow-Driven Piezoelectric Energy Harvesting Devices	404
	1 Introduction	404
	1.1 Harvesting Mechanical Vibrations	406
	1.2 Models of Piezoelectric Energy Harvesting Devices	407
	2 Flow Driven Piezoelectric Energy Harvesters	409
	3 Model of a Flow-Driven Piezoelectric EHD	410
	3.1 Fluid	411
	3.2 Piezoelectric Structure	412
	3.3 Circuit	414
	3.4 Coupling Conditions	414
	4 Weak Form of the Governing Equations	415
	4.1 Fluid	416
	4.2 Structure	417
	4.3 Piezoelectric Material	418
	4.4 Circuit	418
	5 Discretization with Space-Time Finite Elements	419
	5.1 Elements and Space-Time Interpolation	419
	5.2 Monolithic Solution Strategy	425
	6 Numerical Example	426
	6.1 Problem Setup	426
	References	430
	Comparison of Numerical Approaches to Bayesian Updating	432
	1 Introduction	433
	2 Model Problem	434
	3 Identification via Bayesian Regularisation	435
	4 Computational Approaches	439
	4.1 Markov Chain Monte Carlo	439
	4.2 Proxy Modelling	441
	4.3 Linear Bayesian Inference	442
	5 Numerical Results	445
	5.1 One Dimensional Heat Problem	445
	5.2 Two Dimensional Heat Problem	456
	5.3 Forward Problem	457
	5.4 Identification	457
	6 Conclusions	461
	References	465
	Two Models for Hydraulic Cylinders in Flexible Multibody Simulations	467
	1 Introduction	467
	2 Equations of Motion	469
	3 Coupled Multibody System	469
	4 Finite Element Formulations	472
	4.1 Truss-Element Cylinder	472
	4.2 Bending Flexible Hydraulic Cylinders	479
	4.3 Bending Flexible Hydraulic Cylinder with Friction	484
	5 Integration of the Coupled Two-Field Problem	486
	5.1 The Rosenbrock Method	486
	6 Numerical Examples	488
	6.1 Influence of the Stribeck Effect	488
	6.2 Discussion	489
	6.3 Sudden Stop of a Boom	491
	6.4 System Responses with Friction	493
	7 Concluding Remarks	495
	References	496