Virtual Design and Validation

Preface
Contents
Experiments and Virtual Design
Digital Volume Correlation of Laminographic and Tomographic Images: Results and Challenges
	1 Introduction
	2 Challenges
		2.1 Material Microstructure
		2.2 CT Imaging and Artifacts
		2.3 Volume of Data/Duration of Acquisition
		2.4 Detecting Features Invisible to the Eye
	3 Recent Solutions
		3.1 Filtering 3D Images
		3.2 Global DVC
		3.3 Reduced Bases and Integrated DVC
		3.4 Regularized DVC
		3.5 Projection-Based DVC
	4 Conclusion
	References
Manufacturing and Virtual Design to Tailor the Properties of Boron-Alloyed Steel Tubes
	1 Introduction
	2 Material
	3 Technological Process
	4 Phase Transformations During Heat-Treatment
		4.1 Austenite Formation During Inductive Heating
		4.2 Austenite Decomposition During Spray Cooling
	5 Non-destructive Microstructure Characterization
	6 Virtual Design of Tube Heat-Treatment
	7 Conclusions
	References
Mathematical Modelling and Analysis  of Temperature Effects in MEMS
	1 Introduction
	2 The Full Model
		2.1 The Evolution of the Membrane
		2.2 The Electrostatic Potential
		2.3 The Temperature
		2.4 Transformation of the System
		2.5 Examples for the Temperature Dependence
	3 The Small Aspect Ratio Limit
		3.1 The System
		3.2 Solution to the Thermal and Electrostatic Problems
		3.3 Well-Posedness of the Deflection Problem
	References
Multi-fidelity Metamodels Nourished by Reduced Order Models
	1 Introduction
	2 Multi-fidelity Kriging in a Nutshell
	3 Presentation of the Mechanical Problem  and the LATIN Solver
		3.1 Mechanical Problem
		3.2 Chaboche\'s Elasto-Viscoplastic Behavior Law
		3.3 LATIN-PGD Solver
	4 Presentation of the Test-Cases
		4.1 Test-Case 1: Plate with Inclusion
		4.2 Test-Case 2 : Damping Part
	5 Implementation of the Coupling Strategy
		5.1 Correlation Between Error on the Quantity of Interest and LATIN Error Indicator
		5.2 Method Used for Test Campaigns
	6 Results of the Test Campaign
		6.1 Full Generation of the Metamodel—Test-Case 1
		6.2 Full Generation of the Metamodel—Test-Case 2
		6.3 EGO Method for Finding the Global Optimum—Test-Case 1
		6.4 EGO Method for Finding the Global Optimum - Test-Case 2
	7 Conclusion
	References
Application of Enhanced Peridynamic Correspondence Formulationpg  for Three-Dimensional Simulationspg  at Large Strains
	1 Introduction
	2 General Framework
	3 Correspondence Formulation
		3.1 Meshfree Discretisation
		3.2 Time Integration
		3.3 Stability Problems
		3.4 Enhanced Formulation
	4 Numerical Examples
		4.1 Tension of a Rod
		4.2 Punch Test
		4.3 Torsion of Rod
	5 Conclusion
	References
Isogeometric Multiscale Modeling with Galerkin and Collocation Methods
	1 Introduction
	2 Basis Functions
		2.1 B-Splines
		2.2 Non-uniform Rational B-Splines
	3 Computational Homogenization
		3.1 Macroscopic Equilibrium Problem
		3.2 Microscopic Equilibrium Problem
	4 Isogeometric Formulation
		4.1 Isogeometric Galerkin Formulation
		4.2 Isogeometric Collocation Formulation
	5 Numerical Examples
		5.1 Microscale Problem
	6 Conclusion
	References
Composites
Experimental and Numerical Investigations on the Combined Forming Behaviour of DX51 and Fibre Reinforced Thermoplastics Under Deep Drawing Conditions
	1 Introduction
	2 Methodology
		2.1 Experimental Procedure
		2.2 Forming Tests
		2.3 Numerical Methods
	3 Results and Discussion
		3.1 Material Characterization and Modelling
		3.2 Hemispherical Dome Tests
	4 Summary and Outlook
	References
The Representation of Fiber Misalignment Distributions in Numerical Modeling of Compressive Failure of Fiber Reinforced Polymers
	1 Introduction
		1.1 Previous Work
		1.2 Current Work
	2 Measurement Data Driven Model Generation
		2.1 Fiber Misalignment Distribution Generation from Experimentally Characterized Spectral Density
		2.2 Generated Distributions Examples
		2.3 Mapping of Fiber Misalignment Distribution to Numerical Model
	3 Numerical Example Results
	4 Concluding Remarks
	References
A Multiscale Projection Method  for the Analysis of Fiber Microbuckling in Fiber Reinforced Composites
	1 Introduction
	2 Fine Scale Modeling
	3 Transversely Isotropic Material Model  for the Coarse Scale
	4 Geometrically Nonlinear Cohesive Element
		4.1 Weak Formulation and Kinematics
		4.2 Finite Element Discretization
	5 Multiscale Modeling
	6 Numerical Examples
	7 Conclusion
	References
Topology Optimization of 1-3 Piezoelectric Composites
	1 Introduction
	2 Constitutive Relation of the 1-3 Piezocomposite
	3 Materials Microstructure Topology Optimization  by the Level Set Method
	4 Optimization Algorithm
	5 Results
	6 Conclusion
	References
Fracture and Fatigue
Treatment of Brittle Fracture in Solids with the Virtual Element Method
	1 Introduction
	2 Governing Equations of Brittle Fracture
		2.1 Basic Equations of Elastic Body
		2.2 Crack Propagation Based on Stress Intensity Factors
		2.3 Phase-Field Approach for Brittle Crack Propagation
	3 Formulation of the Virtual Element Method
		3.1 Ansatz Functions for VEM
		3.2 Residual and Stiffness Matrix of the Virtual Elements
	4 Construction of the Crack Path
	5 Numerical Examples
		5.1 Crack Propagation Using Phase-Field Approach
		5.2 Crack Propagation Using Stress Intensity Factors
	6 Conclusion
	References
A Semi-incremental Scheme for Cyclic Damage Computations
	1 Introduction
		1.1 Notation
	2 An Overview of the LATIN-PGD Method
		2.1 Local Stage
		2.2 Global Stage
	3 Variable Amplitude and Frequency Loading
		3.1 Hybrid Search Direction Formulation
	4 Optimality of the Generated ROB
		4.1 Randomised Singular Value Decomposition (RSVD) Compression of PGD Bases
	5 Numerical Results
		5.1 Model Verification
		5.2 Comparison Between Deterministic and Randomised SVD Schemes
		5.3 Variable Amplitude and Frequency Loading
	6 Conclusions
	References
Robust Contact and Friction Model  for the Fatigue Estimate of a Wire Rope in the Mooring Line of a Floating Offshore Wind Turbine
	1 Introduction
	2 Detailed Wire Rope Model
		2.1 A New Contact and Friction Element for Wire Rope
		2.2 Comparison to Analytical and Surface to Surface Solutions
		2.3 Boundary Conditions
		2.4 Wire Rope Properties
	3 Application to a FOWT Model
		3.1 Global Hydrodynamic FOWT Model
		3.2 Global Model Results
		3.3 Results of the Detailed Wire Rope Model
	4 Conclusion
	References
Micromechanically Motivated Model  for Oxidation Ageing of Elastomers
	1 Introduction
	2 Current State of the Art
	3 Network Degradation Dynamics
		3.1 Compartment Model
		3.2 Reduction Factor
	4 Continuum Model
		4.1 Primary Network Stress
		4.2 Secondary Network Stress
		4.3 Kirchhoff Stress and Material Tangent
	5 Numerical Results
		5.1 Stress Softening and Stiffening
		5.2 Network Degradation and Permanent Set
		5.3 Finite Element Example
	6 Conclusion
	References
Uncertainty Quantification
A Bayesian Approach for Uncertainty Quantification in Elliptic Cauchy Problem
	1 Introduction
	2 The Steklov-Poincaré Approach for the Cauchy Problem
		2.1 Forward and Cauchy Problems in Linear Elasticity
		2.2 The Steklov-Poincaré Method
		2.3 Conjugate Gradient and Ritz Values Computation
	3 Bayesian Inference for the Cauchy Problem
		3.1 Bayes\' Theory and Its Application in the Linear Gaussian Case
		3.2 Application to the Cauchy Problem
	4 Reduction by Ritz Modes
	5 Numerical Example
	6 Conclusion and Perspectives
	References
On-the-Fly Bayesian Data Assimilation Using Transport Map Sampling  and PGD Reduced Models
	1 Introduction
	2 Posterior Sampling in Bayesian Data Assimilation
		2.1 Basics on Bayesian Inference
		2.2 Transport Map Sampling
	3 PGD Model Order Reduction in Bayesian Inference
		3.1 Basics on PGD
		3.2 Transport Map Sampling with PGD Models
	4 Illustrative Example
		4.1 Inference Problem
		4.2 PGD Solution
		4.3 Sequential Data Assimilation
		4.4 Uncertainty Propagation on Outputs of Interest
	5 Conclusions and Prospects
	References
Stochastic Material Modeling for Fatigue Damage Analysis
	1 Introduction
	2 Deterministic Modelling of Fatigue Damage
		2.1 Material Model
		2.2 Numerical Approach
	3 Stochastic Modelling of Fatigue Damage
		3.1 From a Deterministic to a Stochastic Process
		3.2 Numerical Properties of the Damage Process
		3.3 Proposed Diffusion Random Process
		3.4 Drift Term
		3.5 Diffusion Term
		3.6 Introduction of the Stochastic Damage Model  in the Finite-Element Framework
	4 Numerical Example
		4.1 Influence of the Numerical Parameters on the Stochastic Results
		4.2 Evolution of Stochastic Fatigue Damage
		4.3 Virtual S-N Curves
	5 Summary
	References