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