Current Trends and Open Problems in Computational Mechanics

✍ Scribed by Fadi Aldakheel (editor), Blaž Hudobivnik (editor), Meisam Soleimani (editor), Henning Wessels (editor), Christian Weißenfels (editor), Michele Marino (editor)

• Publisher: Springer
• Year: 2022
• Tongue: English
• Leaves: 587
• Category: Library

✦ Synopsis

This Festschrift is dedicated to Professor Dr.-Ing. habil. Peter Wriggers on the occasion of his 70th birthday. Thanks to his high dedication to research, over the years Peter Wriggers has built an international network with renowned experts in the field of computational mechanics. This is proven by the large number of contributions from friends and collaborators as well as former PhD students from all over the world. The diversity of Peter Wriggers network is mirrored by the range of topics that are covered by this book. To name only a few, these include contact mechanics, finite & virtual element technologies, micromechanics, multiscale approaches, fracture mechanics, isogeometric analysis, stochastic methods, meshfree and particle methods. Applications of numerical simulation to specific problems, e.g. Biomechanics and Additive Manufacturing is also covered. The volume intends to present an overview of the state of the art and current trends in computational mechanics for academia and industry.

✦ Table of Contents

Preface
Contents
Multiphysics Computation of Thermomechanical Fatigue in Electronics Under Electrical Loading
1 Introduction
2 Governing Equations
3 Model Problem
4 Simulation and Results
5 Conclusion
References
Phase-Field Modeling of Fatigue Crack Propagation in Brittle Materials
1 Introduction
2 Phase-Field Modeling of Brittle Fracture
2.1 Basic Kinematics at Small Strains
2.2 Constitutive Work Density Function
2.3 Governing Equations
3 Phase-Field Model for Fatigue Crack Growth
4 Numerical Examples
4.1 Single-Edge Notched Test
4.2 Block with Multiple Holes Under Cyclic Loading
5 Conclusion
References
A Non-intrusive Global/Local Cycle-Jumping Techniques: Application to Visco-Plastic Structures
1 Introduction
2 Reference Problem and Solution
3 Summary of the Chosen Cycle-Jumping Technique
4 Coupling with the Global/Local Method
5 Conclusion
References
VEM Approach for Homogenization of Fibre-Reinforced Composites with Curvilinear Inclusions
1 Introduction
2 Asymptotic Homogenization of Doubly Periodic Fibre Reinforced Composite Materials
2.1 Homogenized Equilibrium Equation and Effective Material Moduli
3 C0 Curved Virtual Element Method
3.1 The Virtual Element Space
3.2 Numerical Test
4 Conclusion
References
Free Bloch Wave Propagation in Periodic Cauchy Materials: Analytical and Computational Strategies
1 Introduction
2 Wave Propagation in Periodic Cauchy Materials
2.1 Direct Strategy
2.2 Indirect Strategy
3 Dispersion Properties via Finite Element Formulation
3.1 Direct Strategy
3.2 Indirect Strategy
4 Conclusions
References
Divergence Free VEM for the Stokes Problem with No Internal Degrees of Freedom
1 Introduction
2 Discrete Velocity Spaces
3 A Projection Operator and the Discrete Problem
4 Numerical Tests
References
Strategy for Preventing Membrane Locking Through Reparametrization
1 Introduction
2 Curved Bernoulli Beam
2.1 Standard Displacement Formulation (u,w)
2.2 Mixed Displacement Formulation (u,w,uε)
3 Membrane Locking
4 Reparametrizations to Avoid Membrane Locking
4.1 First Reparametrization (u,uε)
4.2 Second Reparametrization (uε,w)
4.3 Third Reparametrization (uε,Aw)
4.4 Mechanical Interpretation of uε
5 Numerical Example
6 Conclusions
References
Model-Free Fracture Mechanics and Fatigue
1 Introduction
2 Classical Formulation
3 Data-Driven Approach
3.1 Rate-Independent Fracture
3.2 Rate-Dependent Fracture and Fatigue
4 Summary and Outlook
References
Node Based Non-invasive Form Finding Revisited—The Challenge of Remeshing
1 Introduction
2 A Brief Outline of Non-invasive Form Finding
2.1 The Quasi-Newton Update Iteration Step
2.2 Non-invasive Optimization
3 Mesh Transformation for Dealing with Remeshing
4 Academic Example
5 Summary
References
Micropolar Modelling of Periodic Cauchy Materials Based on Asymptotic Homogenization
1 Introduction
2 Microscopic and Macroscopic Governing Equations
3 Micro-Macro Kinematic Relations and Asymptotic Expansion of the Microscopic Governing Equations
4 Upscaling Relations and Third Order Polynomial Kinematic Map
5 Generalized Macro-Homogeneity Condition
6 Benchmark Test
7 Conclusions
References
Experimental and Numerical Investigation of Granules as Crash-Absorber in Ship Building
1 Introduction
2 Experimental Testing
3 Numerical Simulation
4 Conclusions
References
On Hydraulic Fracturing in Fully and Partially Saturated Brittle Porous Material
1 Introduction
2 Governing Equations
2.1 Fracturing of Brittle Porous Solids
2.2 Fluid Components
2.3 Equations Governing the Numerical Computations
3 Numerical Example
4 Conclusion
References
Efficient Two-Scale Modeling of Porous Media Using Numerical Model Reduction with Fully Computable Error Bounds
1 Introduction
2 Computational Homogenization with Model Reduction
3 Estimation of the NMR Error for the RVE Problem
4 Conclusions
References
Perspectives on the Master-Master Contact Formulation
1 Introduction
1.1 Master-Slave Scheme
1.2 Contact Contributions in a Numerical Model
2 Pointwise Contact
2.1 Master-Master Scheme
3 Challenges for Future Research
References
Remarks on the History of Glacier Research and the Flow Law of Ice
1 Beginnings of Glacier Ice Research
2 First Measurements and Link with Young Thermodynamics
3 Creep Law for Ice
4 Beyond the Power Law
References
Anisotropic Failure Criteria in Relation to Crack Phase-Field Modeling at Finite Strains
1 Introduction
2 Anisotropic Crack Phase-Field Modeling
2.1 Geometrical Aspects of Anisotropic Phase-Field Modeling
2.2 Balance Equations of Phase-Field Modeling of Rupture
2.3 Constitutive Aspects of Anisotropic Phase-Field Modeling
3 Discussion
References
A Poroelastic Element for FEAP Using AceGen
1 Introduction to Poroelasticity
2 Linear Poroelasticity
2.1 Theory
2.2 Variational Equations
2.3 Finite Element Solution
3 Automated Computational Modeling Using AceGen
4 Results and Discussion
4.1 Mandel Problem
4.2 Consolidation Problem
5 Closure
References
Contact Formulation for Second Gradient Materials
1 Introduction
2 Finite Strain Second Gradient Material
3 Contact Constraints
4 Conclusions
References
Locking-Free Mixed Finite Element Methods and Their Spurious Hourglassing Patterns
1 Introduction
2 The Five-Field Finite Element Formulation
2.1 Deformation Gradient
2.2 Variational Framework
2.3 Discretization
3 Numerical Investigations
3.1 Cook's Membrane
3.2 Stability Test
3.3 Necking Plane Strain
3.4 Necking Circular Bar
3.5 Spherical Shell with Opening
4 Conclusion
References
Adaptive Virtual Element Method for Large-Strain Phase-Field Fracture
1 Introduction
2 Phase-Field Modeling of Brittle Fracture
2.1 Basic Kinematics
2.2 Constitutive Work Density Function
2.3 Governing Equations
3 The VEM
3.1 The VEM Projection
3.2 Construction of the Virtual Element
4 Mesh Refinement
5 Numerical Examples
5.1 Single-Edge Notched Tension Test
5.2 Single-Edge Notched Shear Test
6 Conclusion
References
Galerkin Formulations with Greville Quadrature Rules for Isogeometric Shell Analysis: Higher Order Elements and Locking
1 Introduction
2 Greville Quadrature
2.1 Definition of Greville Quadrature
2.2 Greville Quadrature for Shells
2.3 Scordelis–Lo Roof
3 Conclusions
References
Thermodynamic Topology Optimization of Layered Anisotropic Materials
1 Introduction
2 Thermodynamic Optimization
2.1 Design Variables
2.2 Material Definition
2.3 Optimization Model
2.4 Stationarity Conditions and Evolution Equations
3 Numerical Solution
3.1 Program Structure
3.2 Initial Conditions
3.3 Material Orientation Filter
4 Numerical Results
4.1 Material Parameters and Boundary Conditions
4.2 Results Without Material Orientation Filter
4.3 Material Orientation Filter
4.4 Prescribing the Layer Normal
5 Conclusions and Outlook
References
A Review of Nonlocality in Computational Contact Mechanics
1 Introduction
2 Nonlocal Interactions in Discretized Models
3 Nonlocal Interaction Through a Fictitious Medium
4 Nonlcal Interaction Through Integral Operators
5 Borrowing from Peridynamics: Frictional Nonlocal Contact
6 Conclusions and Future Directions
References
Optimal Control for Phase-Field Fracture: Algorithmic Concepts and Computations
1 Introduction
2 Problem Statements
2.1 Phase-Field Fracture Forward Problem
2.2 Optimization Problem
3 Reduced Optimization Problem
4 Algorithmic Realization
5 Numerical Example
References
A Strong Form Meshfree Collocation Method: Engineering Applications Including Frictional Contact
1 A Strong Form Meshfree Collocation Method
1.1 Approximation of Derivative Operators
1.2 Discretization of a Strong Form for Frictional Contact
2 Applications Including Frictional Contact
References
A Mixed XFEM Formulation to Simulate Dynamic Wave Propagation in Nearly Incompressible Materials
1 Introduction
2 The XQ1XP0 Formulation for Small Deformations and Dynamic Problems
3 Quasi-longitudinal Wave Reflection Pattern of a Cylindrical Heterogeneity
4 Conclusions
References
What Machine Learning Can Do for Computational Solid Mechanics
1 Introduction
2 Material Modeling
2.1 Accelerating Multiscale Simulations
2.2 Data-Driven Constitutive Models: Beyond Simulation-Based Training
2.3 Learning to Solve PDEs
3 Design of (meta-)materials
3.1 Accelerating Topology Optimization
3.2 Efficiently Exploring Design Spaces
3.3 Inverting Structure-Property Maps
4 Conclusions and Outlook
References
On a Physics-Compatible Approach for Data-Driven Computational Mechanics
1 Introduction
2 Basic Ideas
2.1 The Computation Problem
2.2 Principle P1: Separation of Equations
2.3 Principle P2: The Experimental Constitutive Manifold
2.4 Structure Computation
3 The Experimental Constitutive Manifold—Illustration
4 Conclusion
References
Wave Propagation in Layered Fiber Composites with Nonlinear Material Laws
1 Introduction
2 Nonlinear Plate Structure
3 Cumulative Higher Harmonic Wave Modes
4 Analysis and Results
5 Concluding Remarks
References
Finite Element Modelling of In-Stent Restenosis
1 Introduction
1.1 Structure of the Arterial Wall
1.2 In-Stent Restenosis and Platelet-Derived Growth Factor
2 Mathematical Modelling
2.1 Transport Phenomena
2.2 Arterial Wall Mechanics
2.3 Kinematics
2.4 Hyperelastic Constitutive Model
3 Numerical Methods
4 Numerical Investigation
5 Conclusion and Outlook
Appendix
References
It's Too Stiff: On a Novel Mixed Finite Element Formulation for Nearly-Inextensible Materials
1 Introduction
2 Theory
2.1 Nearly-Inextensible Transversely Isotropic Materials
2.2 Variational Formulation for Nearly-Inextensible Materials
2.3 On Nearly-Incompressible Transversely Isotropic Materials
3 Mixed Finite Element Models and Numerical Results
3.1 Near-Inextensibility: A Bias-Extension Test
3.2 Near-Inextensibility and Near-Incompressibility: A Punch Test
4 Conclusions
References
A Comparison of Matrix-Free Isogeometric Galerkin and Collocation Methods for Karhunen–Loève Expansion
1 Introduction
2 Karhunen–Loève Expansion of Random Fields
3 Numerical Methods
3.1 Algorithmic Complexity
4 Numerical Examples
5 Conclusions
References
Forerunning and Bridging in Dry and Saturated Fracturing Solids
1 Introduction
2 Forerunning in Dry Solids
3 Forerunning in Solids with Fluid Presence
3.1 2D Lattice Model Under Fluid Injection
3.2 Forerunning in a Dry Double Beam
3.3 Forerunning in a Dry and a Saturated Porous Medium Under Mechanical Load and Under Fluid Injection
4 Conclusions
References
An Optimized Material Removal Process
1 Introduction
2 Micro-Mechanics of Wear
2.1 Wear Criteria
2.2 Elastic Energy Computation
3 Material Removal
3.1 Problem Statement
3.2 Optimization
4 Results
4.1 Optimal Shape
4.2 Example of Application: Ice Cream Scoop
5 Conclusion
References
How to Push Computational Bio-Mechanics to Clinical Application?
1 Introduction
2 The High-Fidelity Modeling Approach
2.1 Model Parametrization
2.2 Implicit Implementation of Osseointegration and Bone-Remodeling
3 The Surrogate-Model
4 Numerical Example
5 Conclusion
References
VARTOP: A New Variational Approach to Structural and Thermal Topology Optimization Problems
1 Introduction
2 Problem Formulation
2.1 VARTOP: Variational Topology Optimization
2.2 State Problem
3 Applications
3.1 Minimum Mean Compliance
3.2 Compliant Mechanism
3.3 Thermal Cloaking in Terms of Heat Flux
4 Conclusions
References
From the Pioneering Contributions by Wriggers to Recent Advances in Computational Tribology
1 Introduction
2 High Precision Contact Solution Using Interface Finite Elements with Embedded Roughness
3 Upscaling of Contact Problems with a Concurrent BEM-FEM Coupling
4 Hydrodynamic Lubrication with Complex Rough Boundaries
5 Conclusions
References
Assessment of the Structural Response of Steel Reinforced and Steel-Fibre Reinforced Concrete Structures with 3D Detailed Modeling: Limitations and Remedies
1 Introduction
2 Modeling Remarks of Steel Reinforced Concrete (SRC) Structures
3 Limitations in Modeling of Steel Fibre Reinforced Concrete (SFRC) Structures
4 Conclusions
References
Dynamic Fracture of Brittle Shells in a Space-Time Adaptive Isogeometric Phase Field Framework
1 Introduction
2 Fracture of Deforming Surfaces
2.1 Thin Shell Theory
2.2 Brittle Fracture
2.3 Computational Aspects
3 Numerical Examples
3.1 Crack Propagation Around Obstacles
3.2 Fracturing Balloon
4 Conclusion
References
Higher Order Geometrically Exact Shear-Rigid Beam Finite Elements
1 Introduction
2 The Geometrically-Exact Shear Rigid Rod Theory
3 Finite Element Implementation
4 Numerical Example—Lateral Buckling Analysis
5 Conclusions
References
Finite Element Formulations for Beam-to-Solid Interaction–from Embedded Fibers Towards Contact
1 Introduction
2 Governing Equations
3 Spatial Discretization
4 Numerical Examples
5 Conclusion
References
Alternative Approaches to the Stabilization of Virtual Element Formulations for Hyperelasticity
1 Introduction
2 The Governing Equations
3 The Virtual Element Method
4 Numerical Results
5 Concluding Remarks
References
Finite Element Formulations for Gradient Damage at Finite Strains
1 Introduction
2 Continuum Damage Mechanics
3 Finite Element Formulation
4 Numerical Tests
5 Conclusion
References
New Approaches for Progressive Damage Analysis of Fiber Reinforced Composites and Fiber Metal Laminates
1 Introduction
2 Theoretical Aspects
2.1 A Progressive Damage Model for FRP Composites Under Cyclic Loading
2.2 A Progressive Damage Model for Fiber Metal Laminates in Static Bolted Joint Applications
3 Application Examples and Discussion
3.1 Fatigue Prediction of FRP Composites Under Complex Stress States
3.2 Progressive Fatigue Damage Analysis of a GFRP T-Bolted Joint
3.3 Progressive Static Damage Analysis of an FML Bolted Joint
4 Conclusion
References
Differential Geometry of Surfaces with Application to Shell Structures
1 Surfaces in Euclidean Three-Dimensional Space
1.1 Surface Basis Vectors and Metric Coefficients
1.2 Surface Christoffel Symbols. Gauss and Weingarten Formulas
1.3 Surface First Covariant Derivative
2 Application of Differential Geometry in Shells
3 Results and Discussions
4 Conclusions
References
Phase Field Modeling of Fatigue Fracture
1 Introduction
2 Model Formulation
3 Numerical Examples
3.1 R-ratio and Sequence Effects
3.2 Mode II Loading
4 Conclusion
References
Challenges for the Least-Squares Finite Element Method in Solid Mechanics
1 Challenges in the LSFEM
2 Approximation of Reaction Forces Within the LSFEM
3 Hybrid Mixed FEM Based on a Least-Squares Approach
4 Conclusion
References
On Two-Scale Modelling of Softening Material Responses
1 Introduction
2 Modelling of Quasi-brittle Damage
3 Modelling of Ductile Damage
3.1 Three MVE First-Order Homogenization
3.2 Second-Order Homogenization
References
A Novel Approach to Phasefield-Fracture for Inelastic Materials and Finite Deformations
1 Introduction
2 Concept of Representative Crack Elements
3 Applications
4 Conclusions
References
Space–Time Flow Computation with Contact Between the Moving Solid Surfaces
1 Introduction
2 Methods
3 Ventricle-Valve-Aorta Flow Analysis
3.1 Geometry and Motion
3.2 Mesh, Boundary Conditions, Blood Properties, and Computational Conditions
3.3 Results and Concluding Remarks
References
Higher-Order Finite Element Methods for Kohn-Sham Density Functional Theory
1 Introduction
2 Density Functional Theory
3 Finite Element Discretization
4 Numerical Investigations
5 Conclusion
References
Space–Time Computational FSI and Flow Analysis: 2004 and Beyond
1 Introduction
2 2004
3 2005–2010
4 2011–2020
References
Synthesis of Computational Mesoscale Modeling of Cementitious Materials and Coda Wave Based Damage Identification
1 Introduction
2 Simulation of Concrete Damage at the Mesoscale
2.1 The Concrete Mesostructure Generator
2.2 DEM Simulation of Uniaxial Compression
3 Finite Difference Simulation of Wave Propagation
4 Damage Classification Using a Deep Convolutional Neural Network
5 Conclusion
References
On a Nonlinear Elastic Composite Shell Model with a Refined 3D Stress Analysis
1 Introduction
2 Governing Equations
2.1 Kinematics
2.2 Weak Form of the Boundary Value Problem
2.3 Representative Volume Element
3 Example
4 Conclusions
References
Computational Homogenization Using Convolutional Neural Networks
1 Introduction
2 Methods
2.1 µCT Imaging
2.2 Micro-Mechanical Modeling of Concrete
2.3 Computational Homogenization
2.4 Artificial Neural Networks
3 Integrating CNN Homogenization into Virtual Design Loops
4 Summary and Outlook
References
Residual Stress Formation on the Powder Scale of Metal Powder Bed Fusion Processes
1 Phase Change at Finite Deformations
1.1 Kinematics of Finite Deformation Phase Change Problems
1.2 A Free Energy Functional for the Phase Change Problem
2 Consolidation Analysis
3 Summary
References
Computational Modelling of Flexoelectricity: State-of-the-art and Challenges
1 Introduction
2 Continuum Model
3 Flexoelectric Effects
3.1 Soft Dielectric Material
3.2 Semiconducting Material
3.3 Optimization of Energy Harvester
4 Atomic-Scale Characterization of Flexoelectricity
5 Discussions on Future Challenges and Directions
5.1 Machine Learning Based Potential and Multiscale Model
5.2 Nonlinear Dynamic Flexoelectric Effect
References
Peter Wriggers