Note: Intro -- Preface -- Contents -- Hybrid Discretizations in Solid Mechanics for Non-linear and Non-smooth Problems -- 1 Introduction -- 2 Continuous, Discontinuous and Hybrid Discretizations -- 2.1 A Weakly Conforming Method -- 2.2 Incomplete Interior Penalty Galerkin Method -- 2.3 Hybrid Discontinuous Galerkin Method -- 2.4 Symmetric Hybrid Discontinuous Galerkin Method -- 2.5 Cohesive Discontinuous Galerkin Method -- 3 Numerical Evaluation of the Numerical Schemes -- 3.1 An Illustrating Smooth Example in 2D -- 3.2 A Corner Singularity in 3D -- 3.3 Cook's Membrane: A Benchmark Problem -- 3.4 Elasto-Plastic Deformation of an Annulus -- 3.5 Material Discontinuities at Interfaces: A Ring with Different Materials -- 3.6 A Fiber Composite with Nearly Incompressible Inclusions -- 3.7 A Benchmark Configuration for Thin Structures -- 3.8 An Inelastic Model Combining Plasticity and Damage -- 3.9 A Hybrid Approximation of a Contact Problem -- 4 Conclusion -- References -- Novel Finite Elements - Mixed, Hybrid and Virtual Element Formulations at Finite Strains for 3D Applications -- 1 Introduction and State of the Art -- 2 Brief Continuum-Mechanical Background -- 3 Mixed FE Technology for Large Deformations -- 3.1 Consistent Stabilization for Displacement-Pressure Elements -- 3.2 Hellinger-Reissner Principle for Large Deformations -- 4 Virtual Element Technology for Large Deformations -- 4.1 Displacement VEM Space and Projector Operators -- 4.2 Construction of Displacement Based and Two-Field Mixed VEM Approximation -- 4.3 Numerical Example -- 5 Conclusion and Outlook -- References -- Robust and Efficient Finite Element Discretizations for Higher-Order Gradient Formulations -- 1 Introduction -- 1.1 Definitions -- 2 Formulation for Finite Strain Gradient Elasticity -- 2.1 Gradient Elasticity Fundamentals -- 2.2 Rot-Free Finite Element Formulation. , 2.3 Finite Element Discretization -- 2.4 Numerical Examples -- 3 Gradient Enhanced Damage at Finite Strains -- 3.1 Continuum Damage Mechanics with Gradient Enhancement -- 3.2 Finite Elements for Gradient Damage -- 3.3 Numerical Examples -- 4 Conclusion -- References -- Stress Equilibration for Hyperelastic Models -- 1 Introduction -- 2 Hyperelasticity and Stress Equilibration -- 3 Localized Stress Equilibration -- 4 Error Estimation -- 5 Computational Experiments -- References -- Adaptive Least-Squares, Discontinuous Petrov-Galerkin, and Hybrid High-Order Methods -- 1 Introduction -- 1.1 Motivation -- 1.2 Three Nonstandard Discretizations -- 1.3 Adaptive Mesh-Refinement -- 1.4 Outline of the Presentation -- 2 Notation -- 3 Least-Squares Finite Element Methods in Computational Mechanics -- 3.1 Least-Squares Finite Element Methods -- 3.2 Natural Adaptive Mesh-Refinement -- 3.3 Alternative A posteriori Error Control -- 3.4 Axioms of Adaptivity -- 4 Least-Squares Finite Element Methods in Nonlinear Computational Mechanics -- 4.1 Convex Energy Minimization -- 4.2 Least-Squares Formulation -- 4.3 Numerical Experiments -- 4.4 Comments -- 5 Discontinuous Petrov-Galerkin -- 5.1 Optimal Test Functions -- 5.2 Breaking Spaces and Forms -- 5.3 Adaptive Mesh-Refinement -- 5.4 Axioms of Adaptivity -- 6 Discontinuous Petrov-Galerkin in Nonlinear Computational Mechanics -- 6.1 Nonlinear Discontinuous Petrov-Galerkin -- 6.2 Alternative Formulations -- 6.3 Existence and Uniqueness of Discrete Solutions -- 6.4 Numerical Experiments -- 7 Hybrid High-Order Method -- 7.1 Discrete Ansatz Space -- 7.2 Reconstruction Operators and Stabilization -- 7.3 HHO in Computational Mechanics -- 7.4 Reliable and Efficient Error Control -- 7.5 Numerical Experiment on L-Shaped Domain with Corner Singularity -- 8 HHO in Nonlinear Computational Mechanics. , 8.1 A Class of Degenerate Convex Minimization Problems -- 8.2 The Unstabilized HHO Method -- 8.3 A priori Analysis -- 8.4 A posteriori Analysis -- 8.5 A Topology Optimization Problem: Optimal Design -- References -- Least-Squares Finite Element Formulation for Finite Strain Elasto-Plasticity -- 1 Introduction -- 2 Elasto-Plasticity for the Framework of Finite Strains -- 3 Least-Squares Finite Element Formulation for Finite Strain Elasto-Plasticity -- 4 The Least-Squares Functional as an Error Estimator -- 5 Numerical Analysis -- 6 Conclusion -- References -- Hybrid Mixed Finite Element Formulations Based on a Least-Squares Approach -- 1 Introduction -- 2 Continuous Least-Squares Finite Element Formulation -- 3 Hybrid Mixed Finite Element Based on a Least-Squares Approach -- 3.1 Weak Form and Linearization of the Hybrid Mixed Formulation -- 3.2 Discretization and Implementation Aspects -- 4 Numerical Analysis for Hybrid Mixed Formulations -- 4.1 Cook's Membrane Problem -- 4.2 Quartered Plate Example -- 5 Conclusion -- References -- Adaptive and Pressure-Robust Discretization of Incompressible Pressure-Driven Phase-Field Fracture -- 1 Introduction -- 2 Notation and Equations -- 2.1 Pressurized Phase-Field Fracture in a Displacement Formulation -- 2.2 Pressurized Phase-Field Fracture in a Mixed Formulation -- 3 Discrete Formulation -- 4 Residual-Type a Posteriori Error Estimator -- 5 Numerical Tests -- 5.1 Sneddon-Inspired Test Cases (Example 1) -- 5.2 Incompressible Material Surrounded with a Compressible Layer (Example 2) -- 5.3 Nonhomogeneous Pressure Test Case with a Compressible Layer (Example 3) -- 6 Conclusions -- References -- A Phase-Field Approach to Pneumatic Fracture -- 1 Introduction -- 2 Phase-Field Model -- 2.1 Linear Elasticity -- 2.2 Finite Elasticity -- 2.3 Discretization -- 3 Multilevel Solution Strategies. , 4 Discussions and Extensions of the Phase-Field Model -- 4.1 Influencing Parameters -- 4.2 Externally Driven Fracture -- 5 Numerical Examples -- 5.1 Conchoidal Fracture -- 5.2 Pressure Driven Crack Growth -- 6 Summary -- References -- Adaptive Isogeometric Phase-Field Modeling of Weak and Strong Discontinuities -- 1 Introduction -- 2 Local Mesh Refinement -- 2.1 Truncated Hierarchical B-Splines -- 2.2 T-Splines -- 2.3 Unstructured T-Splines -- 3 Spline-Based Analysis -- 3.1 Spectral Superiority of Splines -- 3.2 Adapted Heterogeneous Spline Spaces -- 4 Adaptive Isogeometric Analysis -- 4.1 THB-Splines or T-Splines - A Computational Comparison -- 4.2 Mesh Adaptivity for Incremental Solution Schemes -- 5 Weak and Strong Discontinuities in Solid Mechanics -- 5.1 Embedded Material Interfaces in Linear Elasticity -- 5.2 Brittle and Ductile Fracture in Homogeneous and Heterogeneous Materials -- 6 Conclusion -- References -- Phase Field Modeling of Brittle and Ductile Fracture -- 1 Phase Field Model of Brittle Fracture -- 2 Exponential Shape Functions -- 2.1 Quadratic Shape Functions -- 2.2 Exponential Shape Functions -- 2.3 3d Exponential Shape Functions -- 2.4 Numerical Test -- 2.5 Adaptive Numerical Integration -- 2.6 Blending Elements -- 2.7 Adaptive Orientation 2d -- 3 Phase Field Model for Ductile Fracture -- 3.1 Phase Field Modeling of Ductile Fracture -- 3.2 Analysis of a 1D-Bar Problem -- 3.3 Plane Strain Simulations -- 3.4 3D Simulations -- 4 Concluding Remarks -- References -- Adaptive Quadrature and Remeshing Strategies for the Finite Cell Method at Large Deformations -- 1 Introduction -- 2 The Finite Cell Method -- 3 Adaptive Quadrature Based on the Moment Fitting -- 3.1 Moment Fitting -- 3.2 Adaptive Moment Fitting -- 3.3 Numerical Examples -- 4 A Remeshing Strategy for the Finite Cell Method -- 4.1 Kinematics -- 4.2 Remeshing Procedure. , 4.3 Numerical Examples -- 5 Conclusion -- References -- The Finite Cell Method for Simulation of Additive Manufacturing -- 1 Introduction -- 2 The Finite Cell Method -- 3 The Finite Cell Method Combined with Locally-Refined p-FEM -- 4 The Finite Cell Method Combined with Locally-Refined IGA -- 5 Simulation of Additive Manufacturing -- 5.1 The Thermal Model -- 5.2 Experimental Validation -- 5.3 The Finite Cell Method in SLM Process Simulations -- 5.4 Thermo-Mechanical Part-Scale Simulation -- 6 Credits and Permissions -- References -- Error Control and Adaptivity for the Finite Cell Method -- 1 Introduction -- 2 The Finite Cell Method for the Poisson Problem -- 3 Basis Functions for Finite Cell Meshes with Hanging Nodes -- 4 Residual-Based Error Estimation for the Finite Cell Method -- 4.1 Reliability -- 4.2 Numerical Example -- 5 Dual Weighted Residual Error Estimation for the Finite Cell Method -- 5.1 Error Identity -- 5.2 Refinement Strategy -- 5.3 Numerical Example -- 6 Conclusion and Outlook -- References -- Frontiers in Mortar Methods for Isogeometric Analysis -- 1 Introduction -- 2 Coupled Simulations with Mortar Methods in HPC -- 3 Basic Equations and Isogeometric Analysis -- 4 Mortar Techniques for Isogeometric Analysis -- 4.1 Biorthogonal Splines for Isogeometric Analysis -- 4.2 Multi-patch Analysis for Kirchhoff-Love Shells -- 4.3 Weak Cn Coupling for Solids -- 4.4 Crosspoint Modification -- 4.5 Hybrid Approaches for Higher-Order Continuity Constraints -- 5 Mortar Contact Formulations for Isogeometric Analysis -- 5.1 Biorthogonal Basis Functions Applied to Contact Mechanics -- 5.2 Thermomechanical Contact Problems -- 6 Multi-dimensional Coupling -- 7 Conclusions -- References -- Collocation Methods and Beyond in Non-linear Mechanics -- 1 Introduction -- 1.1 Collocation and Isogeometric Analysis. , 1.2 Beyond Collocation in Uncertainty Quantification.

Note: Intro -- Preface -- Contents -- Composites -- Evolution of Failure Mechanisms in Composite Shell Structures Using Different Models -- 1 Introduction -- 2 Two-Scale Shell Model -- 2.1 Theoretical Background -- 2.2 Finite Element Formulation -- 3 Failure Models of Hashin, Puck and Cuntze -- 3.1 The Modified Hashin-Model -- 3.2 The Puck-Model -- 3.3 The Cuntze-Model -- 4 Example-Four Point Bending Test -- 4.1 Problem Description -- 4.2 Hashin-Model -- 4.3 Puck-Model -- 4.4 Cuntze-Model -- 5 Conclusions -- References -- Micro-Macro Modelling of Metallic Composites -- 1 Introduction -- 2 Unidirectional Composite (Micro-scale) -- 2.1 Geometry Generation -- 2.2 Fiber and Matrix Material -- 2.3 Determination of Unidirectional Composite Yield Surface -- 3 Macro-model -- 3.1 Constitutive Model of Unidirectional Composite -- 3.2 Parameter Identification and Validation -- 4 Conclusion -- References -- Comparison of Mechanical Tests for the Identification of Composite Defects Using Full-Field Measurements and the Modified Constitutive Relation Error -- 1 Introduction -- 2 MCRE Method and Formulation -- 2.1 The MCRE Functional -- 2.2 The MCRE Formulation for Linearized Buckling -- 3 Comparison of the Identification Results for Different Loading Conditions -- 3.1 The Simulated Specimen -- 3.2 Pseudo-experimental Tests: Simulated Responses of the Specimen -- 3.3 Identification Results: The Case of a Small Geometric Defect -- 3.4 Identification Results: The Case of a Big Geometric Defect -- 3.5 Conclusions on the Comparison -- 4 Real Tests: Identification Employing Buckling Experimental Results -- 4.1 Identification Results for a Defective Specimen (Specimen 4) -- 4.2 Identification Results for a Nominally Perfect Specimen (Specimen 2) -- 5 Conclusions -- References -- Snap-Through of Bistable Configurations Generated from Variable Stiffness Composites. , 1 Introduction -- 2 Variable Stiffness Model -- 3 Semi-analytical Approach -- 3.1 Governing Equations -- 3.2 Snap-Through Force -- 4 Finite Element Analysis -- 4.1 Cool-Down Process -- 4.2 Snap-Through Process -- 5 Results and Discussion -- 6 Calculation of Snap-Through Forces -- 7 Conclusion -- References -- Invariant-Based Finite Strain Anisotropic Material Model for Fiber-Reinforced Composites -- 1 Introduction -- 2 Continuous Formulation -- 2.1 Basic Kinematics -- 2.2 Balance Laws -- 3 Constitutive Model: Invariant-Based Formulation -- 3.1 Fundamental Aspects -- 3.2 Transversely Isotropic Yield Function -- 3.3 Plastic Potential Function -- 3.4 Evolution Equations of the Internal Variables -- 3.5 Parameter Identification -- 4 Numerical Treatment -- 4.1 Numerical Time Integration: General Return Mapping Algorithm -- 4.2 Algorithmic-Consistent Tangent Moduli -- 5 Applications -- 5.1 Model Verification and Validation -- 5.2 Structural Application: Three-Point Bending Test -- 6 Concluding Remarks -- References -- Computational Solution Approaches -- Unified Approach to Sensitivity Analysis Based Automation of Multi-scale Modelling -- 1 Multi-scale Methods -- 2 Automation of Multi-scale Methods -- 2.1 Automation of Boundary Condition Sensitivity Analysis -- 2.2 Automation of FE2 -- 2.3 Automation of MIEL -- 3 Unified Approach -- 4 Two-Level Path-Following Procedure -- 5 Numerical Example -- 6 Conclusions -- References -- Efficient Multiscale FE-FFT-Based Modeling and Simulation of Macroscopic Deformation Processes with Non-linear Heterogeneous Microstructures -- 1 Introduction -- 2 Material Model Formulation -- 2.1 Macroscopic Relations and Scale-Bridging -- 2.2 Local Problem -- 3 Crystal Plasticity Constitutive Law -- 4 Algorithmic Formulation -- 4.1 Fast Fourier Transforms -- 5 Solution Procedure -- 6 Numerical Examples -- 6.1 Three Point Bending. , 7 Discussion -- References -- Experimental-Numerical Validation Framework for Micromechanical Simulations -- 1 Introduction -- 2 Experimental and Numerical Framework -- 2.1 Experiments -- 2.2 Digital Volume Correlation -- 2.3 Simulations -- 3 Results -- 3.1 Error Estimators -- 3.2 Damage Analysis -- 4 Discussion -- References -- Stochastic Upscaling via Linear Bayesian Updating -- 1 Introduction -- 2 Stochastic Upscaling -- 2.1 Bayesian Inverse Problems -- 3 The Coarse-Scale Model -- 4 The Fine-Scale Model -- 5 Numerical Results -- 5.1 The Homogeneous Case -- 5.2 The Heterogeneous Case -- 6 Conclusion -- References -- A Model Reduction Technique in Space and Time for Fatigue Simulation -- 1 Introduction -- 1.1 Different Modelling Approaches for Fatigue Analysis -- 1.2 Model Reduction Technique for Fatigue Computation -- 1.3 Efficient Time Schemes for Fatigue Computations -- 2 Continuum Damage Mechanics Approach -- 3 LATIN-Based Model Order Reduction Approach for Damage Computation -- 3.1 Local Stage -- 3.2 Global Stage Including Model Order Reduction -- 3.3 Numerical Example of a Plate Under Cyclic Loading -- 4 A Two-Time Scale Approach -- 4.1 Initialisation -- 4.2 Local Stage -- 4.3 Global Stage -- 4.4 A Numerical Example of a Bar Under Fatigue Loading to Build Virtual εa-N Curves -- 5 Conclusion -- References -- Finite and Virtual Element Formulations for Large Strain Anisotropic Material with Inextensive Fibers -- 1 Introduction -- 2 Anisotropic Material with Inextensive Fibers at Large Strain -- 2.1 Continuum Mechanics -- 2.2 Kinematical Anisotropic Constraint -- 2.3 Lagrange Multiplier Formulation -- 2.4 Perturbed Lagrangian and Penalty Formulation -- 3 Mixed Element Formulation -- 4 Formulation of the Virtual Element Projection -- 4.1 Ansatz Functions for VEM -- 4.2 Construction of the Virtual Element -- 5 Examples. , 5.1 Cook's Membrane Problem -- 5.2 Shear Deformation of a Beam -- 5.3 Bias Extension Test -- 6 Conclusions -- References -- Gradient Enhanced Modeling -- A Micromorphic Damage-Plasticity Model to Counteract Mesh Dependence in Finite Element Simulations Involving Material Softening -- 1 Introduction -- 2 Constitutive Theory -- 2.1 Micromorphic Extension, Strong and Weak Form of the Problem -- 2.2 Kinematic Assumptions and Thermodynamic Considerations -- 2.3 State Potential in Terms of the Helmholtz Free Energy -- 2.4 State Relations and Thermodynamic Conjugate Forces -- 2.5 Modeling of Plasticity -- 2.6 Modeling of Damage -- 3 Numerical and Algorithmic Aspects -- 3.1 Discretization of the Evolution Equations and Remarks on the Incremental Problem -- 3.2 Enforcing Stress Constraints for 3D Gradient-Extended Material Models in Finite Elements -- 4 Numerical Example -- 5 Conclusions -- References -- Modeling of Material Deformation Responses Using Gradient Elasticity Theory -- 1 Introduction -- 2 Formulation of C1 Continuity Triangular Finite Element -- 3 Computational Homogenization and Micro-Macro Scale Transition -- 3.1 Numerical Implementation of Multiscale Algorithm -- 4 Damage Algorithm Based on Strain Gradient Theory -- 5 Numerical Examples -- 5.1 Multiscale Analysis of Plate Tension with Pre-existing Crack -- 5.2 Damage Analysis of Plate Tension with Pre-existing Crack -- 6 Conclusions -- References -- 3D Dynamic Crack Propagation by the Extended Finite Element Method and a Gradient-Enhanced Damage Model -- 1 Introduction -- 2 Governing Equations -- 3 Gradient-Enhanced Damage Model -- 4 Extended Finite Element Method (XFEM) -- 4.1 The Level Set Method for Crack Front Tracking -- 4.2 XFEM Approximation -- 4.3 Explicit Time Integration and Mass Lumping for XFEM -- 5 Solution Procedure. , 6 Crack Propagation Criterion and Direction Based on Gradient-Enhanced Damage -- 6.1 Using Damage as the Crack Propagation Criterion -- 6.2 Crack Propagation Increment Based on the Damage Field -- 6.3 Finding the Propagation Direction from the Damage Field -- 7 Numerical Example -- 7.1 Specimen Geometry, Boundary Conditions and Material Properties -- 7.2 Kalthoff's Test Simulation Results -- 8 Conclusion -- References -- Multiphysics -- A 3D Magnetostrictive Preisach Model for the Simulation of Magneto-Electric Composites on Multiple Scales -- 1 Introduction -- 2 A Two-Scale Homogenization Scheme -- 2.1 Boundary Value Problem and Scale Transition -- 2.2 Discretizations of the Boundary Value Problems -- 2.3 Consistent Linearization of Macroscopic Field Equations -- 3 Material Modeling -- 3.1 Linear Piezomagnetic Model -- 3.2 Ferroelectric Preisach Model -- 4 Numerical Examples -- 4.1 Preisach Model Applied on One Orientation -- 4.2 Preisach Model Applied on an ODF -- 4.3 Simulation of Two-Phase Magneto-Electric Composites -- 4.4 Conclusion -- References -- A Multiscale Framework for Thermoplasticity -- 1 Introduction -- 2 Macroscale Continuum Mechanics Framework -- 2.1 Deformation and Temperature Gradients at the Macro- and Microscale -- 2.2 Balance Equations at the Macroscale -- 3 Enforcement of Thermodynamical Consistency -- 3.1 Energy and Entropy in Micro-Macro Transition -- 3.2 Internal Dissipation and the Microscale Mechanical Step -- 3.3 Dissipation due to Heat Conduction and the Microscale Thermal Step -- 4 Numerical Aspects -- 5 Example -- 6 Conclusions -- References -- A Method of Numerical Viscosity Measurement for Solid-Liquid Mixture -- 1 Introduction -- 2 Multiscale Modeling of Solid-Liquid Mixture -- 2.1 Separation of Spatial and Temporal Scales -- 2.2 Microscopic Problem -- 2.3 Macroscopic Problem -- 3 Numerical Viscosity Measurement. , 3.1 Viscosity Measurement with Hagen-Poiseuille Equation.