Materials with Internal Structure: Multiscale and Multifield Modeling and Simulation (Springer Tracts in Mechanical Engineering)

The book presents a series of concise papers by researchers specialized in various fields of continuum and computational mechanics and of material science. The focus is on principles and strategies for multiscale modeling and simulation of complex heterogeneous materials, with periodic or random microstructure, subjected to various types of mechanical, thermal, chemical loadings and environmental effects. A wide overview of complex behavior of materials (plasticity, damage, fracture, growth, etc.) is provided. Among various approaches, attention is given to advanced non-classical continua modeling which, provided by constitutive characterization for the internal and external actions (in particular boundary conditions), is a very powerful frame for the gross mechanical description of complex material behaviors, able to circumvent the restrictions of classical coarse–graining multiscale approaches. Preface 6 Acknowledgements 7 Contents 8 Scale Transition Rules Applied to Crystal Plasticity 9 1 Introduction 9 2 Time-Independent Elastic–Plastic Behavior 11 3 Homogenization Methods Applied to EVP Behavior 14 4 Effect of a Heterogeneous Elasticity on Both Local and Global Responses of Non-textured Polycrystalline Aggregates 18 References 21 A Numerical Assessment of Phase-Field Models for Fracture 24 1 Introduction 24 2 Phase-Field Representation for a Crack 25 3 Brittle Fracture 26 3.1 Derivation 26 3.2 Analysis of a One-Dimensional Bar 28 4 Phase-Field Model for Cohesive Fracture 31 4.1 Continuum Formulation 31 4.2 Numerical Examples for the Phase-Field Model for Cohesive Fracture 33 5 Concluding Remarks 34 References 35 On the Effective Properties of Elastic Materials and Structures at the Micro- and Nano-Scale Considering Various Models of Surface Elasticity 36 1 Introduction 36 2 Models of Surface Elasticity 38 2.1 Gurtin–Murdoch Model of Surface Elasticity 39 2.2 Steigmann–Ogden Model of Surface Reinforcements 41 2.3 Classic Approach 41 3 On Effective Properties of Nanomaterials Considering Surface Stresses 42 3.1 Stiffness of a Nanoporous Rod 42 3.2 Scaling Law 43 3.3 On Spectrum of Eigen-Oscillations of Solids with Surface Stresses 43 3.4 On Effective Properties of Solids with Coatings of Complex Inner Structure 44 4 Conclusions 45 References 46 Microstructure Sensitive Fatigue Crack Nucleation in Titanium Alloys Using Accelerated Crystal PlasticityFE Simulations 49 1 Introduction 49 2 Rate-Dependent Crystal Plasticity and Nonlocal Crack Evolution Models for Ti-6242 51 3 Wavelet Transformation Based Multi-time Scale Method for Accelerated Cyclic CPFEM Simulations 54 3.1 WATMUS Method Based Dwell Fatigue Simulation of Ti-6242 Microstructure 58 4 Calibration and Validation of Critical Crack Nucleation Parameter Rc 59 5 Influence of Microstructural and Loading Characteristics on Crack Nucleation in Ti-6242 61 5.1 Sensitivity of Crack Nucleation to Microstructural Features 63 5.2 Sensitivity of Crack Nucleation to Characteristics of Applied Loading 64 6 Conclusion 67 References 68 Advances in Multiscale Modeling of Granular Materials 69 1 Introduction 69 2 Gradient Cosserat Continuum Model 72 3 Generalized Hill's Lemma and RVE Boundary Conditions: Downscaling 73 4 Meso-Mechanically Informed Macroscopic Stress Variables and Constitutive Model: Upscaling 73 5 Numerical Results 76 6 Concluding Remarks 77 References 78 Tensor-Valued Random Fields in Continuum Physics 80 1 Introduction 80 2 Representations of Rank 1 and Rank 2 TRFs 81 2.1 Rank 1 TRF 82 2.2 Rank 2 TRF 82 3 Spectral Expansions of Homogeneous and Isotropic TRFs 85 4 The Spectral Expansion of the Elasticity Random Field 85 5 TRFs Dependent Fields 86 5.1 Fourier Conductivity 86 5.1.1 Correlation of Heat Flux TRF 86 5.1.2 Correlation of Temperature Gradient TRF 87 5.2 Anti-plane Elasticity 88 5.2.1 Correlation of Stress TRF 88 5.2.2 Correlation of Strain TRF 89 5.3 3d Classical Elasticity 89 5.3.1 Correlation of Stress TRF 90 5.3.2 Correlations of Strain, Rotation, and Curvature-Torsion TRFs 90 6 Conclusion 91 References 91 Designing Particulate Composites: The Effect of Variability of Filler Properties and Filler Spatial Distribution 93 1 Introduction 94 1.1 Structural Stochasticity in Composite Materials and Formulation of the Problem 95 1.2 Background 97 2 Models and Methods 99 3 Effect of Filler Distribution 103 3.1 The Elastic-Plastic Behavior 103 3.2 The Damping Behavior 105 4 Effect of Fluctuations of Filler Properties 106 4.1 The Elastic-Plastic Behavior 106 4.2 The Damping Behavior 109 5 Conclusions 110 References 111 Discrete to Scale-Dependent Continua for Complex Materials: A Generalized Voigt Approach Using the Virtual Power Equivalence 113 1 Introduction 114 2 Corpuscular Micro-Model 115 3 Micro–Macro Transition via Virtual Power Equivalence 117 3.1 First Order Continuum Approximation: Continuum with Rigid and Affine Local Structure 117 3.2 Second Order Continuum Approximation 121 3.3 Classical Continum Approximation 123 4 Structure of External Power and Balance Equations for Bulk and Contact Actions of the Equivalent Non-Classical Continua 124 4.1 Continuum with Rigid and Affine Microstructure 124 4.2 Second Gradient Continuum 126 5 Numerical Simulations 128 5.1 Porous Fibre Reinforced Composites 129 5.2 Masonry-Like Materials 130 6 Final Remarks 133 References 134 Front Matter....Pages i-vii Scale Transition Rules Applied to Crystal Plasticity....Pages 1-15 A Numerical Assessment of Phase-Field Models for Fracture....Pages 17-28 On the Effective Properties of Elastic Materials and Structures at the Micro- and Nano-Scale Considering Various Models of Surface Elasticity....Pages 29-41 Microstructure Sensitive Fatigue Crack Nucleation in Titanium Alloys Using Accelerated Crystal Plasticity FE Simulations....Pages 43-62 Advances in Multiscale Modeling of Granular Materials....Pages 63-73 Tensor-Valued Random Fields in Continuum Physics....Pages 75-87 Designing Particulate Composites: The Effect of Variability of Filler Properties and Filler Spatial Distribution....Pages 89-108 Discrete to Scale-Dependent Continua for Complex Materials: A Generalized Voigt Approach Using the Virtual Power Equivalence....Pages 109-131