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Table of Contents
Preface; Acknowledgements; Contents; Scale Transition Rules Applied to Crystal Plasticity; 1 Introduction; 2 Time-Independent Elastic-Plastic Behavior; 3 Homogenization Methods Applied to EVP Behavior; 4 Effect of a Heterogeneous Elasticity on Both Local and Global Responses of Non-textured Polycrystalline Aggregates; References; A Numerical Assessment of Phase-Field Models for Fracture; 1 Introduction; 2 Phase-Field Representation for a Crack; 3 Brittle Fracture; 3.1 Derivation; 3.2 Analysis of a One-Dimensional Bar; 4 Phase-Field Model for Cohesive Fracture; 4.1 Continuum Formulation
4.2 Numerical Examples for the Phase-Field Model for Cohesive Fracture5 Concluding Remarks; References; On the Effective Properties of Elastic Materials and Structures at the Micro- and Nano-Scale Considering Various Models of Surface Elasticity; 1 Introduction; 2 Models of Surface Elasticity; 2.1 Gurtin-Murdoch Model of Surface Elasticity; 2.2 Steigmann-Ogden Model of Surface Reinforcements; 2.3 Classic Approach; 3 On Effective Properties of Nanomaterials Considering Surface Stresses; 3.1 Stiffness of a Nanoporous Rod; 3.2 Scaling Law
3.3 On Spectrum of Eigen-Oscillations of Solids with Surface Stresses3.4 On Effective Properties of Solids with Coatings of Complex Inner Structure; 4 Conclusions; References; Microstructure Sensitive Fatigue Crack Nucleation in Titanium Alloys Using Accelerated Crystal PlasticityFE Simulations; 1 Introduction; 2 Rate-Dependent Crystal Plasticity and Nonlocal Crack Evolution Models for Ti-6242; 3 Wavelet Transformation Based Multi-time Scale Method for Accelerated Cyclic CPFEM Simulations; 3.1 WATMUS Method Based Dwell Fatigue Simulation of Ti-6242 Microstructure
4 Calibration and Validation of Critical Crack Nucleation Parameter Rc5 Influence of Microstructural and Loading Characteristics on Crack Nucleation in Ti-6242; 5.1 Sensitivity of Crack Nucleation to Microstructural Features; 5.2 Sensitivity of Crack Nucleation to Characteristics of Applied Loading; 6 Conclusion; References; Advances in Multiscale Modeling of Granular Materials; 1 Introduction; 2 Gradient Cosserat Continuum Model; 3 Generalized Hill's Lemma and RVE Boundary Conditions: Downscaling; 4 Meso-Mechanically Informed Macroscopic Stress Variables and Constitutive Model: Upscaling
5 Numerical Results6 Concluding Remarks; References; Tensor-Valued Random Fields in Continuum Physics; 1 Introduction; 2 Representations of Rank 1 and Rank 2 TRFs; 2.1 Rank 1 TRF; 2.2 Rank 2 TRF; 3 Spectral Expansions of Homogeneous and Isotropic TRFs; 4 The Spectral Expansion of the Elasticity Random Field; 5 TRFs Dependent Fields; 5.1 Fourier Conductivity; 5.1.1 Correlation of Heat Flux TRF; 5.1.2 Correlation of Temperature Gradient TRF; 5.2 Anti-plane Elasticity; 5.2.1 Correlation of Stress TRF; 5.2.2 Correlation of Strain TRF; 5.3 3d Classical Elasticity; 5.3.1 Correlation of Stress TRF
4.2 Numerical Examples for the Phase-Field Model for Cohesive Fracture5 Concluding Remarks; References; On the Effective Properties of Elastic Materials and Structures at the Micro- and Nano-Scale Considering Various Models of Surface Elasticity; 1 Introduction; 2 Models of Surface Elasticity; 2.1 Gurtin-Murdoch Model of Surface Elasticity; 2.2 Steigmann-Ogden Model of Surface Reinforcements; 2.3 Classic Approach; 3 On Effective Properties of Nanomaterials Considering Surface Stresses; 3.1 Stiffness of a Nanoporous Rod; 3.2 Scaling Law
3.3 On Spectrum of Eigen-Oscillations of Solids with Surface Stresses3.4 On Effective Properties of Solids with Coatings of Complex Inner Structure; 4 Conclusions; References; Microstructure Sensitive Fatigue Crack Nucleation in Titanium Alloys Using Accelerated Crystal PlasticityFE Simulations; 1 Introduction; 2 Rate-Dependent Crystal Plasticity and Nonlocal Crack Evolution Models for Ti-6242; 3 Wavelet Transformation Based Multi-time Scale Method for Accelerated Cyclic CPFEM Simulations; 3.1 WATMUS Method Based Dwell Fatigue Simulation of Ti-6242 Microstructure
4 Calibration and Validation of Critical Crack Nucleation Parameter Rc5 Influence of Microstructural and Loading Characteristics on Crack Nucleation in Ti-6242; 5.1 Sensitivity of Crack Nucleation to Microstructural Features; 5.2 Sensitivity of Crack Nucleation to Characteristics of Applied Loading; 6 Conclusion; References; Advances in Multiscale Modeling of Granular Materials; 1 Introduction; 2 Gradient Cosserat Continuum Model; 3 Generalized Hill's Lemma and RVE Boundary Conditions: Downscaling; 4 Meso-Mechanically Informed Macroscopic Stress Variables and Constitutive Model: Upscaling
5 Numerical Results6 Concluding Remarks; References; Tensor-Valued Random Fields in Continuum Physics; 1 Introduction; 2 Representations of Rank 1 and Rank 2 TRFs; 2.1 Rank 1 TRF; 2.2 Rank 2 TRF; 3 Spectral Expansions of Homogeneous and Isotropic TRFs; 4 The Spectral Expansion of the Elasticity Random Field; 5 TRFs Dependent Fields; 5.1 Fourier Conductivity; 5.1.1 Correlation of Heat Flux TRF; 5.1.2 Correlation of Temperature Gradient TRF; 5.2 Anti-plane Elasticity; 5.2.1 Correlation of Stress TRF; 5.2.2 Correlation of Strain TRF; 5.3 3d Classical Elasticity; 5.3.1 Correlation of Stress TRF