Materials with Internal Structure (eBook)

Patrizia Trovalusci (PhD, MSc), Full Professor of ‘Solids and Structural Mechanics’. Author of about 140 publications in peer-reviewed scientific journals, books, conference proceedings and reports on: non-classical continua; multiscale modelling, masonry materials and structures; composites; plasticity theory, non-standard limit analysis; non-linear finite element analysis; structural architecture. Member of several scientific committees  (ICCM16; AIMETA15; ICSA2016-13;  CSMA2013; THERMEC2011-09-06) and organizer of international symposia/sessions on: “Multiscale and Multiphysics Modelling for Complex Materials” (8 editions, within international conferences: ICCM, WCCM, ECCOMAS, ECCM, THERMEC); “Mechanics of Interfaces and Evolving Microstructures” (1, EMMC); “History of Mechanics” (1, GAMM); “On the “Tectonics" in Architecture: between Aesthetics and Ethics” (4, ICSA). Organizer and lecturer of advanced courses:”Multiscale Modelling of Complex Materials”, CISM; “Masonry Constructions. Seismic Safety, Conservation”, Sapienza Doctoral School of Engineering and Architecture. Member of the Board of Directors of CISTeC and of the Academic Board of the PhD Program in Structural Engineering.  Guest editor of international journal special issues (4); editor of  Springer volumes (2). Member of the editorial boards of international journals: J. Civil Engn. Sci.; ISRN Mech. Engn. J. Reviewer for tens of international journals and books; for scientific evaluation committees (ERC Advanced Grants, other). Coordinator of several funded research projects (University La Sapienza). Coordinator of PRIN2010-11 Sapienza Unit. Coordinator of Bachelor Degree’s Courses: “Science of Architecture”; “Techniques of Architecture and Construction”; “Restoration and Conservation of Monuments”. Sapienza, School of Architecture. Teacher of solid and structural mechanics, statics, behaviour of masonry materials in historical structures'; Coordinator of the ”Atelier of Ecological Islands and Recycling Centres”. CV:http://dsg.uniroma1.it/trovalusci/pubblicazioni_pdf/Curriculum_PatriziaTrovalusci.pdf

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