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Advanced Computational Materials Modeling: From Classical to Multi-Scale Techniques; Contents; Preface; List of Contributors; 1 Materials Modeling - Challenges and Perspectives; 1.1 Introduction; 1.2 Modeling Challenges and Perspectives; 1.2.1 Mechanical Degradation and Failure of Ductile Materials; 1.2.1.1 Remarks; 1.2.2 Modeling of Cellular Structures; 1.2.2.1 Remarks; 1.2.3 Multiscale Constitutive Modeling; 1.3 Concluding Remarks; Acknowledgments; References; 2 Local and Nonlocal Modeling of Ductile Damage; 2.1 Introduction; 2.2 Continuum Damage Mechanics; 2.2.1 Basic Concepts of CDM
2.2.2 Ductile Plastic Damage2.3 Lemaitre's Ductile Damage Model; 2.3.1 Original Model; 2.3.1.1 The Elastic State Potential; 2.3.1.2 The Plastic State Potential; 2.3.1.3 The Dissipation Potential; 2.3.1.4 Evolution of Internal Variables; 2.3.2 Principle of Maximum Inelastic Dissipation; 2.3.3 Assumptions Behind Lemaitre's Model; 2.4 Modified Local Damage Models; 2.4.1 Lemaitre's Simplified Damage Model; 2.4.1.1 Constitutive Model; 2.4.1.2 Numerical Implementation; 2.4.2 Damage Model with Crack Closure Effect; 2.4.2.1 Constitutive Model; 2.4.2.2 Numerical Implementation
2.5 Nonlocal Formulations2.5.1 Aspects of Nonlocal Averaging; 2.5.1.1 The Averaging Operator; 2.5.1.2 Weight Functions; 2.5.2 Classical Nonlocal Models of Integral Type; 2.5.2.1 Nonlocal Formulations for Lemaitre's Simplified Model; 2.5.3 Numerical Implementation of Nonlocal Integral Models; 2.5.3.1 Numerical Evaluation of the Averaging Integral; 2.5.3.2 Global Version of the Elastic Predictor/Return Mapping Algorithm; 2.6 Numerical Analysis; 2.6.1 Axisymmetric Analysis of a Notched Specimen; 2.6.2 Flat Grooved Plate in Plane Strain; 2.6.3 Upsetting of a Tapered Specimen
2.6.3.1 Damage Prediction Using the Lemaitre's Simplified Model2.6.3.2 Damage Prediction Using the Lemaitre's Model with Crack Closure Effect; 2.7 Concluding Remarks; Acknowledgments; References; 3 Recent Advances in the Prediction of the Thermal Properties of Metallic Hollow Sphere Structures; 3.1 Introduction; 3.2 Methodology; 3.2.1 Lattice Monte Carlo Method; 3.2.2 Finite Element Method; 3.2.2.1 Basics of Heat Transfer; 3.2.2.2 Weighted Residual Method; 3.2.2.3 Discretization and Principal Finite Element Equation; 3.2.3 Numerical Calculation Models
3.3 Finite Element Analysis on Regular Structures3.4 Finite Element Analysis on Cubic-Symmetric Models; 3.5 LMC Analysis of Models of Cross Sections; 3.5.1 Modeling; 3.5.2 Results; 3.6 Computed Tomography Reconstructions; 3.6.1 Computed Tomography; 3.6.2 Numerical Analysis; 3.6.2.1 Microstructure; 3.6.2.2 Mesostructure; 3.6.3 Results; 3.7 Conclusions; References; 4 Computational Homogenization for Localization and Damage; 4.1 Introduction; 4.1.1 Mechanics Across the Scales; 4.1.2 Some Historical Notes on Homogenization; 4.1.3 Separation of Scales
4.1.4 Computational Homogenization and Its Application to Damage and Fracture
With its discussion of strategies for modeling complex materials using new numerical techniques, mainly those based on the finite element method, this monograph covers a range of topics including computational plasticity, multi-scale formulations, optimization and parameter identification, damage mechanics and nonlinear finite elements.