Content: Introduction Image Extraction and Virtual Microstructure Simulation Multi-Scale Simulation of High-Resolution Microstructures Three-Dimensional Simulation of Microstructures with Dispersed Particulates Summary 2D- and 3D-Mesh Generation by Voronoi Tessellation Two-Dimensional Dirichlet Tessellations in Plane Mesh Generator Algorithm Numerical Examples Voronoi Tessellation for Three-Dimensional Mesh Generation Summary Microstructure Characterization and Morphology-Based Domain Partitioning Characterization of Computer-Generated Microstructures Quantitative Characterization of Real 3D Microstructures Domain Partitioning: A Pre-Processor for Multi-Scale Modeling Summary The Voronoi Cell Finite Element Method (VCFEM) for 2D Elastic Problems Introduction Energy Minimization Principles in VCFEM Formulation Element Interpolations and Assumptions Weak Forms in the VCFEM Variational Formulation Solution Methodology and Numerical Aspects in VCFEM Stability and Convergence of VCFEM Error Analysis and Adaptivity in VCFEM Numerical Examples with 2D Adaptive VCFEM Numerical Examples with NCM-VCFEM for Irregular Heterogeneities VCFEM for Elastic Wave Propagation in Heterogeneous Solids Summary 3D Voronoi Cell Finite Element Method for Elastic Problems Introduction Three-Dimensional Voronoi Cell FEM Formulation Numerical Implementation Numerical Examples for 3D-VCFEM Validation Multi-Level Parallel 3D VCFEM Code Summary 2D Voronoi Cell FEM for Small Deformation Elastic-Plastic Problems Introduction Incremental VCFEM Formulation for Elasto-Plasticity Numerical Examples for Validating the Elastic-Plastic VCFEM Adaptive Methods in VCFEM for Elasto-Plasticity Summary Voronoi Cell FEM for Heat Conduction Problems Introduction The Assumed Heat Flux Formulation for Heat Conduction in VCFEM VCFEM for Heat Conduction in Heterogeneous Materials Summary Extended Voronoi Cell FEM for Multiple Brittle Crack Propagation Introduction Voronoi Cell FEM Formulation for Multiple Propagating Cracks Solution Method Aspects of Numerical Implementation Adaptive Criteria for Cohesive Crack Growth Numerical Examples Concluding Remarks VCFEM/X-VCFEM for Debonding and Matrix Cracking in Composites Introduction The Voronoi Cell FEM for Microstructures with Interfacial Debonding Numerical Examples Extended VCFEM for Interfacial Debonding with Matrix Cracking Conclusions VCFEM for Inclusion Cracking in Elastic-Plastic Composites Introduction Voronoi Cell Finite Element Method with Brittle Inclusion Cracking Numerical Examples for Validating the Inclusion Cracking VCFEM Model An Experimental Computational Study of Damage in Discontinuously Reinforced Aluminum Concluding Remarks Locally Enhanced VCFEM (LE-VCFEM) for Ductile Failure Introduction VCFEM Formulation for Nonlocal Porous Plasticity in the Absence of Localization Locally Enhanced VCFEM for Matrix Localization and Cracking Coupling Stress and Displacement Interpolated Regions in LEVCFEM Numerical Examples of Ductile Fracture with LE-VCFEM Summary Multi-Scale Analysis of Heterogeneous Materials: Hierarchical Concurrent Multi-Level Models Introduction Hierarchy of Domains for Heterogeneous Materials Adaptive Multi-Level Computational Model for Hierarchical Concurrent Multi-Scale Analysis Coupling Levels in the Concurrent Multi-Level FEM Model Numerical Examples with the Adaptive Multi-Level Model Summary Level-0 Continuum Models from RVE-Based Micromechanical Analysis Introduction Identification of the RVE Size for Homogenization Homogenization-Based Continuum Plasticity and Damage Models for Level-0 Computations Summary and Conclusions Adaptive Hierarchical Concurrent Multi-Level Models for Materials Undergoing Damage Introduction Coupling Different Levels in the Concurrent Multi-Scale Algorithm Modified VCFEM Formulation for SERVE in Level-1 Elements Criteria for Adaptive Mesh Refinement and Level Transitions Numerical Examples with the Adaptive Multi-Level Model Conclusions Bibliography Index