Micromechanical Analysis and Multi-Scale Modeling ─ Using the Voronoi Cell Finite Element Method

As multi-phase metal/alloy systems and polymer, ceramic, or metal matrix composite materials are increasingly being used in industry, the science and technology for these heterogeneous materials has advanced rapidly. By extending analytical and numerical models, engineers can analyze failure characteristics of the materials before they are integrated into the design process. Micromechanical Analysis and Multi-Scale Modeling Using the Voronoi Cell Finite Element Method addresses the key problem of multi-scale failure and deformation of materials that have complex microstructures. The book presents a comprehensive computational mechanics and materials science–based framework for multi-scale analysis.

The focus is on micromechanical analysis using the Voronoi cell finite element method (VCFEM) developed by the author and his research group for the efficient and accurate modeling of materials with non-uniform heterogeneous microstructures. While the topics covered in the book encompass the macroscopic scale of structural components and the microscopic scale of constituent heterogeneities like inclusions or voids, the general framework may be extended to other scales as well.

The book presents the major components of the multi-scale analysis framework in three parts. Dealing with multi-scale image analysis and characterization, the first part of the book covers 2D and 3D image-based microstructure generation and tessellation into Voronoi cells. The second part develops VCFEM for micromechanical stress and failure analysis, as well as thermal analysis, of extended microstructural regions. It examines a range of problems solved by VCFEM, from heat transfer and stress-strain analysis of elastic, elastic-plastic, and viscoplastic material microstructures to microstructural damage models including interfacial debonding and ductile failure. Establishing the multi-scale framework for heterogeneous materials with and without damage, the third part of the book discusses adaptive concurrent multi-scale analysis incorporating bottom-up and top-down modeling.

Including numerical examples and a CD-ROM with VCFEM source codes and input/output files, this book is a valuable reference for researchers, engineers, and professionals involved with predicting the performance and failure of materials in structure-materials interactions.

Somnath Ghosh is the Michael G. Callas Professor in the Department of Civil Engineering and Professor of Mechanical Engineering at Johns Hopkins University. Prior to this, he was the John B. Nordholt Professor in the Department of Mechanical Engineering at the Ohio State University until March 2011.
His research has been at the leading edge of multiple-scale modeling of mechanical behavior and failure response of heterogeneous material systems such as composites, polycrystalline metals and alloys, etc., for structure–material interaction. Specific areas of his contributions include multiple-scale modeling in spatial and temporal domains, failure modeling of composite materials and structures, reliability, fatigue and failure modeling of metals, composites and thermal barrier coatings, molecular dynamics simulations of thin films and nano-composites, metal forming and casting and process design.
He was awarded the prestigious NSF Young Investigator award in 1994. He is a fellow of the American Society for Mechanical Engineers, ASM International, the National Materials Society, the American Academy of Mechanics, the International Association of Computational Mechanics, the U.S. Association of Computational Mechanics, and the American Association for the Advancement of Science.

Introduction
Image Extraction and Virtual Microstructure SimulationMulti-Scale Simulation of High-Resolution MicrostructuresThree-Dimensional Simulation of Microstructures with Dispersed Particulates Summary
2D- and 3D-Mesh Generation by Voronoi TessellationTwo-Dimensional Dirichlet Tessellations in PlaneMesh Generator Algorithm Numerical ExamplesVoronoi Tessellation for Three-Dimensional Mesh GenerationSummary
Microstructure Characterization and Morphology-Based Domain PartitioningCharacterization of Computer-Generated MicrostructuresQuantitative Characterization of Real 3D MicrostructuresDomain Partitioning: A Pre-Processor for Multi-Scale ModelingSummary
The Voronoi Cell Finite Element Method (VCFEM) for 2D Elastic ProblemsIntroductionEnergy Minimization Principles in VCFEM FormulationElement Interpolations and AssumptionsWeak Forms in the VCFEM Variational Formulation Solution Methodology and Numerical Aspects in VCFEMStability and Convergence of VCFEMError Analysis and Adaptivity in VCFEMNumerical Examples with 2D Adaptive VCFEMNumerical Examples with NCM-VCFEM for Irregular HeterogeneitiesVCFEM for Elastic Wave Propagation in Heterogeneous SolidsSummary
3D Voronoi Cell Finite Element Method for Elastic ProblemsIntroductionThree-Dimensional Voronoi Cell FEM FormulationNumerical ImplementationNumerical Examples for 3D-VCFEM ValidationMulti-Level Parallel 3D VCFEM CodeSummary
2D Voronoi Cell FEM for Small Deformation Elastic-Plastic ProblemsIntroductionIncremental VCFEM Formulation for Elasto-PlasticityNumerical Examples for Validating the Elastic-Plastic VCFEMAdaptive Methods in VCFEM for Elasto-PlasticitySummary
Voronoi Cell FEM for Heat Conduction ProblemsIntroductionThe Assumed Heat Flux Formulation for Heat Conduction in VCFEMVCFEM for Heat Conduction in Heterogeneous MaterialsSummary
Extended Voronoi Cell FEM for Multiple Brittle Crack PropagationIntroductionVoronoi Cell FEM Formulation for Multiple Propagating CracksSolution MethodAspects of Numerical ImplementationAdaptive Criteria for Cohesive Crack GrowthNumerical ExamplesConcluding Remarks
VCFEM/X-VCFEM for Debonding and Matrix Cracking in CompositesIntroductionThe Voronoi Cell FEM for Microstructures with Interfacial DebondingNumerical ExamplesExtended VCFEM for Interfacial Debonding with Matrix CrackingConclusions
VCFEM for Inclusion Cracking in Elastic-Plastic CompositesIntroductionVoronoi Cell Finite Element Method with Brittle Inclusion CrackingNumerical Examples for Validating the Inclusion Cracking VCFEM Model An Experimental Computational Study of Damage in Discontinuously Reinforced AluminumConcluding Remarks
Locally Enhanced VCFEM (LE-VCFEM) for Ductile FailureIntroductionVCFEM Formulation for Nonlocal Porous Plasticity in the Absence of LocalizationLocally Enhanced VCFEM for Matrix Localization and CrackingCoupling Stress and Displacement Interpolated Regions in LEVCFEMNumerical Examples of Ductile Fracture with LE-VCFEMSummary
Multi-Scale Analysis of Heterogeneous Materials: Hierarchical Concurrent Multi-Level ModelsIntroductionHierarchy of Domains for Heterogeneous MaterialsAdaptive Multi-Level Computational Model for Hierarchical Concurrent Multi-Scale AnalysisCoupling Levels in the Concurrent Multi-Level FEM ModelNumerical Examples with the Adaptive Multi-Level ModelSummary
Level-0 Continuum Models from RVE-Based Micromechanical AnalysisIntroductionIdentification of the RVE Size for HomogenizationHomogenization-Based Continuum Plasticity and Damage Models for Level-0 ComputationsSummary and Conclusions
Adaptive Hierarchical Concurrent Multi-Level Models for Materials Undergoing DamageIntroductionCoupling Different Levels in the Concurrent Multi-Scale AlgorithmModified VCFEM Formulation for SERVE in Level-1 ElementsCriteria for Adaptive Mesh Refinement and Level TransitionsNumerical Examples with the Adaptive Multi-Level ModelConclusions
BibliographyIndex