1st Edition

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

ISBN 9781138372788
Published September 18, 2018 by CRC Press
730 Pages 328 B/W Illustrations

USD $73.95

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Book Description

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.

Table of Contents


Image Extraction and Virtual Microstructure Simulation
Multi-Scale Simulation of High-Resolution Microstructures
Three-Dimensional Simulation of Microstructures with Dispersed Particulates

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

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

The Voronoi Cell Finite Element Method (VCFEM) for 2D Elastic Problems
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

3D Voronoi Cell Finite Element Method for Elastic Problems
Three-Dimensional Voronoi Cell FEM Formulation
Numerical Implementation
Numerical Examples for 3D-VCFEM Validation
Multi-Level Parallel 3D VCFEM Code

2D Voronoi Cell FEM for Small Deformation Elastic-Plastic Problems
Incremental VCFEM Formulation for Elasto-Plasticity
Numerical Examples for Validating the Elastic-Plastic VCFEM
Adaptive Methods in VCFEM for Elasto-Plasticity

Voronoi Cell FEM for Heat Conduction Problems
The Assumed Heat Flux Formulation for Heat Conduction in VCFEM
VCFEM for Heat Conduction in Heterogeneous Materials

Extended Voronoi Cell FEM for Multiple Brittle Crack Propagation
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
The Voronoi Cell FEM for Microstructures with Interfacial Debonding
Numerical Examples
Extended VCFEM for Interfacial Debonding with Matrix Cracking

VCFEM for Inclusion Cracking in Elastic-Plastic Composites
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
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

Multi-Scale Analysis of Heterogeneous Materials: Hierarchical Concurrent Multi-Level Models
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

Level-0 Continuum Models from RVE-Based Micromechanical Analysis
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
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


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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.