Micromechanical Analysis and Multi-Scale Modeling Using the Voronoi Cell Finite Element Method: 1st Edition (Paperback) book cover

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

1st Edition

By Somnath Ghosh

CRC Press

730 pages | 328 B/W Illus.

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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




About the Author/Editor

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.

About the Series

Applied and Computational Mechanics

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TECHNOLOGY & ENGINEERING / Electronics / Microelectronics