Multiscale Modeling Approaches for Composites
- 1st Edition - January 7, 2022
- Imprint: Elsevier
- Authors: George Chatzigeorgiou, Fodil Meraghni, Nicolas Charalambakis
- Language: English
- Paperback ISBN:9 7 8 - 0 - 1 2 - 8 2 3 1 4 3 - 2
- eBook ISBN:9 7 8 - 0 - 1 2 - 8 2 3 3 7 0 - 2
Multiscale Modeling Approaches for Composites outlines the fundamentals of common multiscale modeling techniques and provides detailed guidance for putting them into practice.… Read more
Purchase options
Institutional subscription on ScienceDirect
Request a sales quoteMultiscale Modeling Approaches for Composites outlines the fundamentals of common multiscale modeling techniques and provides detailed guidance for putting them into practice. Various homogenization methods are presented in a simple, didactic manner, with an array of numerical examples.
The book starts by covering the theoretical underpinnings of tensors and continuum mechanics concepts, then passes to actual micromechanic techniques for composite media and laminate plates. In the last chapters the book covers advanced topics in homogenization, including Green’s tensor, Hashin-Shtrikman bounds, and special types of problems. All chapters feature comprehensive analytical and numerical examples (Python and ABAQUS scripts) to better illustrate the theory.
- Bridges theory and practice, providing step-by-step instructions for implementing multiscale modeling approaches for composites and the theoretical concepts behind them
- Covers boundary conditions, data-exchange between scales, the Hill-Mandel principle, average stress and strain theorems, and more
- Discusses how to obtain composite properties using different boundary conditions
- Includes access to a companion site, featuring the numerical examples, Python and ABACUS codes discussed in the book
Upper level undergrad and graduate students studying the mechanics of heterogeneous solids and materials science; academic researchers working in these same areas. Industrial engineers performing experiments in composites and looking to acquire access to simple and fast models for these materials
- Cover image
- Title page
- Table of Contents
- Copyright
- About the authors
- Foreword
- Preface
- Acknowledgments
- Part I: Tensors and continuum mechanics concepts
- Chapter 1: Tensors
- Abstract
- 1.1. Tensors in Cartesian coordinates
- 1.2. Cartesian systems and tensor rotation
- 1.3. Tensor calculus
- 1.4. Examples in tensor operations
- 1.5. Voigt notation: general aspects
- 1.6. Operations using the Voigt notation
- 1.7. Tensor rotation in Voigt notation
- 1.8. Examples in Voigt notation operations
- References
- Chapter 2: Continuum mechanics
- Abstract
- 2.1. Strain
- 2.2. Stress
- 2.3. Elasticity
- 2.4. Reduction to 2–D problems
- 2.5. Examples
- References
- Part II: Micromechanics for composite media
- Chapter 3: General concepts of micromechanics
- Abstract
- 3.1. Heterogeneous media
- 3.2. Homogenization
- 3.3. Homogenization principles
- 3.4. Bounds in the overall response
- 3.5. Examples
- References
- Chapter 4: Voigt and Reuss bounds
- Abstract
- 4.1. Theory
- 4.2. Simple methods for fiber composites
- 4.3. Composite beams
- 4.4. Examples
- References
- Chapter 5: Eshelby solution–based mean–field methods
- Abstract
- 5.1. Inclusion problems
- 5.2. Eshelby–based homogenization approaches
- 5.3. Examples
- References
- Chapter 6: Periodic homogenization
- Abstract
- 6.1. Preliminaries
- 6.2. Theoretical background
- 6.3. Computation of the overall elasticity tensor
- 6.4. Particular case: multilayered composite
- 6.5. Examples
- References
- Chapter 7: Classical laminate theory
- Abstract
- 7.1. Introduction
- 7.2. Stress–strain relation for an orthotropic material
- 7.3. Hooke's law for an orthotropic lamina under the assumption of plane stress
- 7.4. Stress–strain relations for a lamina of arbitrary orientation: off–axis loading
- 7.5. Macromechanical response of a laminate composite thin plate
- References
- Part III: Special topics in homogenization
- Chapter 8: Composite sphere/cylinder assemblage
- Abstract
- 8.1. Composite sphere assemblage
- 8.2. Composite cylinder assemblage
- 8.3. Eshelby's energy principle
- 8.4. Universal relations for fiber composites
- 8.5. Examples
- References
- Chapter 9: Green's tensor
- Abstract
- 9.1. Preliminaries
- 9.2. Definition and properties
- 9.3. Applications of Green's tensor
- 9.4. Examples
- References
- Chapter 10: Hashin–Shtrikman bounds
- Abstract
- 10.1. Preliminaries
- 10.2. Hashin–Shtrikman variational principle
- 10.3. Bounds in a bi–phase composite
- 10.4. Examples
- References
- Chapter 11: Mathematical homogenization theory
- Abstract
- 11.1. Preliminaries
- 11.2. Variational formulation
- 11.3. Convergence of the heterogeneous problem
- 11.4. Asymptotic expansion approach
- 11.5. Examples
- References
- Chapter 12: Nonlinear composites
- Abstract
- 12.1. Introduction
- 12.2. Inelastic mechanisms in periodic homogenization
- 12.3. Inelastic mechanisms in mean–field theories
- 12.4. Examples
- References
- Appendix A: Fiber orientation in composites
- A.1. Introduction
- A.2. Reinforcement orientation in a plane
- A.3. Reinforcement orientation in 3–D space
- A.4. Examples
- References
- Index
- Edition: 1
- Published: January 7, 2022
- Imprint: Elsevier
- No. of pages: 364
- Language: English
- Paperback ISBN: 9780128231432
- eBook ISBN: 9780128233702
GC
George Chatzigeorgiou
George Chatzigeorgiou is a Research Scientist at CNRS (CR-HDR) based at the Arts et Métiers Institute of Technology, France, and a member of the LEM3-UMR CNRS 7239 laboratory in France. His research is devoted to constitutive modeling of multifunctional materials and homogenization theories of composites.
Affiliations and expertise
Senior Research Scientist, LEM3-UMR CNRS 7239 laboratory, FranceFM
Fodil Meraghni
Fodil Meraghni is a Distinguished Professor at the Arts et Métiers Institute of Technology, France. He is the head of the Composites and Smart Materials Research Group at LEM3-UMR CNRS 7239 in France, working on multiscale modeling using micromechanical approaches for homogenization of polymer composites and shape memory alloys.
Affiliations and expertise
Distinguished Professor, Arts et Metiers Institute of Technology, France; LEM3-UMR CNRS 7239 laboratory, FranceNC
Nicolas Charalambakis
Nicolas Charalambakis is a Professor Emeritus in the Department of Civil Engineering at Aristotle University of Thessaloniki, Greece, and a member of the Center for Research and Development of Advanced Materials AUTH and Texas A&M, USA. His research focuses on homogenization and material instabilities.
Affiliations and expertise
Professor Emeritus, Department of Civil Engineering, Aristotle University of Thessaloniki, GreeceRead Multiscale Modeling Approaches for Composites on ScienceDirect