Applied RVE Reconstruction and Homogenization of Heterogeneous Materials

By Yves Rémond, Said Ahzi, Majid Baniassadi and Hamid Garmestani

Statistical correlation functions are a well-known class of statistical descriptors that can be used to describe the morphology and the microstructure-properties relationship. A comprehensive study has been performed for the use of these correlation functions for the reconstruction and homogenization in nano-composite materials. Correlation functions are measured from different techniques such as microscopy (SEM or TEM), small angle X-ray scattering (SAXS) and can be generated through Monte Carlo simulations.  In this book, different experimental techniques such as SAXS and image processing are presented, which are used to measure two-point correlation function correlation for multi-phase polymer composites.

Higher order correlation functions must be calculated or measured to increase the precision of the statistical continuum approach. To achieve this aim, a new approximation methodology is utilized to obtain N-point correlation functions for multiphase heterogeneous materials. The two-point functions measured by different techniques have been exploited to reconstruct the microstructure of heterogeneous media.

Statistical continuum theory is used to predict the effective thermal conductivity and elastic modulus of polymer composites. N-point probability functions as statistical descriptors of inclusions have been exploited to solve strong contrast homogenization for effective thermal conductivity and elastic modulus properties of heterogeneous materials.  Finally, reconstructed microstructure is used to calculate effective properties and damage modeling of heterogeneous materials.

• Language: English
• Publisher: Wiley
• Release date: Jun 14, 2016
• ISBN: 9781119307631

Yves Rémond

Prof. Yves Rémond is a Distinguished Professor (Exceptional Class) at Strasbourg University in France. He is working at Icube (Engineering Science, Computer Science, and Imaging Laboratory), which is affiliated with both the University of Strasbourg and the CNRS. He teaches in the fields of continuum mechanics, polymer mechanics, composite materials, and mechano-biology at the European Engineering School of Chemistry, Polymers, and Materials Science (ECPM). He graduated from the Ecole Normale Supérieure de Cachan (now Paris-Saclay) with a degree in mechanics and obtained his PhD from the University Paris VI in 1984. (Pierre et Marie Curie). He has been the Scientific Deputy Director of INSIS, the Institute for Engineering and Systems Sciences, at the CNRS headquarters in Paris since 2012. He was also a member of the Academic Palms Order as an officer. In the fields of composite materials, polymers, and bioengineering, he advised over 30 PhD and Habilitation students and wrote about 150 scholarly papers.

Book preview

Preface

Statistical correlation functions are a well-known class of statistical descriptors that can be used to describe the morphology and the microstructure–properties relationship. A comprehensive study has been performed for the use of these correlation functions for the reconstruction and homogenization in nanocomposite materials. Correlation functions are measured from different techniques such as microscopy (SEM or TEM), small angle X-ray scattering (SAXS) and can be generated through Monte Carlo simulations. In this book different experimental techniques such as SAXS and image processing are presented that are used to measure two-point correlation function for multi-phase polymer composite.

Higher order correlation functions must be calculated or measured to increase the precision of the statistical continuum approach. To achieve this aim, a new approximation methodology is utilized to obtain N-point correlation functions for multiphase heterogeneous materials. The two-point functions measured by different techniques have been exploited to reconstruct the microstructure of heterogeneous media.

Statistical continuum theory is used to predict the effective thermal conductivity and elastic modulus of polymer composites. N-point probability functions as statistical descriptors of inclusions have been exploited to solve strong contrast homogenization for effective thermal conductivity and elastic modulus properties of heterogeneous materials.

Finally, reconstructed microstructure is used to calculate effective properties and damage modeling of heterogeneous materials.

Professor Yves Rémond is currently Distinguished Professor (Exceptional Class) at the University of Strasbourg in France. He is working at Icube – The Engineering Science, Computer Science and Imaging Laboratory – which belongs both to the University of Strasbourg and to the CNRS. His teaching activity is conducted at the European Engineering School of Chemistry, Polymers and Materials Science (ECPM) in the field of continuum mechanics, mechanics of polymers, composite materials and mechano-biology. He graduated in Mechanics from Ecole Normale Supérieure of Cachan and received his Ph.D degree from the University Paris VI in 1984 (Pierre et Marie Curie). Since 2012, he held a position of Scientific Deputy Director at CNRS Headquarters in Paris – INSIS, Institute for Engineering and Systems Sciences. He was also distinguished as an officer in the order of Academic Palms. He is a member of the International Research Center for Mathematics and Mechanics of Complex Systems, at the Universita dell’Aquila (Italy) and was the President of the French Association for Composite Materials (AMAC). He is collaborating with different scientists from GeorgiaTech (USA), Qatar Foundation, and the Russian Academy of Science. He has advised about 30 PhD and Habilitations and published about 150 scientific papers in the field of mechanics of composite materials, polymers and bioengineering.

Professor Saïd Ahzi is currently a Research Director of the Materials Science and Engineering group at Qatar Environment and Energy Research Institute (QEERI) and Professor at the College of Science & Engineering, Hamad Bin Khalifa University, Qatar Foundation, Qatar. He holds a position as a Distinguished Professor at the University of Strasbourg (Exceptional Class). He also holds an Adjunct Professor position with the School of Materials Science and Engineering at Georgia Institute of Technology, USA. In January 2000, he joined the University of Strasbourg, France, Faculty of Physics and Engineering, as full Professor. From 1995 to 2000, he held the position of Professor (Assistant then Associate) at the Department of Mechanical Engineering at Clemson University, USA. Prior to this, he spent four years as a Research Scientist & Lecturer at the University of California at San Diego, USA, and four years as a Postdoctoral Research Associate at Massachusetts Institute of Technology, USA. From 2007 to 2011, he held an Adjunct Research Professor position with the University of Aveiro, Portugal. Dr. Saïd Ahzi advised about 25 PhDs, 24 Masters degrees, and was the scientific advisor for six Habilitations. He published more than 250 scientific papers in the areas of materials science, applied mechanics and processing.

Dr. Majid Baniassadi is an Assistant Professor at the School of Mechanical Engineering, University of Tehran, Iran. He holds a PhD in Mechanics of Materials from the University of Strasbourg (2011). He received his Master’s degree from the University of Tehran (2007) and his undergraduate degree from Isfahan University of Technology (2004), in Mechanical Engineering. His research interests include multiscale analysis and micromechanics of heterogeneous materials, numerical methods in engineering, electron microscopy image processing for microstructure identification.

Dr. Baniassadi is also collaborating with ICube laboratory in Strasbourg with activities in Engineering Science, Computer Science and Imaging. Since 2012, he has been an acting editor of the Journal of Energy Equipment and Systems. Thus far, he has published more than 30 scientific journal papers and as the reviewer of five international scientific journals, he is often contacted for peer reviewing submitted papers. Right now, he is the advisor or co-advisor of 7 PhD students and 15 Master’s students. Additionally, he has been a member of Iranian National Elites Foundation since 2008.

Professor Hamid Garmestani is a Professor of Materials Science and Engineering at Georgia Institute of Technology and a Fellow of the American Society of Materials (ASM International). He has developed methodologies in Microstructure Sensitive Design (MSD) framework that addresses an inverse methodology and innovations in various aspects of processing, structure-property relationships, simulation-based design of materials, and statistical continuum mechanics for homogenization in composites and polycrystalline materials. He has applied the methodologies above to structural alloys (AL, Mg, Ti and Steel) and more recently in Microstructure design of Solid Oxide Fuel Cell (SOFC).

He is a member of the texture, forming and composite committees of ASM and TMS. He has organized more than 30 workshops and symposia in the emerging subject of materials design. He was awarded Superstar in Research by FSU-CRC in year 2000. He was also the recipient of the 2000 Engineering Research Award of the FAMU-FSU College of Engineering and recipient of the Faculty Award for Research from NASA. He is a member of the editorial board for the International Journal of Plasticity, Journal of Mechanics of Materials, Computers, Materials and Continua and Theoretical and Applied Multi-scale Modeling of Materials.

Introduction

Development of advanced microstructure reconstruction methodologies is essential to access a variety of analytical information associated with complexities in the microstructure of multi-phase materials. Several experimental and theoretical techniques such as X-ray computed tomography (CT), scanning and computer generated micrographs have been used to obtain a sequence of two-dimensional (2D) images that can be further reconstructed in a three-dimensional (3D) space. However, due to cost of sample preparation processes, simulation methods are often more applicable in the reconstruction of heterogeneous microstructures in different applications [BOC 04, CHU 10, LIA 98, PIE 02, SUN 05, TAL 02, TAR 11].

Using lower order statistical correlation functions, Torquato [TOR 02] established the reconstruction of one- and two-dimensional microstructures with short-range order using stochastic optimization. However, he later showed that the lower-order correlation functions cannot solely represent a two-phase heterogeneous material and therefore more than one solution may exist for a specific low-order correlation function [TOR 02]. Sheehan and Torquato [SHE 01] later introduced more orientations in the correlation functions to effectively eliminate the effect of artificial anisotropy. In the case of multi-phase materials, Kröner [KRO 77] and Beran [BER 68] developed statistical mathematical formulations to link correlation functions to properties in multiphase materials. Using higher order correlation functions, one can account for the contribution of shape and geometry effects [TOR