Representative Volume Elements and Unit Cells

Numerical methods to estimate material properties usually involve analysis of a representative volume element (RVE) or unit cell (UC). The representative volume element (RVE) or unit cell (UC) is the smallest volume over which a measurement can be made that will yield a value representative of the whole. RVEs and UCs are widely used in the characterisation of materials with multiscale architectures such as composites. However, finite element (FE) software packages such as Abaqus and Comsol MultiPhysics do not offer the capability for RVE and UC modelling directly on their own. To apply them to analyse RVEs and UCs, the generation of the FE models for them, the imposition of boundary conditions, and the extraction of directly relevant results are essentially the responsibility of the user. These have tended to be incorrectly implemented by users! For the first time, this book will provide a comprehensive account on correct modelling of RVEs and UCs, which will eliminate any uncertainties and ambiguities.The book offers a complete and thorough review on the subject of RVEs and UCs, establishing a framework on a rigorous mathematical and mechanical basis to ensure that basic concepts, such as symmetry and free body diagrams, are applied correctly and consistently. It also demonstrates to readers that rigorous applications of mathematics and mechanics are meant to make things clear, consistent, thorough and, most of all, simple and easy to follow, rather than the opposite as many perceive. As a result, the book shows that the appropriate use of RVEs and UCs can deliver an effective and reliable means of material characterisation. It not only provides a much needed comprehensive account on material characterisation but, more importantly, explains how such characterisation can be conducted in a consistent and systematic manner. It also includes a ready-to-use open source code for UCs that can be downloaded from a companion site for potential users to utilise, adapt and expand as they wish.

Autorentext
Shuguang Li is a Professor of Aerospace Composites at the Institute for Aerospace Technology, Faculty of Engineering, University of Nottingham, UK. He obtained his PhD from the University of Manchester in 1993 and returned to his academic track as a lecturer at the University of Manchester in 1995 and was appointed to his present position in 2012. Professor Li has published well over 100 academic papers, most of them in highly reputable international journals. His main research interest is in the area of analysis of composite materials and structures, in particular, on modelling damage and failure, micromechanics and material characterisation. As an outcome of his research on micromechanical modelling of composites, a piece of software UnitCells© has emerged which offers material scientists and structural designers a useful tool for characterisation of composites in terms of effective elastic properties as well as strength properties.Elena Sitnikova is currently a Research Fellow at the Faculty of Engineering, the University of Nottingham. She received her MSc degree in Applied Mathematics, Mechanics from Saint Petersburg State University in 2004 and PhD in Engineering from the University of Aberdeen in 2010. Prior to joining the University of Nottingham in 2013, she took a position of Research Associate at the University of Liverpool. Dr Sitnikova authored a number of research papers in several fields of engineering. Her current interests are in the field of textile composites, with particular emphasis on problems of damage, material characterisation and high strain rate response of these materials.

Inhalt
Preface

Part One: Basics

1. Introduction d background, objectives and basic concepts
2. Symmetry, symmetry transformations and symmetry conditions
3. Material categorisation and material characterisation
4. Representative volume elements and unit cells

5. Common erroneous treatments and their conceptual sources of errors

   Part Two: Consistent formulation of unit cells and representative volume elements

6. Formulation of unit cells
7. Periodic traction boundary conditions and the key degrees of freedom for unit cells
8. Further symmetries within a UC
9. RVE for media with randomly distributed inclusions
10. The diffusion problem

11. Boundaries of applicability of representative volume elements and unit cells

    Part Three: Further developments

12. Applications to textile composites
13. Application of unit cells to problems of finite deformation

14. Automated implementation: UnitCells© composites characterisation code

    Index