Representative Volume Elements and Unit Cells - 1st Edition - ISBN: 9780081026380

Representative Volume Elements and Unit Cells

1st Edition

Concepts, Theory, Applications and Implementation

Authors: Shuguang Li Elena Sitnikova
Paperback ISBN: 9780081026380
Imprint: Woodhead Publishing
Published Date: 29th November 2019
Page Count: 360
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Table of Contents

1. Introduction
2 Common erroneous treatments and their conceptual sources of errors
3. Length Scales
4. Symmetry
5. Continuity and Free Body Diagrams
6. Symmetry Conditions
7. Material Categorisation
8. Material Characterisation
9. RVEs and Unit Cells
10. Relative Displacement Field
11. Relative Displacement Boundary Conditions for Unit Cells
12. Key degrees of freedom
13. Average Stresses, Average Strains and Effective Material Properties
14. Further Symmetries within a Unit Cell
15. The Roles of Each Type of Symmetry in Material Categorisation and Characterisation
16. ‘Sanity Checks’ as Basic Verifications
17. UD Composites and Transverse Isotropy
18. RVE for Randomly Distributed Inclusions
19. Diffusion Problems
20. Boundary of Applicability of RVEs and UCs
21. Applications to Textile Composites
22. UnitCells© Composites Characterisation Code
23. Other Related Theoretical Frameworks and Deceptions
24. Concluding Remarks


Representative Volume Elements and Unit Cells: Concepts, Theory, Applications and Implementation clearly explains how representative volume elements and unit cells should to be accurately constructed in terms of finite element analysis, the imposition of boundary conditions, prescription of loads, meshing and post-processing. The theoretical background for using FEA in materials characterization is given in full, hence readers will gain a clear and detailed understanding of the underlying principles that they can use in the development of their own models. Full derivations for some commonly used unit cells are presented so that users can directly apply them in their own developments.

Finally, a piece of code designed as an add-on to Abaqus software, UnitCells©, is provided on a companion site for the material characterization of some of the common types of composites. in addition, a user manual and relevant templates are included.

Key Features

  • Give users the information they need to feel more confident when using REV/UC models to analysis large structures with accuracy and efficiency
  • Includes systematic explanations of REV and UC theories, as well as their applications in composites
  • Illustrates, in detail, how to set up unit cell models and provides the open source code to implement via Abaqus


Researchers analyzing the multiscale behaviour and characteristics of composite materials. Engineers working in materials selection and characterisation. Materials scientists working on micro-architectures. Software engineers interested in virtual testing platforms for composites characterization.


No. of pages:
© Woodhead Publishing 2020
29th November 2019
Woodhead Publishing
Paperback ISBN:

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About the Authors

Shuguang Li Author

Shuguang Li, Professor of Aerospace Composites, the Institute for Aerospace Technology, Faculty of Engineering, University of Nottingham, UK. He was awarded BEng and MEng from Nanjing University of Aeronautics and Astronautics (NUAA), China in 1982 and 1984, respectively. His first academic career was at NUAA between 1984 and1988 as a lecturer. He then obtained his PhD from the University of Manchester in 1993. He returned back 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 was one of the two advisors to the 2nd World Wide Failure Exercise for Polymer Composites (on 3D failure theories). He is one of the organisers for the 3rd Exercise of the same (on damage theories). The outcomes have been published in Journal of Composite Materials. He is on the editorial board of the International Journal of Mechanical Sciences. He is a visiting professor of NUAA and Zhejiang University, China. He is one of the Qinling Experts at AVIC Aircraft Strength Research Institute and a Technical Advisor to Sinoma Science and Technology, China. 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 characterization. As an outcome of his research on micromechanical modelling of composites, a piece of software UnitCells© has been commercialized 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.

Affiliations and Expertise

Professor of Aerospace Composites, the Institute for Aerospace Technology, Faculty of Engineering, University of Nottingham, UK

Elena Sitnikova Author

Dr Elena Sitnikova is currently a Research Fellow at the Faculty of Engineering, the University of Nottingham since 2013. 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. Her thesis was on the problem of vibration reduction and control in impact systems using shape memory alloys. Prior to joining the UoN, she took a position of Research Associate at the University of Liverpool, where she worked on blast failure of fibre metal laminates. Dr Sitnikova authored a number of research papers in the field 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.

Affiliations and Expertise

The Faculty of Engineering, The University of Nottingham, University Park, Nottingham, UK