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.
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Table of Contents
PrefacePart 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
