Abstract
The microscopic mechanical response of composites can provide direct and critical insights for meso- and macro- scale material analyses, and the representative volume element microstructural model is an effective computational medium to virtually characterize and describe the microscale behaviour of the material. This paper presents a comprehensive review of micro-scale mathematical characterizations and demonstrations of unidirectional continuous fibre-reinforced composites. The representative volume element, including its definition and homogenization, is examined in detail. Geometric parameters of the virtual microstructure are analysed, and the microstructure generation algorithms are systematically classified into six categories. Statistical methodologies are introduced to assess the spatial distribution of fibres in the microstructure and explore the structure–property relationships between graphical descriptors and mechanical responses. In addition, defects in the representative volume element microstructure are presented in detail, along with their statistical evaluation methods from different perspectives. A critical discussion of the advantages, differences and limitations of each method (or model) is also provided.