Statistically equivalent representative volume elements (SERVE) for material behaviour analysis and multiscale modelling

Mechanical properties of materials and associated engineered components are controlled by the material structure at various lengths and time scales. As materials are being further utilised to the maximum extent of their capabilities, tails on property distributions become significant. These tails are often driven by the extremities of microstructural feature distributions, suggesting the need for a statistically relevant description of the microstructure and a reciprocity relationship with the range of property measurement capabilities and the models that represent this information.Representative volume elements (RVE) and statistically equivalent representative volume elements (SERVE) have emerged as frameworks for such microstructural characterisation and quantification.This review covers the evolution of quantitative microstructure description for use in material behaviour predictions from homogenised representations, large volume statistical representation, to the determination of the minimum spatial size to statistically represent a microstructure based on features of interest and properties of interest.