Mesoscopic and multiscale modelling in materials

Multiscale modelling is a powerful tool to simulate materials behaviour, which has important features across multiple length and time scales. This Review provides an overview of multiscale computation methods and discusses their development for use in material design. The concept of multiscale modelling has emerged over the last few decades to describe procedures that seek to simulate continuum-scale behaviour using information gleaned from computational models of finer scales in the system, rather than resorting to empirical constitutive models. A large number of such methods have been developed, taking a range of approaches to bridging across multiple length and time scales. Here we introduce some of the key concepts of multiscale modelling and present a sampling of methods from across several categories of models, including techniques developed in recent years that integrate new fields such as machine learning and material design.