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Mesoscopic and multiscale modelling in materials

Abstract

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.

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Fig. 1: Modelling the effects of manufacturing on performance of composites.

adapted with permission from ref. 68, Wiley

Fig. 2: Physics-based upscaling approaches for coarse graining of MD.

panel a reproduced with permission from ref. 70, Elsevier; panel b adapted with permission from ref. 124, American Chemical Society

Fig. 3: Data-driven model for high-pressure densification of silica glass.

adapted with permission from ref. 77, Springer

Fig. 4: QC modelling of atomistic and continuum lattice systems.

panels reproduced with permission from: a, ref. 86, IOP; b, ref. 92, Elsevier

Fig. 5: Schematic showing a single multigrid V cycle consisting of three scales.
Fig. 6: Gartner cycle for multiscale science and engineering.
Fig. 7: A single level of the multilevel directly computable physics framework.

adapted with permission from from ref. 64, Wiley

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Fish, J., Wagner, G.J. & Keten, S. Mesoscopic and multiscale modelling in materials. Nat. Mater. 20, 774–786 (2021). https://doi.org/10.1038/s41563-020-00913-0

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