Multiscale computational solid mechanics: data and machine learning

Multiscale computational solid mechanics concurrently connects complex material physics and macroscopic structural analysis to accelerate the application of advanced materials in the industry rather than resorting to empirical constitutive models. The rise of data-driven multiscale material modeling opens a major paradigm shift in multiscale computational solid mechanics in the era of material big data. This paper reviews state-of-the-art data-driven methods for multiscale simulation, focusing on data-driven multiscale finite element method (data-driven FE2) and data-driven multiscale finite element-deep material network method (data-driven FE-DMN). Both types of data-driven multiscale methods aim to resolve the past challenge of concurrent multiscale simulation. Numerical examples are designed to demonstrate the effectiveness of data-driven multiscale simulation methods. Future research directions are discussed, including data sampling strategy and data generation technique for the data-driven FE2 method and generalization of data-driven FE-DMN method.