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Data-driven multiscale finite element method: from concurrence to separation. (English) Zbl 1436.74077

Summary: This paper aims to propose a novel data-driven multiscale finite element method (data-driven \(\mathrm{FE}^2\)) for composite materials and structures. The correlated scales in the classical \(\mathrm{FE}^2\) method are here split to be computed sequentially and separately: the microscopic problems are calculated in advance to construct an offline material genome database, which is later used in the macroscopic data-driven analysis. In this new framework, the difficulties in formulating and solving complicated multiscale system are avoided by dealing with single scale problems. Moreover, the online computation of microscopic problems in classical \(\mathrm{FE}^2\) method is replaced by searching data points over the offline database resulting in a data-driven \(\mathrm{FE}^2\) method. Thus, the online computing efficiency of structural analysis is significantly improved.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74Q05 Homogenization in equilibrium problems of solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74E30 Composite and mixture properties

Software:

PERMIX
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Full Text: DOI

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