A review of nonlinear FFT-based computational homogenization methods. (English) Zbl 1491.74099
Summary: Since their inception, computational homogenization methods based on the fast Fourier transform (FFT) have grown in popularity, establishing themselves as a powerful tool applicable to complex, digitized microstructures. At the same time, the understanding of the underlying principles has grown, in terms of both discretization schemes and solution methods, leading to improvements of the original approach and extending the applications. This article provides a condensed overview of results scattered throughout the literature and guides the reader to the current state of the art in nonlinear computational homogenization methods using the fast Fourier transform.
MSC:
| 74S25 | Spectral and related methods applied to problems in solid mechanics |
| 74Q05 | Homogenization in equilibrium problems of solid mechanics |
| 74Q10 | Homogenization and oscillations in dynamical problems of solid mechanics |
| 74-02 | Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids |
Keywords:
nonlinear computational homogenization; discretization scheme; nonlinear solution method; Newton method; convergence; dual scheme; composite; crystal; granular material; fracture mechanicsReferences:
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