# Finite strain FFT-based non-linear solvers made simple

@article{Geus2017FiniteSF, title={Finite strain FFT-based non-linear solvers made simple}, author={Tom W. J. de Geus and Jaroslav Vondrejc and Jan Zeman and Ron H. J. Peerlings and Marc G. D. Geers}, journal={Computer Methods in Applied Mechanics and Engineering}, year={2017}, volume={318}, pages={412-430} }

## 82 Citations

DBFFT: A displacement based FFT approach for non-linear homogenization of the mechanical behavior

- Computer ScienceInternational Journal of Engineering Science
- 2019

FFT-based homogenization of hypoelastic plasticity at finite strains

- Computer ScienceComputer Methods in Applied Mechanics and Engineering
- 2019

DBFFT: A displacement based FFT approach for homogenization of the mechanical behavior

- Computer ScienceArXiv
- 2019

A new, fast, robust and memory-efficient FFT approach in which the displacement field on the Fourier space is the unknown: the displacement based FFT (DBFFT) algorithm, which results in a linear equation defined in terms of linear operators in the Fouriers space and that does not require a reference medium.

A comparative study on low-memory iterative solvers for FFT-based homogenization of periodic media

- Computer ScienceJ. Comput. Phys.
- 2016

Energy-based comparison between Fourier-Galerkin and finite element method within numerical homogenisation

- Engineering
- 2017

This work compares the two Fourier-Galerkin methods using the energetic norm of local fields, which has the clear physical interpretation as being the error in the homogenized properties, and shows that the methods' effectiveness rely on the smoothness (regularity) of the solution and thus on the material coefficients.

A multiscale FE-FFT framework for electro-active materials at finite strains

- Computer ScienceComputational Mechanics
- 2019

It turns out that while the fully coupled scheme leads to quadratic convergence rates, the uncoupled scheme may allow for shorter computation times under certain boundary conditions.

Adaptation and validation of FFT methods for homogenization of lattice based materials

- Computer ScienceComputer Methods in Applied Mechanics and Engineering
- 2022

FFT-based homogenisation accelerated by low-rank tensor approximations

- Computer ScienceComputer Methods in Applied Mechanics and Engineering
- 2020

Development and comparison of spectral algorithms for numerical modeling of the quasi-static mechanical behavior of inhomogeneous materials

- Computer ScienceArXiv
- 2020

Comparison of the performance and convergence behavior of AFB/R- and DGO-based algorithms shows that the former is more efficient than the latter for larger phase contrasts, and one based on so-called averaged-forward-backward-differencing (AFB) is shown to result in the greatest improvement in convergence rate.

FFT based approaches in micromechanics: fundamentals, methods and applications

- EngineeringModelling and Simulation in Materials Science and Engineering
- 2021

FFT methods have become a fundamental tool in computational micromechanics since they were first proposed in 1994 by Moulinec and Suquet for the homogenization of composites. Since then many…

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A comparative study on low-memory iterative solvers for FFT-based homogenization of periodic media

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