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

@article{Lucarini2022AdaptationAV,
  title={Adaptation and validation of FFT methods for homogenization of lattice based materials},
  author={Sergio Lucarini and Laura Cobian and A. Voitus and Javier Segurado},
  journal={Computer Methods in Applied Mechanics and Engineering},
  year={2022}
}
An FFT framework which preserves a good numerical performance in the case of domains with large regions of empty space is proposed and analyzed for its application to lattice based materials. Two spectral solvers specially suited to resolve problems containing phases with zero stiffness are considered (1) a Galerkin approach combined with the MINRES linear solver and a discrete differentiation rule and (2) a modification of a displacement FFT solver which penalizes the indetermination of… Expand

References

SHOWING 1-10 OF 49 REFERENCES
Filtering material properties to improve FFT-based methods for numerical homogenization
TLDR
Filtering material properties is proposed as a third complementary way to improve FFT-based methods and it is evidenced from numerical experiments that the grid refinement and consequently the computation time and/or the spurious oscillations observed on local fields can be significantly reduced. Expand
FFT-based homogenization for microstructures discretized by linear hexahedral elements
Summary The FFT-based homogenization method of Moulinec–Suquet has recently emerged as a powerful tool for computing the macroscopic response of complex microstructures for elastic and inelasticExpand
An FFT-based Galerkin method for homogenization of periodic media
TLDR
This work demonstrates that the Moulinec-Suquet setting is actually equivalent to a Galerkin discretization of the cell problem, based on approximation spaces spanned by trigonometric polynomials and a suitable numerical integration scheme, and proves convergence of the approximate solution to the weak solution. Expand
Finite strain FFT-based non-linear solvers made simple
Computational micromechanics and homogenization require the solution of the mechanical equilibrium of a periodic cell that comprises a (generally complex) microstructure. Techniques that apply theExpand
DBFFT: A displacement based FFT approach for non-linear homogenization of the mechanical behavior
TLDR
A fast, robust and memory-efficient FFT homogenization framework in which the displacement field on the Fourier space is the unknown: the displacement based FFT (DBFFT) algorithm which allows any general non-linear constitutive behavior for the phases and direct strain, stress and mixed control of the macroscopic load. Expand
Computational homogenization of elasticity on a staggered grid
Summary In this article, we propose to discretize the problem of linear elastic homogenization by finite differences on a staggered grid and introduce fast and robust solvers. Our method shares someExpand
A finite element perspective on non-linear FFT-based micromechanical simulations
Fourier solvers have become efficient tools to establish structure–property relations in heterogeneous materials. Introduced as an alternative to the finite element (FE) method, they are based onExpand
FFT-based methods for the mechanics of composites: A general variational framework
TLDR
A new FFT-based scheme is proposed which is as simple as the basic scheme, while remaining valid for infinite contrasts, and provides an energetically consistent rule for the homogenization of boundary voxels. Expand
A FFT-Based Numerical Method for Computing the Mechanical Properties of Composites from Images of their Microstructures
TLDR
A numerical method is presented here that directly uses images of the microstructure to compute the composite overall properties, as well as the local distribution of stresses and strains, without requiring further geometrical interpretation by the user. Expand
On the accuracy of spectral solvers for micromechanics based fatigue modeling
TLDR
A framework based on FFT allows predicting fatigue life with a similar accuracy than using FEM but strongly reducing the computational cost. Expand
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