Approximation of periodic Green's operator in real space using numerical integration and its use in fast Fourier transform-based micromechanical models

Micromechanics of solids (74M25) Numerical methods for discrete and fast Fourier transforms (65T50) Numerical and other methods in solid mechanics (74S99) Fundamental solutions, Green's function methods, etc. for boundary value problems involving PDEs (65N80)

Cites Work

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Filtering material properties to improve FFT-based methods for numerical homogenization
Combining Galerkin approximation techniques with the principle of Hashin and Shtrikman to derive a new FFT-based numerical method for the homogenization of composites
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Guaranteed upper-lower bounds on homogenized properties by FFT-based Galerkin method
Use of composite voxels in FFT-based homogenization
A Note on Alternating Series in Several Dimensions
Source-neutral Green'functions for periodic problems in electrostatics, and their equivalents in electromagnetism
The Theory of Composites
FFT‐based homogenization for microstructures discretized by linear hexahedral elements
Decomposition and pointwise estimates of periodic Green functions of some elliptic equations with periodic oscillatory coefficients
Texture and strain localization prediction using a \(N\)-site polycrystal model
Computational homogenization of elasticity on a staggered grid
Reconstructing displacements from the solution to the periodic Lippmann-Schwinger equation discretized on a uniform grid

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