An Efficient Algorithm to Include Sub-Voxel Data in FFT-Based Homogenization for Heat Conductivity

Merkert, Dennis; Andrä, Heiko; Kabel, Matthias; Schneider, Matti; Simeon, Bernd

doi:10.1007/978-3-319-22997-3_16

Cited by 6 publications

(10 citation statements)

References 16 publications

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“…As this fact is of independent interest, we will discuss it in this central and prominent part of the manuscript. The strategy introduced by Merkert et al 99 proceeds as follows. Suppose there is a (possibly non-normalized) level-set function L e ∶ [0, 1] 3 → R on the voxel in question which is sampled on a subvoxel grid with m 3 voxels, that is, the signs of the values…”

Section: Contributionsmentioning

confidence: 99%

Assumed strain methods in micromechanics, laminate composite voxels and level sets

Lendvai,

Schneider

2024

Numerical Meth Engineering

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This work deals with the composite voxel method, which—in its original form—furnishes voxels containing more than one material with a surrogate material law accounting for the heterogeneity in the voxel. We show that the laminate composite voxel technique naturally arises as an assumed strain method, that is, the general framework introduced by Simo‐Rifai, for a specific choice of enhanced strain field. As a consequence, laminate composite voxels may be regarded as a kinematic assumption within a discretization scheme rather than a part of material modeling, as suggested originally. We discuss how to seamlessly integrate composite voxels into the framework of a level‐set description of the microstructure, in particular the accurate and efficient computation of normals and cut‐volume fractions. In contrast to more traditional strategies based on subvoxelizations, the introduced method avoids systematic errors when computing composite voxel properties. We demonstrate the applicability of the developed technology for a number of relevant computational examples.

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Section: Contributionsmentioning

confidence: 99%

Assumed strain methods in micromechanics, laminate composite voxels and level sets

Lendvai,

Schneider

2024

Numerical Meth Engineering

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“…Recall that the critical difference of composite voxels and composite boxels for the article at hand is the way the interface normal is estimated. For composite voxels, this estimation is performed by connecting the centroid of a phase (e.g., of the matrix phase) to the centroid of the voxel, and normalizing the vector to unity 53 . Unfortunately, this procedure is not convergent under grid refinement 54 .…”

Section: Computational Investigationsmentioning

confidence: 99%

“…For composite voxels, this estimation is performed by connecting the centroid of a phase (e.g., of the matrix phase) to the centroid of the voxel, and normalizing the vector to unity. 53 Unfortunately, this procedure is not convergent under grid refinement. 54 The alternative strategy of Keshav et al 48(section 5.2) is based on Laplacian smoothing, and was shown to be more accurate.…”

Section: A Cross-plymentioning

confidence: 99%

Adaptive material evaluation by stabilized octree and sandwich coarsening in FFT‐based computational micromechanics

Kabel,

Schneider

2023

Numerical Meth Engineering

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The computational efficiency of FFT‐based computational micromechanics is deeply rooted in the underlying regular, that is, Cartesian, discretization. The bottleneck for most industrial applications is evaluating the typically rather expensive constitutive law on the regular grid. In the work at hand, we exploit coarsening strategies to evaluate the material law with the intention of speeding up the overall computation time while retaining the level of achieved accuracy. Inspired by wavelet‐compression techniques, we form aggregates of voxels where the local strain tensors are close, and compute the stresses on these coarsened elements. If done naively, such a strategy will lead to intrinsic instabilities whose origin is apparent from a mathematical perspective. As a remedy, we introduce a stabilization technique which is inspired by hourglass control well‐known for underintegrated finite elements. We introduce octree as well as sandwich coarsening, discuss the handling of internal variables, report on the efficient implementation of the concepts and demonstrate the effectiveness of the developed technology on simple as well as industrial examples.

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“…In order to capture the microscale effects sufficiently, a high grid resolution is hence needed, which-in turn-calls for high computational cost. In order to limit or even eliminate the staircase phenomenon without the need for a (distinct) grid refinement, so-called composite voxels were previously suggested in [15][16][17]37]. They enhance the existing binary discretization using special voxels with effective material properties that depend on the phase volume fractions and the normal orientation N of the laminate.…”

Section: Composites Voxelsmentioning

confidence: 99%

FFT-based homogenization at finite strains using composite boxels (ComBo)

2022

Self Cite

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Computational homogenization is the gold standard for concurrent multi-scale simulations (e.g., FE2) in scale-bridging applications. Often the simulations are based on experimental and synthetic material microstructures represented by high-resolution 3D image data. The computational complexity of simulations operating on such voxel data is distinct. The inability of voxelized 3D geometries to capture smooth material interfaces accurately, along with the necessity for complexity reduction, has motivated a special local coarse-graining technique called composite voxels (Kabel et al. Comput Methods Appl Mech Eng 294: 168–188, 2015). They condense multiple fine-scale voxels into a single voxel, whose constitutive model is derived from the laminate theory. Our contribution generalizes composite voxels towards composite boxels (ComBo) that are non-equiaxed, a feature that can pay off for materials with a preferred direction such as pseudo-uni-directional fiber composites. A novel image-based normal detection algorithm is devised which (i) allows for boxels in the firsts place and (ii) reduces the error in the phase-averaged stresses by around 30% against the orientation cf. Kabel et al. (Comput Methods Appl Mech Eng 294: 168–188, 2015) even for equiaxed voxels. Further, the use of ComBo for finite strain simulations is studied in detail. An efficient and robust implementation is proposed, featuring an essential selective back-projection algorithm preventing physically inadmissible states. Various examples show the efficiency of ComBo against the original proposal by Kabel et al. (Comput Methods Appl Mech Eng 294: 168–188, 2015) and the proposed algorithmic enhancements for nonlinear mechanical problems. The general usability is emphasized by examining various Fast Fourier Transform (FFT) based solvers, including a detailed description of the Doubly-Fine Material Grid (DFMG) for finite strains. All of the studied schemes benefit from the ComBo discretization.

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An Efficient Algorithm to Include Sub-Voxel Data in FFT-Based Homogenization for Heat Conductivity

Cited by 6 publications

References 16 publications

Assumed strain methods in micromechanics, laminate composite voxels and level sets

Assumed strain methods in micromechanics, laminate composite voxels and level sets

Adaptive material evaluation by stabilized octree and sandwich coarsening in FFT‐based computational micromechanics

FFT-based homogenization at finite strains using composite boxels (ComBo)

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