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Filtering material properties to improve FFT-based methods for numerical homogenization

Lionel Gélébart, Franck Ouaki
2015 Journal of Computational Physics  
In this short note, filtering material properties is proposed as a third complementary way to improve FFT-based methods.  ...  FFT-based solvers introduced in the 1990s for the numerical homogenization of heterogeneous elastic materials have been extended to a wide range of physical properties.  ...  -Introduction The spectral methods based on the Lippmann-Schwinger equation associated to a discrete Green operator are efficient numerical iterative methods devoted to the evaluation of physical properties  ... 
doi:10.1016/ fatcat:xnc7mjxxl5c7hpzs335owo27ei

Macroscopically consistent non-local modeling of heterogeneous media

François Bignonnet, Karam Sab, Luc Dormieux, Sébastien Brisard, Antoine Bisson
2014 Computer Methods in Applied Mechanics and Engineering  
The non-local stiffness tensor is intrinsically non symmetric, but its spatial fluctuations are smoothed, allowing for a less refined discretization in numerical methods.  ...  The second step is the numerical homogenization of the obtained sampled filtered stiffness.  ...  of simplicity and opportunity to use FFT-based homogenization methods.  ... 
doi:10.1016/j.cma.2014.05.014 fatcat:yjn3yhhytzap7lozexv4ygq3me

Numerical and Experimental Characterization of Elastic Properties of a Novel, Highly Homogeneous Interpenetrating Metal Ceramic Composite

Dominik Horny, Joél Schukraft, Kay André Weidenmann, Katrin Schulz
2020 Advanced Engineering Materials  
The authors thank Morgan Advanced Materials Haldenwanger GmbH for the friendly supply of complimentary preform material.  ...  Acknowledgements The financial support for this work in the context of the DFG research projects SCHU 3074/1-1 and WE 4273/17-1 as well as the support by the European Social Fund and the State Baden-Württemberg  ...  FFT-Based Modeling FFT-based homogenization of composite materials for linear elastic problems was first introduced by Moulinec and Suquet [38] in the  ... 
doi:10.1002/adem.201901556 fatcat:j3mwrrir3bg5jmojdot5lj7rbi

Adaptation and validation of FFT methods for homogenization of lattice based materials [article]

S. Lucarini, L. Cobian, A. Voitus, J. Segurado
2021 arXiv   pre-print
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.  ...  With respect to numerical efficiency it was observed that FFT becomes competitive compared to FEM for cells with relative densities above 7 presented, the FFT frameworks are used to simulate the behavior  ...  Validation for elastic materials The numerical methods proposed to homogenize the mechanical behavior of lattice based materials and their combination with the different geometrical representations are  ... 
arXiv:2110.00733v1 fatcat:2nz6ssf4f5gcbhj7iedga3gche

Fourier-based strength homogenization of porous media

François Bignonnet, Ghazi Hassen, Luc Dormieux
2016 Computational Mechanics  
An efficient numerical method is proposed to upscale the strength properties of heterogeneous media with periodic boundary conditions.  ...  The method is implemented for microstructures with local strength properties governed either by a Green criterion or a Von Mises criterion, including pores or rigid inclusions.  ...  Numerical results This section aims both at validating the FFT-based method and at studying the effect of the microstructure morphology on the homogenized strength properties.  ... 
doi:10.1007/s00466-016-1319-6 fatcat:loyybhbcbravffmc5ad4d3ssqy

A deep learning driven pseudospectral PCE based FFT homogenization algorithm for complex microstructures

Alexander Henkes, Ismail Caylak, Rolf Mahnken
2021 Computer Methods in Applied Mechanics and Engineering  
numerical homogenization method.  ...  This work is directed to uncertainty quantification of homogenized effective properties for composite materials with complex, three dimensional microstructure.  ...  The authors gratefully acknowledge the funding of this project by computing time provided by the Paderborn Center for Parallel Computing (PC2).  ... 
doi:10.1016/j.cma.2021.114070 fatcat:6phadkz2ufdkfb6whxwmdbtlgi

GAKTpore: Stereological Characterisation Methods for Porous Foams in Biomedical Applications

Gareth Sheppard, Karl Tassenberg, Bogdan Nenchev, Joel Strickland, Ramy Mesalam, Jennifer Shepherd, Hugo Williams
2021 Materials  
There are two main algorithm novelties within this work: (1) feature-dependant homogeneity map; (2) a new waviness function providing insights into the convexity/concavity of pores, important for understanding  ...  collagen scaffold formation by relating microstructural formation to the bulk formation environment.  ...  Materials 2021, 14, 1269 Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/ma14051269 pmid:33800080 fatcat:xhffzr4ofvdurhhn5c76zci5cm

Estimation of local stresses and elastic properties of a mortar sample by FFT computation of fields on a 3D image

J. Escoda, F. Willot, D. Jeulin, J. Sanahuja, C. Toulemonde
2011 Cement and Concrete Research  
This study concerns the prediction of the elastic properties of a 3D mortar image, obtained by micro-tomography, using a combined image segmentation and numerical homogenization approach.  ...  Emphasis is made on highly-contrasted properties between aggregates and matrix, to anticipate needs for creep or damage computation.  ...  Numerical homogenization is handled by a FFT-based tool that is directly applied to the microstructure image.  ... 
doi:10.1016/j.cemconres.2011.02.003 fatcat:ivrrbiuqw5a6betr5ziwzhcx2e

Fast Fourier homogenization for elastic wave propagation in complex media

Yann Capdeville, Ming Zhao, Paul Cupillard
2015 Wave motion  
h i g h l i g h t s • We propose an FFT based homogenization method (FFH) to upscale complex elastic media. • The FFH is based on trivial meshes, even for complex media. • FFH method can handle both continuously  ...  or discontinuously varying fine scale models. • The FFH can be used as a preprocess allowing simple meshes for wave equation solvers.  ...  The authors also thank two anonymous reviewers and William Parnell who greatly helped to improve the manuscript.  ... 
doi:10.1016/j.wavemoti.2014.12.006 fatcat:yjz73ejybvdirebkksebb3gifi

Effect of aggregate shapes on local fields in 3D mesoscale simulations of the concrete creep behavior

Fabien Bernachy-Barbe, Benoît Bary
2019 Finite elements in analysis and design  
Results obtained with FE and FFT methods are very close, indicating that while FFT is well adapted, FE remains attractive in this context.  ...  Creep simulations with finite element (FE) and Fast Fourier Transform (FFT) methods are then performed on different spatial refinements.  ...  Acknowledgements The authors would like to thank Dietmar Meinel from BAM for the X-CT images, EDF and the support from ANR MACENA project, and the following colleagues for the development and use of their  ... 
doi:10.1016/j.finel.2019.01.001 fatcat:phvqyts5y5bavorjuedp2narp4

Stochastic reconstruction of the microstructure of equilibrium form snow and computation of effective elastic properties

Hongyan Yuan, Jonah H. Lee, James E. Guilkey
2010 Journal of Glaciology  
Because snow is a random heterogeneous material, it is often helpful to construct stochastic geometric models that can be used to model physical and mechanical properties of snow.  ...  For the snow samples and the reconstructed snow microstructure, we also estimate the mechanical properties and the size of the associated representative volume element using numerical simulations as additional  ...  Löwe for helpful comments on the manuscript. This work was supported in part by a grant of highperformance computing resources from the Arctic Region Supercomputing Center at the University of Alaska  ... 
doi:10.3189/002214310792447770 fatcat:ip2ubty6mzfkvfnzrrw7itdepm

Development of a new consistent discrete green operator for FFT-based methods to solve heterogeneous problems with eigenstrains

Komlavi Sényo Eloh, Alain Jacques, Stéphane Berbenni
2018 International journal of plasticity  
Development of a new consistent discrete Green operator for FFT-based methods to solve heterogeneous problems with eigenstrains.  ...  Numerical examples are reported, such as the computation of the local stresses and displacements of composite materials with homogeneous or heterogeneous elasticity combined with dilatational eigenstrain  ...  Ribarik (Department of Materials Physics, Eötvös University, Budapest, Hungary) for useful advices. SB also thanks R. A. Lebensohn (Los Alamos Nat. Lab., USA) and P.  ... 
doi:10.1016/j.ijplas.2018.10.011 fatcat:vrzek2azyjcxdiw7tcs667syii

Electromagnetic Metamaterial Design Using Finite Element Based Optimization Technique: A Case Study For A Satcom Antenna

Gullu Sendur
2018 Zenodo  
The optimizer will seek for the material distribution within 4 layers to improve the bandwidth of the initially homogeneous substrate with a resonance around 318 MHz. B.  ...  A periodic version of the FE-BI method is employed as described in [16] to provide for additional speed by using only a few modes and the FFT to carry out the matrix vector products.  ... 
doi:10.5281/zenodo.1160308 fatcat:qcoh6npe6neujpjz55rwra6pci

Combining Galerkin approximation techniques with the principle of Hashin and Shtrikman to derive a new FFT-based numerical method for the homogenization of composites

S. Brisard, L. Dormieux
2012 Computer Methods in Applied Mechanics and Engineering  
We report on the mathematical analysis of two different, FFT-based, numerical schemes for the homogenization of composite media within the framework of linear elasticity: the basic scheme of Suquet (1994  ...  Finally, a rule is proposed for handling heterogeneous pixels/voxels, a situation frequently met when images of real materials are used as input to these schemes.  ...  These considerations led Moulinec and Suquet [9, 10] to a now popular numerical method based on the fast Fourier transform (FFT).  ... 
doi:10.1016/j.cma.2012.01.003 fatcat:xvftbzbphndipbnp3a5pkm3qwu

Upscaling the elastic stiffness of foam concrete as a three-phase composite material

M. Ben Youssef, F. Lavergne, K. Sab, K. Miled, J. Neji
2018 Cement and Concrete Research  
Nevertheless, by performing 3D elastic numerical simulations on artificial unit cells in the frame of periodic homogenization, it is shown that describing foam concrete as a porous material is not sufficient  ...  to explain the experimental measurements of the Young modulus for added porosity higher than 40%.  ...  Different algorithms can be applied to solve the elastic problem, including the finite element method and the FFT method.  ... 
doi:10.1016/j.cemconres.2018.04.021 fatcat:7h2an3ukuvby7df7snxr24t3tq
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