Abstract
In the case of highly heterogeneous microstructures, such as textile composites herein, conformal FE meshes are difficult to generate for image-based modeling. As an alternative way regular meshing based on the initial image discretization can be used. However, it requires a large number of elements to reduce undesirable effects due to the voxelized discretization of the phase, such as so-called checkerboard pattern. In this work FAST Fourier transform (FFT) based method has been employed by virtue of its simplicity of meshing and efficiency of parallel computation. One of the major contributions is the extension of the FFT method to nonlinear material modeling based on continuous damage mechanics (CDM). Simple test cases are provided to validate the model. In the last part, the FFT with CDM modeling is applied to a real mesostructure of 3D interlock composite from X-ray computed tomography image.
References
J. Schöberl, An advancing front 2D/3D-mesh generator based on abstract rules. Comput. Vis. Sci. 1, 41–52 (1997)
V.R. Coffman, A.C.E. Reid, S.A. Langer, G. Dogan, OOF3D: an image-based finite element solver for materials science. Math. Comput. Simul. 82, 2951–2961 (2012)
G. Legrain, P. Cartraud, I. Perreard, N. Moes, An X-FEM and level set computational approach for image-based modelling: application to homogenization. Int. J. Numer. Methods Eng. 86, 915–934 (2011)
Y. Liu, I. Straumit, D. Vasiukov, S.V. Lomov, S. Panier, Prediction of linear and non-linear behavior of 3D woven composite using mesoscopic voxel models reconstructed from X-ray micro-tomography. Compos. Struct. 179, 568–579 (2017)
A. Doitrand, C. Fagiano, F.X. Irisarri, M. Hirsekorn, Comparison between voxel and consistent meso-scale models of woven composites. Compos. A Appl. Sci. Manuf. 73, 143–154 (2015)
H. Moulinec, P. Suquet, A numerical method for computing the overall response of nonlinear composites with complex microstructure. Comput. Methods Appl. Mech. Eng. 157, 69–94 (1998)
S. Brisard, L. Dormieux, FFT-based methods for the mechanics of composites: a general variational framework. Comput. Mater. Sci. 49, 663–671 (2010)
L. Gélébart, R. Mondon-Cancel, Non-linear extension of FFT-based methods accelerated by conjugate gradients to evaluate the mechanical behavior of composite materials. Comput. Mater. Sci. 77, 430–439 (2013)
J. Zeman, T.W.J. de Geus, J. Vondřejc, R.H.J. Peerlings, M.G.D. Geers, A finite element perspective on nonlinear FFT-based micromechanical simulations. Int. J. Numer. Methods Eng. 111, 903–926 (2017)
M. Schneider, D. Merkert, M. Kabel, FFT-based homogenization for microstructures discretized by linear hexahedral elements. Int. J. Numer. Methods Eng. 109, 1461–1489 (2017)
J. Li, S. Meng, X. Tian, F. Song, C. Jiang, A non-local fracture model for composite laminates and numerical simulations by using the FFT method. Compos. B Eng. 43, 961–971 (2012)
B. Wang, G. Fang, S. Liu, M. Fu, J. Liang, Progressive damage analysis of 3D braided composites using FFT-based method. Compos. Struct. 192, 255–263 (2018)
Home AMITEX_FFTP 2.3 documentation http://www.maisondelasimulation.fr/projects/amitex/html/. Accessed 1 Jan 2019
Cast3M http://www-cast3m.cea.fr/. Accessed 1 Jan 2019
F. Willot, Fourier-based schemes for computing the mechanical response of composites with accurate local fields. C. R. Mec 343, 232–245 (2015)
B. Rosen, Mechanics of composite strengthening, Fiber composite materials (ACM, Metals Park, 1964)
C. Chamis, Mechanics of composite materials: past, present, and future. J. Compos. Technol. Res. 11, 3–14 (1989). https://doi.org/10.1520/CTR10143J
D. Ashouri Vajari, C. González, J. Llorca, B.N. Legarth, A numerical study of the influence of microvoids in the transverse mechanical response of unidirectional composites. Compos. Sci. Technol. 97, 46–54 (2014)
F. Naya, C. González, C.S. Lopes, S. Van der Veen, F. Pons, Computational micromechanics of the transverse and shear behavior of unidirectional fiber reinforced polymers including environmental effects. Compos. A Appl. Sci. Manuf. 92, 146–157 (2017)
Z.P. Bazant, B.H. Oh, Crack band theory for fracture of concrete. Matériaux Constr. 16, 155–177 (1983)
I. Straumit, S.V. Lomov, M. Wevers, Quantification of the internal structure and automatic generation of voxel models of textile composites from X-ray computed tomography data. Compos. A Appl. Sci. Manuf. 69, 150–158 (2015)
Y. Chen, L. Gélébart, C. Chateau, M. Bornert, C. Sauder, A. King, Analysis of the damage initiation in a SiC/SiC composite tube from a direct comparison between large-scale numerical simulation and synchronoton X-ray micro-tomography. Int. J. Solids Struct. 161, 111–126 (2019)
Acknowledgements
The Nord-Pas-de-Calais Region and the European Community (FEDER funds) partly funds the X-ray tomography equipment ISIS4D platform (LML/LaMcube, France).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chen, Y., Vasiukov, D., Gélébart, L. et al. Fast Fourier transform solver for damage modeling of composite materials. JMST Adv. 1, 49–55 (2019). https://doi.org/10.1007/s42791-019-0004-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s42791-019-0004-2