Data-Driven Computational Homogenization Method Based on Euclidean Bipartite Matching
Publication: Journal of Engineering Mechanics
Volume 146, Issue 2
Abstract
Image processing methods combined with scanning techniques—for example, microscopy or microtomography—are now frequently being used for constructing realistic microstructure models that can be used as representative volume elements (RVEs) to better characterize heterogeneous material behavior. As a complement to those efforts, the present study introduces a computational homogenization method that bridges the RVE and material-scale properties in situ. To define the boundary conditions properly, an assignment problem is solved using Euclidean bipartite matching through which the boundary nodes of the RVE are matched with the control nodes of the rectangular prism bounding the RVE. The objective is to minimize the distances between the control and boundary nodes, which, when achieved, enables the bridging of scale-based features of both virtually generated and image-reconstructed domains. Following the minimization process, periodic boundary conditions can be enforced at the control nodes, and the resulting boundary value problem can be solved to determine the local constitutive material behavior. To verify the proposed method, virtually generated domains of closed-cell porous, spherical particle-reinforced, and fiber-reinforced composite materials are analyzed, and the results are compared with analytical Hashin-Shtrikman and Halpin-Tsai methods. The percent errors are within the ranges from 0.04% to 3.3%, from 2.7% to 14.9%, and from 0.5% to 13.2% for porous, particle-reinforced, and fiber-reinforced composite materials, respectively, indicating that the method has promising potential in the fields of image-based material characterization and computational homogenization.
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Acknowledgments
The authors gratefully acknowledge the support of Tekniikan edistämissäätiö TES through Foundations’ Post Doc Pool, Finland.
References
Babu, K. P., P. M. Mohite, and C. S. Updahyay. 2018. “Development of an RVE and its stiffness predictions based on mathematical homogenization theory for short fibre composites.” Int. J. Solids Struct. 130–131 (Jan): 80–104. https://doi.org/10.1016/j.ijsolstr.2017.10.011.
Bargmann, S., B. Klusemann, J. Markmann, J. E. Schnabel, K. Schneider, C. Soyarslan, and J. Wilmers. 2018. “Generation of 3D representative volume elements for heterogeneous materials: A review.” Prog. Mater Sci. 96 (Jul): 322–384. https://doi.org/10.1016/j.pmatsci.2018.02.003.
Cerquaglia, M. L., G. Deliége, R. Boman, L. Papeleux, and J. P. Ponthot. 2017. “Reprint of: The particle finite element method for the numerical simulation of bird strike.” Int. J. Impact Eng. 110 (Dec): 72–84. https://doi.org/10.1016/j.ijimpeng.2017.09.002.
Duval, L., M. Moreaud, C. Couprie, D. Jeulin, H. Talbot, and J. Angulo. 2014. “Image processing for materials characterization: Issues, challenges and opportunities.” In Proc., 2014 IEEE Int. Conf. on Image Processing (ICIP). New York: IEEE.
Edelsbrunner, H. 1995. “Smooth surfaces for multi-scale shape representation.” In Foundations of software technology and theoretical computer science, 391–412. Berlin, Heidelberg: Springer.
Edelsbrunner, H., D. Kirkpatrick, and R. Seidel. 1983. “On the shape of a set of points in the plane.” IEEE Trans. Inf. Theory 29 (4): 551–559. https://doi.org/10.1109/TIT.1983.1056714.
Evans, J. W. 1993. “Random and cooperative sequential adsorption.” Rev. Mod. Phys. 65 (4): 1281. https://doi.org/10.1103/RevModPhys.65.1281.
Geers, M. G. D., V. G. Kouznetsova, and W. A. M. Brekelmans. 2010. “Multi-scale computational homogenization: Trends and challenges.” J. Comput. Appl. Math. 234 (7): 2175–2182. https://doi.org/10.1016/j.cam.2009.08.077.
Halpin, J. C. 1969. Effects of environmental factors on composite. Dayton, OH: Air Force Materials Laboratory, Wright-Patterson Air Force Base.
Hashin, Z., and S. Shtrikman. 1963. “A variational approach to the elastic behavior of multiphase materials.” J. Mech. Phys. Solids 11 (2): 127–140. https://doi.org/10.1016/0022-5096(63)90060-7.
Hernández, J. A., J. Oliver, A. E. Huespe, M. A. Caicedo, and J. C. Cante. 2014. “High-performance model reduction techniques in computational multiscale homogenization.” Comput. Methods Appl. Mech. Eng. 276 (Jul): 149–189. https://doi.org/10.1016/j.cma.2014.03.011.
Hibbitt, Karlsson and Sorensen. 1992. ABAQUS: Theory manual. Providence, RI: Hibbitt, Karlsson and Sorensen.
Hollister, S. J., and N. Kikuchi. 1994. “Homogenization theory and digital imaging: A basis for studying the mechanics and design principles of bone tissue.” Biotechnol. Bioeng. 43 (Mar): 586–596. https://doi.org/10.1002/bit.260430708.
Huang, X., and B. Wei. 2010. “Mineral particle image processing and parameter extracting.” In Proc., Int. Conf. on Logistics Engineering and Intelligent Transportation System. Linthicum, MD: Institute for Operations Research and the Management Sciences.
Hung, M. S., and W. O. Rom. 1980. “Solving the assignment problem by relaxation.” Oper. Res. 28 (4): 969–982. https://doi.org/10.1287/opre.28.4.969.
Karakoc, A. 2018. “Sensitivity analysis on the effective stiffness properties of 3-D orthotropic honeycomb cores.” Int. J. Comput. Methods Eng. Sci. Mech. 19 (1): 22–30. https://doi.org/10.1080/15502287.2017.1384081.
Karakoc, A., E. Hiltunen, and J. Paltakari. 2017. “Geometrical and spatial effects on fiber network connectivity.” Compos. Struct. 168 (May): 335–344. https://doi.org/10.1016/j.compstruct.2017.02.062.
Karakoc, A., and E Taciroglu. 2017. “Optimal automated path planning for infinitesimal and real-sized particle assemblies.” AIMS Mater. Sci. 4 (4): 847–855. https://doi.org/10.3934/matersci.2017.4.847.
Karakoç, A., P. Tukiainen, J. Freund, and M. Hughes. 2013. “Experiments on the effective compliance in the radial–tangential plane of Norway spruce.” Compos. Struct. 102 (Aug): 287–293. https://doi.org/10.1016/j.compstruct.2013.03.013.
Kushnevsky, V., O. Morachkovsky, and H. Altenbach. 1998. “Identification of effective properties of particle reinforced composite materials.” Comput. Mech. 22 (4): 317–325. https://doi.org/10.1007/s004660050363.
Larsson, F., K. Runesson, S. Saroukhani, and R. Vafadari. 2011. “Computational homogenization based on a weak format of micro-periodicity for RVE-problems.” Comput. Methods Appl. Mech. Eng. 200 (1–4): 11–26. https://doi.org/10.1016/j.cma.2010.06.023.
Legrain, G., P. Cartraud, I. Perreard, and N. Moes. 2011. “An X-FEM and level set computational approach for image-based modelling: Application to homogenization.” Int. J. Numer. Methods Eng. 86 (7): 915–934. https://doi.org/10.1002/nme.3085.
Lian, W. D., G. Legrain, and P. Cartraud. 2013. “Image-based computational homogenization and localization: Comparison between X-FEM/levelset and voxel-based approaches.” Comput. Mech. 51 (3): 279–293. https://doi.org/10.1007/s00466-012-0723-9.
Lopez, E., E. Abisset-Chavanne, C. Ghnatios, S. Comas-Cardona, C. Binetruy, and F. Chinesta. 2014. “Towards image-based homogenization by combining scanning techniques and reduced order modelling.” In ECCM-16th European Conf. on Composite Materials. Nantes, France: European Conference on Composite Materials.
Nazar, A. M., F. A. Silva, and J. J. Ammann. 1996. “Image processing for particle characterization.” Mater. Charact. 36 (4–5): 165–173. https://doi.org/10.1016/S1044-5803(96)00044-7.
Nguyen, V. D., E. Béchet, C. Geuzaine, and L. Noels. 2012. “Imposing periodic boundary condition on arbitrary meshes by polynomial interpolation.” Comput. Mater. Sci. 55 (Apr): 390–406. https://doi.org/10.1016/j.commatsci.2011.10.017.
Nguyen, V. D., and L. Noels. 2014. “Computational homogenization of cellular materials.” Int. J. Solids Struct. 51 (11–12): 2183–2203. https://doi.org/10.1016/j.ijsolstr.2014.02.029.
Ren, W., Z. Yang, R. Sharma, C. Zhang, and P. J. Withers. 2015. “Two-dimensional X-ray CT image based meso-scale fracture modelling of concrete.” Eng. Fract. Mech. 133 (Jan): 24–39. https://doi.org/10.1016/j.engfracmech.2014.10.016.
Rendl, F. 1988. “On the Euclidean assignment problem.” J. Comput. Appl. Math. 23 (3): 257–265. https://doi.org/10.1016/0377-0427(88)90001-5.
Segurado, J., and J. Llorca. 2002. “A numerical approximation to the elastic properties of sphere-reinforced composites.” J. Mech. Phys. Solids 50 (10): 2107–2121. https://doi.org/10.1016/S0022-5096(02)00021-2.
Sjolund, J., A. Karakoc, and J. Freund. 2014. “Accuracy of regular wood cell structure model.” Mech. Mater. 76 (Sep): 35–44. https://doi.org/10.1016/j.mechmat.2014.06.003.
Soden, P. D., M. J. Hinton, and A. S. Kaddour. 1998. “Lamina properties, lay-up configurations and loading conditions for a range of fibre-reinforced composite laminates.” Compos. Sci. Technol. 58 (7): 1011–1022. https://doi.org/10.1016/S0266-3538(98)00078-5.
Takano, N., M. Zako, F. Kubo, and K. Kimura. 2003. “Microstructure-based stress analysis and evaluation for porous ceramics by homogenization method with digital image-based modeling.” Int. J. Solids Struct. 40 (5): 1225–1242. https://doi.org/10.1016/S0020-7683(02)00642-X.
Terada, K., T. Miura, and N. Kikuchi. 1997. “Digital image-based modeling applied to the homogenization analysis of composite materials.” Comput. Mech. 20 (4): 331–346. https://doi.org/10.1007/s004660050255.
Tyrus, J. M., M. Gosz, and E. DeSantiago. 2007. “A local finite element implementation for imposing periodic boundary conditions on composite micromechanical models.” Int. J. Solids Struct. 44 (9): 2972–2989. https://doi.org/10.1016/j.ijsolstr.2006.08.040.
Yuan, Z., and J. Fish. 2008. “Toward realization of computational homogenization in practice.” Int. J. Numer. Methods Eng. 73 (3): 361–380. https://doi.org/10.1002/nme.2074.
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©2019 American Society of Civil Engineers.
History
Received: Oct 12, 2018
Accepted: Jun 19, 2019
Published online: Dec 9, 2019
Published in print: Feb 1, 2020
Discussion open until: May 9, 2020
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