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Efficient multiscale modeling for woven composites based on self-consistent clustering analysis. (English) Zbl 1442.74057

Summary: Multiscale simulation of woven composites structure remains a challenge due to extremely expensive computational cost for solving the nonlinear woven Representative Volume Element (RVE). Recently, an effective and efficient Reduced Order modeling method, namely Self-consistent Clustering Analysis (SCA), is proposed to solve the RVE problem. In this work, the curse of computational cost in woven RVE problem is countered using the SCA, which maintains a considerable accuracy compared with the standard Finite Element Method (FEM). The Hill anisotropic yield surface is predicted efficiently using the woven SCA, which can accelerate the microstructure optimization and design of woven composites. Moreover, a two-scale FEM \(\times\) SCA modeling framework is proposed for woven composites structure. Based on this framework, the complex behavior of the composite structures in macroscale can be predicted using microscale properties. Additionally, macroscale and mesoscale physical fields are captured simultaneously, which are hard, if not impossible, to observe using experimental methods. This will expedite the deformation mechanism investigation of composites. A numerical study is carried out for T-shaped hooking structures under cycle loading to illustrate these advantages.

MSC:

74E30 Composite and mixture properties
62P35 Applications of statistics to physics
Full Text: DOI

References:

[1] Mouritz, A. P.; Bannister, M. K.; Falzon, P.; Leong, K., Manufacturing, review of applications for advanced three-dimensional fibre textile composites, Composites A, 30, 1445-1461 (1999)
[2] Ishikawa, T.; Chou, T.-W., Stiffness and strength behaviour of woven fabric composites, J. Mater. Sci., 17, 3211-3220 (1982)
[3] Park, H. S.; Karpov, E. G.; Klein, P. A.; Liu, W. K., Three-dimensional bridging scale analysis of dynamic fracture, J. Comput. Phys., 207, 588-609 (2005) · Zbl 1213.74267
[4] Kadowaki, H.; Liu, W. K., Bridging multi-scale method for localization problems, Comput. Methods Appl. Mech. Eng., 193, 3267-3302 (2004) · Zbl 1060.74504
[5] Wagner, G. J.; Liu, W. K., Coupling of atomistic and continuum simulations using a bridging scale decomposition, J. Comput. Phys., 190, 249-274 (2003) · Zbl 1169.74635
[6] Kouznetsova, V.; Geers, M. G.; Brekelmans, W. M., Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme, Internat. J. Numer. Methods Engrg., 54, 1235-1260 (2002) · Zbl 1058.74070
[7] Feyel, F.; Chaboche, J.-L., FE2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials, Comput. Methods Appl. Mech. Eng., 183, 309-330 (2000) · Zbl 0993.74062
[8] Gao, J.; Liang, B.; Zhang, W.; Liu, Z.; Cheng, P.; Bostanabad, R.; Cao, J.; Chen, W.; Liu, W. K.; Su, X., Multiscale modeling of carbon fiber reinforced polymer (CFRP) for integrated computational materials engineering process, (Ford Motor Company (2017))
[9] Bostanabad, R.; Liang, B.; Gao, J.; Liu, W. K.; Cao, J.; Zeng, D.; Su, X.; Xu, H.; Li, Y.; Chen, W., Uncertainty quantification in multiscale simulation of woven fiber composites, Comput. Methods Appl. Mech. Eng., 338, 506-532 (2018) · Zbl 1440.74102
[10] Kanit, T.; Forest, S.; Galliet, I.; Mounoury, V.; Jeulin, D., Determination of the size of the representative volume element for random composites: statistical and numerical approach, Int. J. Solids Struct., 40, 3647-3679 (2003) · Zbl 1038.74605
[11] Liu, Y. J.; Chen, X. L., Evaluations of the effective material properties of carbon nanotube-based composites using a nanoscale representative volume element, Mech. Mater., 35, 69-81 (2003)
[12] Sun, C. T.; Vaidya, R. S., Prediction of composite properties, from a representative volume element, Compos. Sci. Technol., 56, 171-179 (1996)
[13] Chen, X. L.; Liu, Y. J., Square representative volume elements for evaluating the effective material properties of carbon nanotube-based composites, Comput. Mater. Sci., 29, 1-11 (2004)
[14] Xia, Z. H.; Zhang, Y. F.; Ellyin, F., A unified periodical boundary conditions for representative volume elements of composites and applications, Int. J. Solids Struct., 40, 1907-1921 (2003) · Zbl 1048.74011
[15] Liu, Z.; Moore, J. A.; Liu, W. K., An extended micromechanics method for probing interphase properties in polymer nanocomposites, J. Mech. Phys. Solids, 95, 663-680 (2016)
[16] Mura, T., Micromechanics of Defects in Solids (2013), Springer Science & Business Media
[17] Hill, R., A self-consistent mechanics of composite materials, J. Mech. Phys. Solids, 13, 213-222 (1965)
[18] Eshelby, J. D., The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 241, 376-396 (1957) · Zbl 0079.39606
[19] Zhang, W.; Ren, H.; Liang, B.; Zeng, D.; Su, X.; Dahl, J.; Mirdamadi, M.; Zhao, Q.; Cao, J., A non-orthogonal material model of woven composites in the preforming process, CIRP Ann., 66, 257-260 (2017)
[20] Michel, J.-C.; Moulinec, H.; Suquet, P., Effective properties of composite materials with periodic microstructure: a computational approach, Comput. Methods Appl. Mech. Eng., 172, 109-143 (1999) · Zbl 0964.74054
[21] Moulinec, H.; Suquet, P., A numerical method for computing the overall response of nonlinear composites with complex microstructure, Comput. Methods Appl. Mech. Eng., 157, 69-94 (1998) · Zbl 0954.74079
[22] Dvorak, G.; Wafa, A.; Bahei-El-Din, Y., Implementation of the transformation field analysis for inelastic composite materials, Comput. Mech., 14, 201-228 (1994) · Zbl 0835.73038
[23] Dvorak, G., Transformation field analysis of inelastic composite materials, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 437, 311-327 (1992) · Zbl 0748.73007
[24] Roussette, S.; Michel, J.-C.; Suquet, P., Nonuniform transformation field analysis of elastic-viscoplastic composites, Compos. Sci. Technol., 69, 22-27 (2009)
[25] Michel, J.-C.; Suquet, P., Computational analysis of nonlinear composite structures using the nonuniform transformation field analysis, Comput. Methods Appl. Mech. Eng., 193, 5477-5502 (2004) · Zbl 1112.74471
[26] Michel, J.-C.; Suquet, P., Nonuniform transformation field analysis, Int. J. Solids Struct., 40, 6937-6955 (2003) · Zbl 1057.74031
[27] Ladevèze, P.; Passieux, J.-C.; Néron, D., The latin multiscale computational method and the proper generalized decomposition, Comput. Methods Appl. Mech. Eng., 199, 1287-1296 (2010) · Zbl 1227.74111
[28] Willcox, K.; Peraire, J., Balanced model reduction via the proper orthogonal decomposition, Aiaa J, 40, 2323-2330 (2002)
[29] Chatterjee, A., An introduction to the proper orthogonal decomposition, Current Sci., 808-817 (2000)
[30] Berkooz, G.; Holmes, P.; Lumley, J. L., The proper orthogonal decomposition in the analysis of turbulent flows, Annu. Rev. Fluid Mech., 25, 539-575 (1993)
[31] Özdemir, I.; Brekelmans, W.; Geers, M. G., FE2 computational homogenization for the thermo-mechanical analysis of heterogeneous solids, Comput. Methods Appl. Mech. Eng., 198, 602-613 (2008) · Zbl 1228.74065
[32] Liu, Z. L.; Bessa, M. A.; Liu, W. K., Self-consistent clustering analysis: An efficient multi-scale scheme for inelastic heterogeneous materials, Comput. Methods Appl. Mech., 306, 319-341 (2016) · Zbl 1436.74070
[33] Liu, Z.; Fleming, M.; Liu, W. K., Microstructural material database for self-consistent clustering analysis of elastoplastic strain softening materials, Comput. Methods Appl. Mech. Eng., 330, 547-577 (2018) · Zbl 1439.74063
[34] Liu, Z.; Kafka, O. L.; Yu, C.; Liu, W. K., Data-driven self-consistent clustering analysis of heterogeneous materials with crystal plasticity, (Advances in Computational Plasticity (2018), Springer), 221-242 · Zbl 1493.74017
[35] Bessa, M.; Bostanabad, R.; Liu, Z.; Hu, A.; Apley, D. W.; Brinson, C.; Chen, W.; Liu, W. K., A framework for data-driven analysis of materials under uncertainty: Countering the curse of dimensionality, Comput. Methods Appl. Mech. Eng., 320, 633-667 (2017) · Zbl 1439.74014
[36] Melro, A.; Camanho, P.; Pires, F. A.; Pinho, S., Micromechanical analysis of polymer composites reinforced by unidirectional fibres: Part I-Constitutive modelling, Int. J. Solids Struct., 50, 1897-1905 (2013)
[37] Ullah, Z.; Kaczmarczyk, L.; Pearce, C. J., Three-dimensional nonlinear micro/meso-mechanical response of the fibre-reinforced polymer composites, Compos. Struct., 161, 204-214 (2017)
[38] Naya, F.; González, C.; Lopes, C.; Van der Veen, S.; Pons, F., Manufacturing, computational micromechanics of the transverse and shear behavior of unidirectional fiber reinforced polymers including environmental effects, Composites A, 92, 146-157 (2017)
[39] Hill, R., A theory of the yielding and plastic flow of anisotropic metals, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 193, 281-297 (1948) · Zbl 0032.08805
[40] Zhang, H.; Guo, J.; Wen, W.; Cui, H.; He, S.; Xu, Y., Bending/tensile tests and simulations of the 2.5 D woven T-shaped hooking composite structure, Compos. Struct., 206, 155-163 (2018)
[41] Abaqus 6.10 online documentation (2010)
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