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A GFEM-based reduced-order homogenization model for heterogeneous materials under volumetric and interfacial damage. (English) Zbl 07340386
Summary: This manuscript presents a multiscale reduced-order modeling framework for heterogeneous materials that accounts for both cohesive interface failure and continuum damage. The model builds on the eigendeformation-based reduced-order homogenization model (EHM), which relies on the pre-calculation of a set of coefficient tensors that account for the effects of linear and nonlinear material behavior between regions of the domain known as parts. A \(k\)-means clustering algorithm is used to optimally construct these parts and a new formulation for the partitioning of interfaces using this method is proposed. The extraction of the volumetric and interfacial influence functions is performed using the Interface-enriched Generalized Finite Element Method (IGFEM), which relies on a finite element discretization that does not conform to the material phase boundaries. A Lagrange multiplier method is used in this preprocessing phase, allowing for the reuse of the matrix factorization for different influence function problems and hence leading to efficiency improvement. A newly proposed traction calculation for the interface partition is also adopted to alleviate the instability caused by traction calculations along interfaces. The accuracy and efficiency of the IGFEM-EHM method is assessed through comparison with reference IGFEM simulations. The method is then used to extract the nonlinear multiscale response of particulate, unidirectional fiber-reinforced, and woven composites.
MSC:
74 Mechanics of deformable solids
78 Optics, electromagnetic theory
Software:
VCFEM-HOMO
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References:
[1] Nairn, J. A., Matrix microcracking in composites, (Kelly, A.; Zweben, C., Comprehensive Composite Materials Volume 2: Polymer Matrix Composites (2000), Elsevier Ltd), 403-432, (Chapter 12)
[2] Babuška, I., Homogenization and its application. Mathematical and computational problems, (Numerical Solution of Partial Differential Equations-III (1975), Academic Press), 89-116
[3] Bensoussan, A.; Lions, J.-L.; Papanicolaou, G., Asymptotic Analysis for Periodic Structures, Vol. 5 (1978), American Mathematical Society · Zbl 0411.60078
[4] Sanchez-Palencia, E., Homogenization method for the study of composite media, (Asymptotic Analysis II. Asymptotic Analysis II, Lecture Notes in Mathematics (1983), Springer), 192-214
[5] Guedes, J. M.; Kikuchi, N., Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods, Comput. Methods Appl. Mech. Engrg., 83, 143-198 (1990) · Zbl 0737.73008
[6] Dvorak, G. J., Transformation field analysis of inelastic composite materials, Proc. R. Soc. A: Math. Phys. Eng. Sci., 437, 311-327 (1992) · Zbl 0748.73007
[7] Ghosh, S.; Lee, K.; Moorthy, S., Two scale analysis of heterogeneous elastic-plastic materials with asymptotic homogenization and voronoi cell finite element model, Comput. Methods Appl. Mech. Engrg., 132, 1, 63-116 (1996) · Zbl 0892.73061
[8] Miehe, C.; Schröder, J.; Schotte, J., Computational homogenization analysis in finite plasticity simulation of texture development in polycrystalline materials, Comput. Methods Appl. Mech. Engrg., 171, 387-418 (1999) · Zbl 0982.74068
[9] Feyel, F.; Chaboche, J.-L., FE2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials, Comput. Methods Appl. Mech. Engrg., 183, 309-330 (2000) · Zbl 0993.74062
[10] Matouš, K.; Geers, M. G.; Kouznetsova, V. G.; Gillman, A., A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials, J. Comput. Phys., 330, 192-220 (2017)
[11] Mosby, M.; Matouš, K., Computational homogenization at extreme scales, Extreme Mech. Lett., 6, 68-74 (2016)
[12] De Rahul, S., Analysis of the Jacobian-free multiscale method (JFMM), Comput. Mech., 56, 5, 769-783 (2015) · Zbl 1329.74285
[13] Yvonnet, J.; He, Q., The reduced model multiscale method (r3m) for the non-linear homogenization of hyperelastic media at finite strains, J. Comput. Phys., 223, 1, 341-368 (2007) · Zbl 1163.74048
[14] Hernández, J. A.; Oliver, J.; Huespe, A. E.; Caicedo, M. A.; Cante, J. C., High-performance model reduction techniques in computational multiscale homogenization, Comput. Methods Appl. Mech. Engrg., 276, 149-189 (2014) · Zbl 1423.74785
[15] Moulinec, H.; Suquet, P., A numerical method for computing the overall response of nonlinear composites with complex microstructure, Comput. Methods Appl. Mech. Engrg., 157, 69-94 (1998) · Zbl 0954.74079
[16] Sharma, L.; Peerlings, R. H.; Shanthraj, P.; Roters, F.; Geers, M. G., An FFT-based spectral solver for interface decohesion modelling using a gradient damage approach, Comput. Mech., 1-15 (2019)
[17] Liu, Z.; Bessa, M. A.; Liu, W. K., Self-consistent clustering analysis: An efficient multi-scale scheme for inelastic heterogeneous materials, Comput. Methods Appl. Mech. Engrg., 306, 319-341 (2016) · Zbl 1436.74070
[18] Yu, C.; Kafka, O. L.; Liu, W. K., Self-consistent clustering analysis for multiscale modeling at finite strains, Comput. Methods Appl. Mech. Engrg., 349, 339-359 (2019) · Zbl 1441.74309
[19] Liu, Z.; Wu, C. T.; Koishi, M., A deep material network for multiscale topology learning and accelerated nonlinear modeling of heterogeneous materials, Comput. Methods Appl. Mech. Engrg., 345, 1138-1168 (2019) · Zbl 1440.74340
[20] Liu, Z., Deep material network with cohesive layers: Multi-stage training and interfacial failure analysis, Comput. Methods Appl. Mech. Engrg., 363, Article 112913 pp. (2020) · Zbl 1436.74015
[21] Michel, J.-C.; Suquet, P., Computational analysis of nonlinear composite structures using the nonuniform transformation field analysis, Comput. Methods Appl. Mech. Engrg., 193, 48-51, 5477-5502 (2004) · Zbl 1112.74471
[22] Oskay, C.; Fish, J., Eigendeformation-based reduced order homogenization for failure analysis of heterogeneous materials, Comput. Methods Appl. Mech. Engrg., 196, 7, 1216-1243 (2007) · Zbl 1173.74380
[23] Yuan, Z.; Fish, J., Multiple scale eigendeformation-based reduced order homogenization, Comput. Methods Appl. Mech. Engrg., 198, 2016-2038 (2009) · Zbl 1227.74051
[24] Zhang, X.; Oskay, C., Eigenstrain based reduced order homogenization for polycrystalline materials, Comput. Methods Appl. Mech. Engrg., 297, 408-436 (2015) · Zbl 1423.74796
[25] Zhang, X.; Oskay, C., Sparse and scalable eigenstrain-based reduced order homogenization models for polycrystal plasticity, Comput. Methods Appl. Mech. Engrg., 326, 241-269 (2017) · Zbl 1439.74328
[26] X. Zhang, Y. Liu, C. Oskay, Coupling crystal plasticity with structural mechanics for prediction of thermo-mechanical response in large scale structures, in: 6th European Conference on Computational Mechanics, Glasgow, UK, 2018.
[27] Liu, Y.; Zhang, X.; Zhu, Y.; Hu, P.; Oskay, C., Dislocation density informed eigenstrain based reduced order homogenization modeling: verification and application on a titanium alloy structure subjected to cyclic loading, Modelling Simulation Mater. Sci. Eng., 28, 2, Article 025004 pp. (2020)
[28] X. Zhang, Y. Liu, C. Oskay, Multiscale reduced-order modeling of a titanium skin panel subjected to thermo-mechanical loading, arXiv. arXiv:2011.03907.
[29] Yuan, Z.; Fish, J., Are the cohesive zone models necessary for delamination analysis?, Comput. Methods Appl. Mech. Engrg., 310, 567-604 (2016) · Zbl 1439.74033
[30] Oskay, C.; Su, Z.; Kapusuzoglu, B., Discrete eigenseparation-based reduced order homogenization method for failure modeling of composite materials, Comput. Methods Appl. Mech. Engrg., 359, Article 112656 pp. (2020) · Zbl 1441.74191
[31] Soghrati, S.; Geubelle, P. H., A 3D interface-enriched generalized finite element method for weakly discontinuous problems with complex internal geometries, Comput. Methods Appl. Mech. Engrg., 217, 46-57 (2012) · Zbl 1253.74117
[32] Ortiz, M.; Pandolfi, A., Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis, Internat. J. Numer. Methods Engrg., 44, 9, 1267-1282 (1999) · Zbl 0932.74067
[33] Phan, V.-T.; Zhang, X.; Li, Y.; Oskay, C., Microscale modeling of creep deformation and rupture in nickel-based superalloy IN 617 at high temperature, Mech. Mater., 114, 215-227 (2017)
[34] Giraldo-Londoño, O.; Spring, D. W.; Paulino, G. H.; Buttlar, W. G., An efficient mixed-mode rate-dependent cohesive fracture model using sigmoidal functions, Eng. Fract. Mech., 192, 307-327 (2018)
[35] Dvorak, G. J.; Benveniste, Y., On transformation strains and uniform fields in multiphase elastic media, Proc. R. Soc. A: Math. Phys. Eng. Sci., 437, 1900, 291-310 (1992) · Zbl 0748.73003
[36] Soghrati, S.; Aragón, A. M.; Armando Duarte, C.; Geubelle, P. H., An interface-enriched generalized FEM for problems with discontinuous gradient fields, Internat. J. Numer. Methods Engrg., 89, 8, 991-1008 (2012) · Zbl 1242.76138
[37] Soghrati, S.; Geubelle, P. H., A 3D interface-enriched generalized finite element method for weakly discontinuous problems with complex internal geometries, Comput. Methods Appl. Mech. Eng., 217-220, 46-57 (2012) · Zbl 1253.74117
[38] Aragon, A. M.; Simone, A., The discontinuity-enriched finite element method, Internat. J. Numer. Methods Engrg., 112, 1589-1613 (2017)
[39] Zhang, X.; Brandyberry, D. R.; Geubelle, P. H., IGFEM-Based shape sensitivity analysis of the transverse failure of a composite laminate, Comput. Mech., 64, 5, 1455-1472 (2019) · Zbl 07147413
[40] Shakiba, M.; Brandyberry, D. R.; Zacek, S.; Geubelle, P. H., Transverse failure of carbon fiber composites: Analytical sensitivity to the distribution of fiber/matrix interface properties, Internat. J. Numer. Methods Engrg., 120, 5, 650-665 (2019)
[41] Zacek, S.; Brandyberry, D.; Klepacki, A.; Montgomery, C.; Shakiba, M.; Rossol, M.; Najafi, A.; Zhang, X.; Sottos, N.; Geubelle, P.; Przybyla, C.; Jefferson, G., Transverse Failure of Unidirectional Composites: Sensitivity to Interfacial Properties, 329-347 (2020), Springer International Publishing: Springer International Publishing Cham
[42] Aragón, A. M.; Liang, B.; Ahmadian, H.; Soghrati, S., On the stability and interpolating properties of the hierarchical interface-enriched finite element method, Comput. Methods Appl. Mech. Engrg., 362, 112-671 (2020)
[43] Brandyberry, D. R.; Najafi, A. R.; Geubelle, P. H., Multiscale design of threedimensional nonlinear composites using an interfaceenriched generalized finite element method, Internat. J. Numer. Methods Engrg., 121, 12, 2806-2825 (2020)
[44] Fish, J., Practical Multiscaling (2014), John Wiley & Sons, Ltd
[45] Zhang, S.; Oskay, C., Reduced order variational multiscale enrichment method for elasto-viscoplastic problems, Comput. Methods Appl. Mech. Engrg., 300, 199-224 (2016) · Zbl 1425.74100
[46] Marfia, S.; Sacco, E., Computational homogenization of composites experiencing plasticity, cracking and debonding phenomena, Comput. Methods Appl. Mech. Eng., 304, 319-341 (2016) · Zbl 1425.74391
[47] Hu, R.; Oskay, C., Nonlocal homogenization model for wave dispersion and attenuation in elastic and viscoelastic periodic layered media, J. Appl. Mech., 84, 3, Article 031003 pp. (2017)
[48] Bogdanor, M. J.; Oskay, C., Prediction of progressive fatigue damage and failure behavior of im7/977-3 composites using the reduced-order multiple space-time homogenization approach, J. Compos. Mater., 51, 15, 2101-2117 (2017)
[49] Covezzi, F.; de Miranda, S.; Marfia, S.; Sacco, E., Multiscale analysis of nonlinear composites via a mixed reduced order formulation, Compos. Struct., 203, 810-825 (2018)
[50] Moyeda, A.; Fish, J., Multiscale analysis of solid, waffle, ribbed and hollowcore reinforced concrete slabs, Comput. Methods Appl. Mech. Engrg., 348, 139-156 (2019) · Zbl 1440.74200
[51] Sparks, P.; Oskay, C., Identification of optimal reduced order homogenization models for failure of heterogeneous materials, J. Multisc. Comput. Eng., 11, 185-200 (2013)
[52] Alaimo, G.; Auricchio, F.; Marfia, S.; Sacco, E., Optimization clustering technique for piecewise uniform transformation field analysis homogenization of viscoplastic composites, Comput. Mech., 64, 6, 1495-1516 (2019) · Zbl 07147415
[53] Lloyd, S. P., Least squares quantization in PCM, IEEE Trans. Inform. Theory, 28, 2, 129-137 (1982) · Zbl 0504.94015
[54] Arthur, D.; Vassilvitskii, S., K-Means++: The Advantages of Careful SeedingTech. rep. (2006)
[55] Kulkarni, M. G.; Geubelle, P. H.; Matouš, K., Multi-scale modeling of heterogeneous adhesives: Effect of particle decohesion, Mech. Mater., 41, 5, 573-583 (2009)
[56] Simo, J. C.; Ju, J. W., Strain- and stress-based continuum damage models-I. Formulation, Int. J. Solids Struct., 23, 7, 821-840 (1987) · Zbl 0634.73106
[57] Matouš, K.; Kulkarni, M. G.; Geubelle, P. H., Multiscale cohesive failure modeling of heterogeneous adhesives, Internat. J. Numer. Methods Engrg., 56, 4, 1511-1533 (2008) · Zbl 1171.74433
[58] A.R. Najafi, M. Safdari, D.A. Tortorelli, P.H. Geubelle, Multiscale design of nonlinear materials using an Eulerian shape optimization scheme, Int. J. Numer. Methods Engrg., accepted for publication. · Zbl 1423.74781
[59] Balay, S.; Abhyankar, S.; Adams, M. F.; Brown, J.; Brune, P.; Buschelman, K.; Dalcin, L.; Dener, A.; Eijkhout, V.; Gropp, W. D.; Karpeyev, D.; Kaushik, D.; Knepley, M. G.; May, D. A.; McInnes, L. C.; Mills, R. T.; Munson, T.; Rupp, K.; Sanan, P.; Smith, B. F.; Zampini, S.; Zhang, H.; Zhang, H., PETSC web page (2019), https://www.mcs.anl.gov/petsc
[60] Galassi, M.; Al, E., GNU Scientific Library Reference ManualTech. rep. (2019), GNU
[61] P. Geubelle, D. Brandyberry, M. Safdari, Par-IGFEM user’s manual.
[62] C. Daux, N. Moës, J. Dolbow, N. Sukumar, T. Belytschko, Arbitrary branched and intersecting cracks with the extended finite element method. Int. J. Numer. Methods Eng., (12) 1741-1760. http://dx.doi.org/10.1002/1097-0207(20000830)48:12<1741::AID-NME956>3.0.CO;2-L. · Zbl 0989.74066
[63] Moës, N.; Belytschko, T., Extended finite element method for cohesive crack growth, Eng. Fract. Mech., 69, 7, 813-833 (2002)
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