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A pruning algorithm preserving modeling capabilities for polycrystalline data. (English) Zbl 1479.74118

Summary: We are exploring the idea of data pruning via hyperreduction modeling. The main novelty of this paper is a lossy data compression/decompression approach for ploycrystalline data, which is based on a hyperreduction scheme that preserves data driven modeling capabilities after compression. We assume to know a mechanical model whose equations are satisfied by the data. It is shown that the proposed reconstruction of the data performs an oblique projection of selected original data. This is achieved by the solution of reduced mechanical equations. High resolution crystal plasticity finite element simulations demand computational and storage resources that are unusual, especially in cases where hundreds of grains are interacting under cyclic loading. The development of image-based modeling via computed tomography highlights the problem of long-term storage of simulation data by using data pruning. The present paper focuses on modeling cyclic strain-ratcheting as an example of numerical modeling that the proposed algorithm preserves. The size of the remaining sampled data can be user-defined, depending on the needs concerning storage space. The relevance of the pruned data is tested afterwards for statistics on the predicted strain, as if full finite element data were available. The proposed method is compared to the Gappy POD method, when no additional modeling step is expected after data pruning.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74E15 Crystalline structure
74C20 Large-strain, rate-dependent theories of plasticity

Software:

MUMPS; SciPy; Python; Z-set; Voro++
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Alharbi, HF; Kalidindi, SR, Crystal plasticity finite element simulations using a database of discrete Fourier transforms, Int J Plast, 66, 71-84 (2015) · doi:10.1016/j.ijplas.2014.04.006
[2] Bacry, E.; Gaiffas, S.; Leroy, F.; Morel, M.; Nguyen, DP; Sebiat, Y.; Sun, D., Scalpel3: a scalable open-source library for healthcare claims databases, Int J Med Inform, 141, 104203 (2020) · doi:10.1016/j.ijmedinf.2020.104203
[3] Barrault M, Maday Y, Nguyen N, Patera A (2004) An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations. C R Math Acad Sci Paris Ser I 339:667-672 · Zbl 1061.65118
[4] Bashtannyk, D.; Hyndman, R., Bandwidth selection for kernel conditional density estimation, Comput Stat Data Anal, 36, 279-298 (2001) · Zbl 1038.62034 · doi:10.1016/S0167-9473(00)00046-3
[5] Besson, J.; Cailletaud, G.; Chaboche, J.; Forest, S., Non-linear mechanics of materials (2009), Berlin: Springer, Berlin · Zbl 0997.74002
[6] Bhattacharyya, M.; Fau, A.; Nackenhorst, U.; Néron, D.; Ladevèze, P., A multi-temporal scale model reduction approach for the computation of fatigue damage, Comput Methods Appl Mech Eng, 340, 630-656 (2018) · Zbl 1440.74022 · doi:10.1016/j.cma.2018.06.004
[7] Boucard, PA; Ladevèze, P.; Poss, M.; Rougée, P., A nonincremental approach for large displacement problems, Comput Struct, 64, 1, 499-508 (1997) · Zbl 0919.73167 · doi:10.1016/S0045-7949(96)00165-4
[8] Busso, EP; Cailletaud, G., On the selection of active slip systems in crystal plasticity, Int J Plast, 21, 11, 2212-2231 (2005) · Zbl 1330.74045 · doi:10.1016/j.ijplas.2005.03.019
[9] Chaturantabut, S.; Sorensen, D., Nonlinear model reduction via discrete empirical interpolation, SIAM J Sci Comput, 32, 5, 2737-2764 (2010) · Zbl 1217.65169 · doi:10.1137/090766498
[10] Chinesta, F.; Ladeveze, P.; Ibanez, R.; Aguado, JV; Abisset-Chavanne, E.; Cueto, E., Data-driven computational plasticity, Procedia Eng, 207, 209-214 (2017) · Zbl 1387.74015 · doi:10.1016/j.proeng.2017.10.763
[11] Cruzado A, Lorca J, Segurado J (2017) Modeling cyclic deformation of inconel 718 superalloy by means of crystal plasticity and computational homogenization. Int J Solids Struct 122-123:148-161. doi:10.1016/j.ijsolstr.2017.06.014
[12] Everson, R.; Sirovich, L., Karhunen-Loève procedure for gappy data, J Opt Soc Am A, 12, 1657-1664 (1995) · doi:10.1364/JOSAA.12.001657
[13] Farhat, C.; Avery, P.; Chapman, T.; Cortial, J., Dimensional reduction of nonlinear finite element dynamic models with finite rotations and energy-based mesh sampling and weighting for computational efficiency, Int J Numer Methods Eng, 98, 9, 625-662 (2014) · Zbl 1352.74348 · doi:10.1002/nme.4668
[14] Farooq, H.; Cailletaud, G.; Forest, S.; Ryckelynck, D., Crystal plasticity modeling of the cyclic behavior of polycrystalline aggregates under non-symmetric uniaxial loading: Global and local analyses, Int J Plast, 126, 102619 (2019) · doi:10.1016/j.ijplas.2019.10.007
[15] Fauque, J.; Ramière, I.; Ryckelynck, D., Hybrid hyper-reduced modeling for contact mechanics problems, Int J Numer Methods Eng, 115, 1, 309-317 (2018) · doi:10.1002/nme.5798
[16] Forest, S.; Rubin, M., A rate-independent crystal plasticity model with a smooth elastic-plastic transition and no slip indeterminacy, Eur J Mech A Solids, 55, 278-288 (2016) · Zbl 1406.74114 · doi:10.1016/j.euromechsol.2015.08.012
[17] Franciosi, P.; Berbenni, S., Heterogeneous crystal and poly-crystal plasticity modeling from a transformation field analysis within a regularized Schmid law, J Mech Phys Solids, 55, 11, 2265-2299 (2007) · Zbl 1171.74011 · doi:10.1016/j.jmps.2007.04.012
[18] Frankel, A.; Jones, R.; Alleman, C.; Templeton, J., Predicting the mechanical response of oligocrystals with deep learning, Comput Mater Sci, 169, 109099 (2019) · doi:10.1016/j.commatsci.2019.109099
[19] Fritzen, F.; Hassani, M., Space-time model order reduction for nonlinear viscoelastic systems subjected to long-term loading, Meccanica, 53, 6, 1333-1355 (2018) · doi:10.1007/s11012-017-0734-x
[20] Fritzen, F.; Leuschner, M., Reduced basis hybrid computational homogenization based on a mixed incremental formulation, Comput Methods Appl Mech Eng, 260, 143-154 (2013) · Zbl 1286.74081 · doi:10.1016/j.cma.2013.03.007
[21] Gao, H.; Wang, JX; Zahr, MJ, Non-intrusive model reduction of large-scale, nonlinear dynamical systems using deep learning, Physica D, 412, 132614 (2020) · Zbl 1489.93013 · doi:10.1016/j.physd.2020.132614
[22] Gérard, C.; Cailletaud, G.; Bacroix, B., Modeling of latent hardening produced by complex loading paths in FCC alloys, Int J Plast, 42, 194-212 (2013) · doi:10.1016/j.ijplas.2012.10.010
[23] Gu T, Medy JR, Klosek V, Castelnau O, Forest S, Hervé-Luanco E, Lecouturier-Dupouy F, Proudhon H, Renault PO, Thilly L, Villechaise P (2019) Multiscale modeling of the elasto-plastic behavior of architectured and nanostructured Cu-Nb composite wires and comparison with neutron diffraction experiments. Int J Plast
[24] Hernández, J.; Oliver, J.; Huespe, A.; Caicedo, M.; Cante, J., High-performance model reduction techniques in computational multiscale homogenization, Comput Methods Appl Mech Eng, 276, 149-189 (2014) · Zbl 1423.74785 · doi:10.1016/j.cma.2014.03.011
[25] Hilth W, Ryckelynck D, Menet C (2019) Data pruning of tomographic data for the calibration of strain localization models. Math Comput Appl 24(1)
[26] 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, 13, 3647-3679 (2003) · Zbl 1038.74605 · doi:10.1016/S0020-7683(03)00143-4
[27] Karhunen, K., Zur spektraltheorie stochastischer prozesse, Ann Acad Sci Finnicae Ser A, 1, 34 (1946) · Zbl 0030.20103
[28] Kotha, S.; Ozturk, D.; Ghosh, S., Parametrically homogenized constitutive models (phcms) from micromechanical crystal plasticity fe simulations, part i: sensitivity analysis and parameter identification for titanium alloys, Int J Plast, 120, 296-319 (2019) · doi:10.1016/j.ijplas.2019.05.008
[29] Lee, K.; Carlberg, KT, Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders, J Comput Phys, 404, 108973 (2020) · Zbl 1454.65184 · doi:10.1016/j.jcp.2019.108973
[30] Liu, Z.; Bessa, M.; Liu, WK, Self-consistent clustering analysis: an efficient multi-scale scheme for inelastic heterogeneous materials, Comput Methods Appl Mech Eng, 306, 319-341 (2016) · Zbl 1436.74070 · doi:10.1016/j.cma.2016.04.004
[31] Loève, M., Probability theory. The university series in higher mathematics, NJ (1963), Princeton: Van Nosterand, Princeton · Zbl 0108.14202
[32] Lorenz EN (1956) Empirical orthogonal functions and statistical weather prediction. Stat Forecast 1
[33] Masui, K.; Amiri, M.; Connor, L.; Deng, M.; Fandino, M.; Höfer, C.; Halpern, M.; Hanna, D.; Hincks, A.; Hinshaw, G.; Parra, J.; Newburgh, L.; Shaw, J.; Vanderlinde, K., A compression scheme for radio data in high performance computing, Astron Comput, 12, 181-190 (2015) · doi:10.1016/j.ascom.2015.07.002
[34] Matouš, K.; Geers, MG; Kouznetsova, VG; Gillman, A., A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials, J Comput Phys, 330, 192-220 (2017) · doi:10.1016/j.jcp.2016.10.070
[35] Méric L, Poubanne P, Cailletaud G (1991) Single crystal modeling for structural calculations: part 1—model presentation. J Eng Mater Technol 113
[36] Michel, J.; Suquet, P., Nonuniform transformation field analysis, Int J Solids Struct, 40, 25, 6937-6955 (2003) · Zbl 1057.74031 · doi:10.1016/S0020-7683(03)00346-9
[37] Olivier, C.; Ryckelynck, D.; Cortial, J., Multiple tensor train approximation of parametric constitutive equations in elasto-viscoplasticity, Math Comput Appl (2019) · doi:10.3390/mca24010017
[38] Pelle, JP; Ryckelynck, D., An efficient adaptive strategy to master the global quality of viscoplastic analysis, Comput Struct, 78, 1, 169-183 (2000) · doi:10.1016/S0045-7949(00)00107-3
[39] Prithivirajan, V.; Sangid, MD, The role of defects and critical pore size analysis in the fatigue response of additively manufactured in718 via crystal plasticity, Mater Des, 150, 139-153 (2018) · doi:10.1016/j.matdes.2018.04.022
[40] Rovinelli, A.; Sangid, MD; Proudhon, H.; Guilhem, Y.; Lebensohn, RA; Ludwig, W., Predicting the 3d fatigue crack growth rate of small cracks using multimodal data via Bayesian networks: in-situ experiments and crystal plasticity simulations, J Mech Phys Solids, 115, 208-229 (2018) · doi:10.1016/j.jmps.2018.03.007
[41] Ryckelynck, D., A priori hyperreduction method: an adaptive approach, J Comput Phys, 202, 1, 346-366 (2005) · Zbl 1288.65178 · doi:10.1016/j.jcp.2004.07.015
[42] Ryckelynck, D., Hyper-reduction of mechanical models involving internal variables, Int J Numer Methods Eng, 77, 1, 75-89 (2009) · Zbl 1195.74299 · doi:10.1002/nme.2406
[43] Ryckelynck, D.; Lampoh, K.; Quilici, S., Hyper-reduced predictions for lifetime assessment of elasto-plastic structures, Meccanica, 51, 2, 309-317 (2016) · doi:10.1007/s11012-015-0244-7
[44] Ryckelynck D, Missoum-Benziane D, Musienko A, Cailletaud G (2010) Toward “green” mechanical simulations in materials science: hyper-reduction of a polycrystal plasticity model. Revue Européenne de Mécanique Numérique/European Journal of Computational Mechanics 19(4):365-388
[45] Rycroft C (2009) Voro++: a three-dimensional voronoi cell library in C++. Chaos 19. doi:10.1063/1.3215722
[46] Sedighiani, K.; Diehl, M.; Traka, K.; Roters, F.; Sietsma, J.; Raabe, D., An efficient and robust approach to determine material parameters of crystal plasticity constitutive laws from macro-scale stress-strain curves, Int J Plast, 134, 102779 (2020) · doi:10.1016/j.ijplas.2020.102779
[47] Shantsev DV, Jaysaval P, de la Kethulle de Ryhove S, Amestoy PR, Buttari A, L’Excellent JY, Mary T (2017) Large-scale 3-D EM modelling with a block low-rank multifrontal direct solver. Geophys J Int 209(3):1558-1571
[48] Sirovich L (1987) Turbulence and the dynamics of coherent structures, parts I, II and III. Q Appl Math XLV(3):561-590 · Zbl 0676.76047
[49] Sun F, Meade ED, ODowd NP (2018) Microscale modelling of the deformation of a martensitic steel using the voronoi tessellation method. J Mech Phys Solids 113:35-55
[50] Verwaerde, R.; Guidault, PA; Boucard, PA, A non-linear finite element connector model with friction and plasticity for the simulation of bolted assemblies, Finite Elem Anal Des, 195, 103586 (2021) · doi:10.1016/j.finel.2021.103586
[51] Virtanen P, Gommers R, Oliphant TE, Haberland M, Reddy T, Cournapeau D, Burovski E, Peterson P, Weckesser W, Bright J, van der Walt SJ, Brett M, Wilson J, Jarrod Millman K, Mayorov N, Nelson ARJ, Jones E, Kern R, Larson E, Carey C, Polat İ, Feng Y, Moore EW, Vand erPlas J, Laxalde D, Perktold J, Cimrman R, Henriksen I, Quintero EA, Harris CR, Archibald AM, Ribeiro AH, Pedregosa F, van Mulbregt P, Contributors S (2020) SciPy 1.0: fundamental algorithms for scientific computing in python. Nat Methods 17:261-272 . doi:10.1038/s41592-019-0686-2
[52] Wang P, Dong XH, Fu LJ (2010) Simulation of bulk metal forming processes using one-step finite element approach based on deformation theory of plasticity. Trans Nonferrous Met Soc China 20(2):276-282 . doi:10.1016/S1003-6326(09)60134-5
[53] Yagawa, G.; Shioya, R., Parallel finite elements on a massively parallel computer with domain decomposition, Comput Syst Eng, 4, 4, 495-503 (1993) · doi:10.1016/0956-0521(93)90017-Q
[54] Z-set package: non-linear material & structure analysis suite (2013). www.zset-software.com
[55] Zhang, H.; Diehl, M.; Roters, F.; Raabe, D., A virtual laboratory using high resolution crystal plasticity simulations to determine the initial yield surface for sheet metal forming operations, Int J Plast, 80, 111-138 (2016) · doi:10.1016/j.ijplas.2016.01.002
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