×

Adaptive spatiotemporal dimension reduction in concurrent multiscale damage analysis. (English) Zbl 1521.74213

Summary: Concurrent multiscale damage models are often used to quantify the impacts of manufacturing-induced micro-porosity on the damage response of macroscopic metallic components. However, these models are challenged by major numerical issues including mesh dependency, convergence difficulty, and low accuracy in concentration regions. In this paper, we make two contributions to address these difficulties. Firstly, we develop a novel adaptive assembly-free implicit-explicit (AAF-IE) temporal integration scheme for nonlinear constitutive models. This scheme prevents the convergence issues that implicit algorithms face amid softening. Our AAF-IE scheme autonomously adjusts step sizes to capture intricate history-dependent deformations. It also dispenses with re-assembling the stiffness matrices in elasto-plasticity and damage models which, in turn, dramatically reduces memory footprints. Secondly, we propose an adaptive clustering-based domain decomposition strategy to dramatically reduce the spatial degrees of freedom by agglomerating close-by finite element nodes into a limited number of clusters. Our adaptive clustering scheme has static and dynamic stages that are carried out during offline and online analyses, respectively. The adaptive strategy updates the cluster density based on the spatial discontinuity of the plastic strain. As demonstrated by numerical experiments, the proposed adaptive method strikes a good balance between efficiency and accuracy for fracture simulations. In particular, we use our efficient concurrent multiscale model to quantify the significance of spatially varying microscopic porosity on a macrostructure’s softening behavior.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74R20 Anelastic fracture and damage

References:

[1] Ammar, HR; Samuel, AM; Samuel, FH, Porosity and the fatigue behavior of hypoeutectic and hypereutectic aluminum-silicon casting alloys, Int J Fatigue, 30, 6, 1024-1035 (2008) · doi:10.1016/j.ijfatigue.2007.08.012
[2] Catalina, AV; Sen, S.; Stefanescu, DM; Kaukler, WF, Interaction of porosity with a planar solid/liquid interface, Metall Mater Trans A, 35, 5, 1525-1538 (2004) · doi:10.1007/s11661-004-0260-z
[3] Stefanescu, DM, Science and engineering of casting solidification (2015), Cham: Springer, Cham · doi:10.1007/978-3-319-15693-4
[4] Deng, S.; Soderhjelm, C.; Apelian, D.; Suresh, K., Estimation of elastic behaviors of metal components containing process induced porosity, Comput Struct, 254, 106558 (2021) · doi:10.1016/j.compstruc.2021.106558
[5] Deng, S.; Soderhjelm, C.; Apelian, D.; Suresh, K., Second-order defeaturing estimator of manufacturing-induced porosity on structural elasticity, Int J Num Methods Eng, 123, 19, 4483-4517 (2022) · Zbl 1534.74083 · doi:10.1002/nme.7042
[6] Geers, MGD; Kouznetsova, VG; Matouš, K.; Yvonnet, J.; Stein, E.; de Borst, R.; Hughes, TJR, Homogenization methods and multiscale modeling: nonlinear problems, Encyclopedia of computational mechanics, 1-34 (2017), Atlanta: American Cancer Society, Atlanta · doi:10.1002/9781119176817.ecm2107
[7] Collot, J., Review of new process technologies in the aluminum die-casting industry, Mater Manuf Process, 16, 5, 595-617 (2001) · doi:10.1081/AMP-100108624
[8] Hill, R., A self-consistent mechanics of composite materials, J Mech Phys Solids, 13, 4, 213-222 (1965) · doi:10.1016/0022-5096(65)90010-4
[9] Cook, RD; Malkus, DS; Plesha, ME; Witt, RJ, Concepts and applications of finite element analysis (2001), New York: Wiley, New York
[10] de Geus, TWJ; Vondřejc, J.; Zeman, J.; Peerlings, RHJ; Geers, MGD, Finite strain FFT-based non-linear solvers made simple, Comput Methods Appl Mech Eng, 318, 412-430 (2017) · Zbl 1439.74045 · doi:10.1016/j.cma.2016.12.032
[11] To, Q-D; Bonnet, G., FFT based numerical homogenization method for porous conductive materials, Comput Methods Appl Mech Eng, 368, 113160 (2020) · Zbl 1506.74331 · doi:10.1016/j.cma.2020.113160
[12] Dvorak, GJ, Transformation field analysis of inelastic composite materials, Proc R Soc Lond Ser A Math Phys Sci, 437, 1900, 311-327 (1992) · Zbl 0748.73007 · doi:10.1098/rspa.1992.0063
[13] Roussette, S.; Michel, JC; Suquet, P., Nonuniform transformation field analysis of elastic-viscoplastic composites, Compos Sci Technol, 69, 1, 22-27 (2009) · doi:10.1016/j.compscitech.2007.10.032
[14] Liu, Z.; Bessa, MA; 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
[15] Tang, S.; Zhang, L.; Liu, WK, From virtual clustering analysis to self-consistent clustering analysis: a mathematical study, Comput Mech, 62, 6, 1443-1460 (2018) · Zbl 1471.74079 · doi:10.1007/s00466-018-1573-x
[16] Cheng, G.; Li, X.; Nie, Y.; Li, H., FEM-Cluster based reduction method for efficient numerical prediction of effective properties of heterogeneous material in nonlinear range, Comput Methods Appl Mech Eng, 348, 157-184 (2019) · Zbl 1440.74383 · doi:10.1016/j.cma.2019.01.019
[17] Deng, S.; Soderhjelm, C.; Apelian, D.; Bostanabad, R., Reduced-order multiscale modeling of plastic deformations in 3D alloys with spatially varying porosity by deflated clustering analysis, Comput Mech, 70, 517-548 (2022) · Zbl 1498.74015 · doi:10.1007/s00466-022-02177-8
[18] Bazant, ZP; Planas, J., Fracture and size effect in concrete and other quasibrittle materials (1997), New York: CRC Press, New York
[19] Bazant, ZP, Can multiscale-multiphysics methods predict softening damage and structural failure?, JMC (2010) · doi:10.1615/IntJMultCompEng.v8.i1.50
[20] Bažant, ZP; Oh, BH, Crack band theory for fracture of concrete, Mat Constr, 16, 3, 155-177 (1983) · doi:10.1007/BF02486267
[21] Bažant, ZP; Jirásek, M., Nonlocal integral formulations of plasticity and damage: survey of progress, J Eng Mech, 128, 11, 1119-1149 (2002) · doi:10.1061/(ASCE)0733-9399(2002)128:11(1119)
[22] Miehe, C.; Hofacker, M.; Schänzel, L-M; Aldakheel, F., Phase field modeling of fracture in multi-physics problems. Part II. Coupled brittle-to-ductile failure criteria and crack propagation in thermo-elastic-plastic solids, Comput Methods Appl Mech Eng, 294, 486-522 (2015) · Zbl 1423.74837 · doi:10.1016/j.cma.2014.11.017
[23] Zienkiewicz, OC; Taylor, RL; Zhu, JZ, The finite element method: its basis and fundamentals (2013), Oxford: Butterworth-Heinemann, Oxford · Zbl 1307.74005
[24] Rodrigues, EA; Manzoli, OL; Bitencourt, LAG; Bittencourt, TN; Sánchez, M., An adaptive concurrent multiscale model for concrete based on coupling finite elements, Comput Methods Appl Mech Eng, 328, 26-46 (2018) · Zbl 1439.74462 · doi:10.1016/j.cma.2017.08.048
[25] Lamichhane, BP; Wohlmuth, BI, Mortar finite elements for interface problems, Computing, 72, 3, 333-348 (2004) · Zbl 1055.65129 · doi:10.1007/s00607-003-0062-y
[26] Wohlmuth, BI, A mortar finite element method using dual spaces for the Lagrange multiplier, SIAM J Numer Anal, 38, 3, 989-1012 (2000) · Zbl 0974.65105 · doi:10.1137/S0036142999350929
[27] Boyd, S.; Vandenberghe, L., Convex optimization (2004), Cambridge: Cambridge University Press, Cambridge · Zbl 1058.90049 · doi:10.1017/CBO9780511804441
[28] Ferreira BP, Pires FMA, Bessa MA (2021) Adaptive clustering-based reduced-order modeling framework: fast and accurate modeling of localized history-dependent phenomena. arXiv:2109.11897 [cond-mat]. Accessed 10 Jan 2022 [Online]. arXiv:abs/2109.11897
[29] Otero, F.; Oller, S.; Martinez, X., Multiscale computational homogenization: review and proposal of a new enhanced-first-order method, Arch Comput Methods Eng, 25, 2, 479-505 (2018) · Zbl 1392.74079 · doi:10.1007/s11831-016-9205-0
[30] Belytschko, T.; Liu, WK; Moran, B.; Elkhodary, K., Nonlinear finite elements for continua and structures (2014), Chichester: Wiley, Chichester
[31] Liu, Z.; Fleming, M.; Liu, WK, 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 · doi:10.1016/j.cma.2017.11.005
[32] ABAQUS/Standard User’s Manual, Version 6.9./Smith, Michael (2009). Dassault Systèmes Simulia Corp, Providence
[33] Simo, JC; Ju, JW, Strain and stress based continuum damage models, Int J Solids Struct, 23, 7, 821-840 (1987) · Zbl 0634.73106 · doi:10.1016/0020-7683(87)90083-7
[34] Oliver, J.; Huespe, AE; Cante, JC, An implicit/explicit integration scheme to increase computability of non-linear material and contact/friction problems, Comput Methods Appl Mech Eng, 197, 21, 1865-1889 (2008) · Zbl 1194.74507 · doi:10.1016/j.cma.2007.11.027
[35] Ciampi, V., M. A. Crisfield, Non-linear finite element analysis of solids and structures, Meccanica, 6, 32, 586-587 (1997) · Zbl 0890.73001 · doi:10.1023/A:1004259118876
[36] Prazeres, PGC; Bitencourt, LAG; Bittencourt, TN; Manzoli, OL, A modified implicit-explicit integration scheme: an application to elastoplasticity problems, J Braz Soc Mech Sci Eng, 38, 1, 151-161 (2016) · doi:10.1007/s40430-015-0343-3
[37] Likas, A.; Vlassis, N.; Verbeek, JJ, The global k-means clustering algorithm, Pattern Recogn, 36, 2, 451-461 (2003) · doi:10.1016/S0031-3203(02)00060-2
[38] Wang K, Zhang J, Li D, Zhang X, Guo T (2008) Adaptive affinity propagation clustering. arXiv:0805.1096 [cs]. Accessed 10 Jan 10 [Online]. arXiv:abs/0805.1096 · Zbl 1164.68395
[39] Ackermann, MR; Blömer, J.; Kuntze, D.; Sohler, C., Analysis of agglomerative clustering, Algorithmica, 69, 1, 184-215 (2014) · Zbl 1307.68082 · doi:10.1007/s00453-012-9717-4
[40] von Luxburg, U., A tutorial on spectral clustering, Stat Comput, 17, 4, 395-416 (2007) · doi:10.1007/s11222-007-9033-z
[41] Giancarlo, R.; Scaturro, D.; Utro, F., Computational cluster validation for microarray data analysis: experimental assessment of Clest, Consensus Clustering, Figure of Merit, Gap Statistics and Model Explorer, BMC Bioinform, 9, 1, 462 (2008) · doi:10.1186/1471-2105-9-462
[42] Integration K-Means Clustering Method and Elbow Method For Identification of The Best Customer Profile Cluster - IOPscience. https://iopscience.iop.org/article/10.1088/1757-899X/336/1/012017/meta. Accessed 10 Jan 2022
[43] Aranganayagi S, Thangavel K (2007) Clustering categorical data using silhouette coefficient as a relocating measure. In: International conference on computational intelligence and multimedia applications (ICCIMA 2007), vol 2, pp 13-17. doi:10.1109/ICCIMA.2007.328
[44] Łukasik S, Kowalski PA, Charytanowicz M, Kulczycki P (2016) Clustering using flower pollination algorithm and Calinski-Harabasz index. In: 2016 IEEE Congress on Evolutionary Computation (CEC), pp 2724-2728. doi:10.1109/CEC.2016.7744132.
[45] Ainsworth, M.; Oden, JT, A posteriori error estimation in finite element analysis, Comput Methods Appl Mech Eng, 142, 1, 1-88 (1997) · Zbl 0895.76040 · doi:10.1016/S0045-7825(96)01107-3
[46] Hardin, RA; Beckermann, C., Effect of porosity on deformation, damage, and fracture of cast steel, Metall Mater Trans A, 44, 12, 5316-5332 (2013) · doi:10.1007/s11661-013-1669-z
[47] Shakoor, M.; Gao, J.; Liu, Z.; Liu, WK; Griebel, M.; Schweitzer, MA, A data-driven multiscale theory for modeling damage and fracture of composite materials, Meshfree methods for partial differential equations IX, 135-148 (2019), Cham: Springer, Cham · Zbl 1428.74229 · doi:10.1007/978-3-030-15119-5_8
[48] Liu, Z., Deep material network with cohesive layers: multi-stage training and interfacial failure analysis, Comput Methods Appl Mech Eng, 363, 112913 (2020) · Zbl 1436.74015 · doi:10.1016/j.cma.2020.112913
[49] Xie, Y.; Li, S., A stress-driven computational homogenization method based on complementary potential energy variational principle for elastic composites, Comput Mech, 67, 2, 637-652 (2021) · Zbl 07360522 · doi:10.1007/s00466-020-01953-8
[50] Bishara, D.; Xie, Y.; Liu, WK; Li, S., A state-of-the-art review on machine learning-based multiscale modeling, simulation, homogenization and design of materials, Arch Comput Methods Eng, 30, 1, 191-222 (2023) · doi:10.1007/s11831-022-09795-8
[51] Xie, Y.; Li, S., Finite temperature atomistic-informed crystal plasticity finite element modeling of single crystal tantalum (α-Ta) at micron scale, Int J Numer Methods Eng, 122, 17, 4660-4697 (2021) · Zbl 07863865 · doi:10.1002/nme.6741
[52] Zhang, L-W; Xie, Y.; Lyu, D.; Li, S., Multiscale modeling of dislocation patterns and simulation of nanoscale plasticity in body-centered cubic (BCC) single crystals, J Mech Phys Solids, 130, 297-319 (2019) · Zbl 1452.74026 · doi:10.1016/j.jmps.2019.06.006
[53] Xie, Y.; Li, S., Geometrically-compatible dislocation pattern and modeling of crystal plasticity in body-centered cubic (BCC) crystal at micron scale, Comput Model Eng Sci, 129, 3, 1419-1440 (2021) · doi:10.32604/cmes.2021.016756
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.