A Parametric, Data-Driven, Non-Intrusive Reduced-Order Model Framework for Crystal Plasticity Simulations of Voids

1. Allison J, Cowles B, DeLoach J, Pollock T, Spanos G et al (2013) Implementing ICME in the aerospace, automotive, and maritime industries. The Minerals Metals and Materials Society, Tech. Rep

2. Voorhees P, Spanos G et al (2015) Modeling across scales: a roadmapping study for connecting materials models and simulations across length and time scales. The Minerals Metals and Materials Society. Tech. Rep

3. Ward C, Scott J et al (2017) Building a materials data infrastructure: opening new pathways to discovery and innovation in science and engineering. The Minerals Metals and Materials Society, Tech. Rep

4. Roters F, Eisenlohr P, Hantcherli L, Tjahjanto DD, Bieler TR, Raabe D (2010) Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications. Acta Mater 58(4):1152–121110.1016/j.actamat.2009.10.058 ↗

5. Roters F, Eisenlohr P, Bieler TR, Raabe D (2011) Crystal plasticity finite element methods in materials science and engineering. John Wiley & Sons10.1002/9783527631483 ↗

6. Panchal JH, Kalidindi SR, McDowell DL (2013) Key computational modeling issues in integrated computational materials engineering. Comput Aided Des 45(1):4–2510.1016/j.cad.2012.06.006 ↗

7. Kalidindi SR, Medford AJ, McDowell DL (2016) Vision for data and informatics in the future materials innovation ecosystem. JOM 68(8):2126–213710.1007/s11837-016-2036-5 ↗

8. Arróyave R, McDowell DL (2019) Systems approaches to materials design: past, present, and future. Annu Rev Mater Res 49(1):103–12610.1146/annurev-matsci-070218-125955 ↗

9. Roters F, Diehl M, Shanthraj P, Eisenlohr P, Reuber C, Wong S, Maiti T, Ebrahimi A, Hochrainer T, Fabritius H-O, Nikolov S, Friák M, Fujita N, Grilli N, Janssens K, Jia N, Kok P, Ma D, Meier F, Werner E, Stricker M, Weygand D, Raabe D (2019) DAMASK-The Düsseldorf advanced material simulation Kit for modeling multi-physics crystal plasticity, thermal, and damage phenomena from the single crystal up to the component scale. Comput Mater Sci 158:420–47810.1016/j.commatsci.2018.04.030 ↗

10. Tran A, Robbe P, Rodgers T, Lim H (2023) Multi-fidelity uncertainty quantification for homogenization problems in structure-property relationships from crystal plasticity finite elements. JOM 76:3007–302010.1007/s11837-023-06182-x ↗

11. Tran A, Robbe P, Lim H (2023) Multi-fidelity microstructure-induced uncertainty quantification by advanced Monte Carlo methods. Materialia 27:10170510.1016/j.mtla.2023.101705 ↗

12. Bishop JE, Emery JM, Field RV, Weinberger CR, Littlewood DJ (2015) Direct numerical simulations in solid mechanics for understanding the macroscale effects of microscale material variability. Comput Methods Appl Mech Eng 287:262–28910.1016/j.cma.2015.01.017 ↗

13. Bishop JE, Emery JM, Battaile CC, Littlewood DJ, Baines AJ (2016) Direct numerical simulations in solid mechanics for quantifying the macroscale effects of microstructure and material model-form error. JOM 68(5):1427–144510.1007/s11837-016-1857-6 ↗

14. Brown JA, Bishop JE (2019) Modeling mechanical behavior of an additively manufactured metal structure with local texture variations: a study on model form error. Modell Simul Mater Sci Eng 27(2):02500310.1088/1361-651X/aaf107 ↗

15. Voce E (1948) The relationship between stress and strain for homogeneous deformation. J Inst Met 74:537–562

16. Swift H (1952) Plastic instability under plane stress. J Mech Phys Solids 1(1):1–1810.1016/0022-5096(52)90002-1 ↗

17. Hill R (1963) Elastic properties of reinforced solids: some theoretical principles. J Mech Phys Solids 11(5):357–37210.1016/0022-5096(63)90036-X ↗

18. Hosford WF, Caddell RM (2011) Metal forming: mechanics and metallurgy, Cambridge University Press10.1017/CBO9780511976940 ↗

19. Edwards HC, Trott CR, Sunderland D (2014) Kokkos: enabling manycore performance portability through polymorphic memory access patterns. J Parallel Distr Comput 74(12):3202–321610.1016/j.jpdc.2014.07.003 ↗

20. Trott CR, Lebrun-Grandié D, Arndt D, Ciesko J, Dang V, Ellingwood N, Gayatri R, Harvey E, Hollman DS, Ibanez D et al (2021) Kokkos 3: programming model extensions for the exascale era. IEEE Trans Parallel Distrib Syst 33(4):805–81710.1109/TPDS.2021.3097283 ↗

21. Hey T, Tansley S, Tolle KM (2009) The fourth paradigm: data-intensive scientific discovery, vol 1. Microsoft research Redmond, WA

22. Agrawal A, Choudhary A (2016) Perspective: materials informatics and big data: realization of the “fourth paradigm’’ of science in materials science. APL Mater 4(5):05320810.1063/1.4946894 ↗

23. Kalidindi SR (2015) Hierarchical materials informatics: novel analytics for materials data, Elsevier

24. Torquato S (2002) Statistical description of microstructures. Annu Rev Mater Res 32(1):77–11110.1146/annurev.matsci.32.110101.155324 ↗

25. Fast T, Kalidindi SR (2011) Formulation and calibration of higher-order elastic localization relationships using the MKS approach. Acta Mater 59(11):4595–460510.1016/j.actamat.2011.04.005 ↗

26. Yabansu YC, Patel DK, Kalidindi SR (2014) Calibrated localization relationships for elastic response of polycrystalline aggregates. Acta Mater 81:151–16010.1016/j.actamat.2014.08.022 ↗

27. Yabansu YC, Kalidindi SR (2015) Representation and calibration of elastic localization kernels for a broad class of cubic polycrystals. Acta Mater 94:26–3510.1016/j.actamat.2015.04.049 ↗

28. de Oca Zapiain DM, Popova E, Kalidindi SR (2017) Prediction of microscale plastic strain rate fields in two-phase composites subjected to an arbitrary macroscale strain rate using the materials knowledge system framework. Acta Mater 141:230–24010.1016/j.actamat.2017.09.016 ↗

29. Liu R, Yabansu YC, Agrawal A, Kalidindi SR, Choudhary AN (2015) Machine learning approaches for elastic localization linkages in high-contrast composite materials. Integr Mater Manuf Innov 4(1):13

30. Mianroodi JR, Siboni NH, Raabe D (2021) Teaching solid mechanics to artificial intelligence—a fast solver for heterogeneous materials. NPJ Comput Mater 7(1):9910.1038/s41524-021-00571-z ↗

31. Ronneberger O, Fischer P, Brox T (2015) U-net: Convolutional networks for biomedical image segmentation. In: Medical Image Computing and Computer-Assisted Intervention–MICCAI 2015: 18th International Conference, Munich, Germany, October 5-9, 2015, Proceedings, Part III 18, Springer, pp. 234–24110.1007/978-3-319-24574-4_28 ↗

32. Bhaduri A, Gupta A, Graham-Brady L (2022) Stress field prediction in fiber-reinforced composite materials using a deep learning approach. Compos B Eng 238:10987910.1016/j.compositesb.2022.109879 ↗

33. Bhaduri A, Ramachandra N, Krishnan Ravi S, Luan L, Pandita P, Balaprakash P, Anitescu M, Sun C, Wang L (2024) Efficient mapping between void shapes and stress fields using deep convolutional neural networks with sparse data. Journal of Computing and Information Science in Engineering 24 (5)10.1115/1.4064622 ↗

34. Liu R, Yabansu YC, Yang Z, Choudhary AN, Kalidindi SR, Agrawal A (2017) Context aware machine learning approaches for modeling elastic localization in three-dimensional composite microstructures. Integr Mater Manuf Innov 6(2):160–17110.1007/s40192-017-0094-3 ↗

35. Yang Z, Yabansu YC, Al-Bahrani R, Liao W-K, Choudhary AN, Kalidindi SR, Agrawal A (2018) Deep learning approaches for mining structure-property linkages in high contrast composites from simulation datasets. Comput Mater Sci 151:278–28710.1016/j.commatsci.2018.05.014 ↗

36. Yang Z, Yabansu YC, Jha D, Liao W-K, Choudhary AN, Kalidindi SR, Agrawal A (2019) Establishing structure-property localization linkages for elastic deformation of three-dimensional high contrast composites using deep learning approaches. Acta Mater 166:335–34510.1016/j.actamat.2018.12.045 ↗

37. Montes de Oca Zapiain D, Shanker A, Kalidindi SR (2022) Convolutional neural networks for the localization of plastic velocity gradient tensor in polycrystalline microstructures. J Eng Mater Technol 144(1):011004

38. Reddy KVK, Adlakha I, Gupta S, Roychowdhury S (2022) Crystal elasticity simulations of polycrystalline material using rank-one approximation. Integr Mater Manuf Innov 11(1):139–15710.1007/s40192-022-00253-8 ↗

39. Bonatti C, Berisha B, Mohr D (2022) From CP-FFT to CP-RNN: recurrent neural network surrogate model of crystal plasticity. Int J Plast 158:10343010.1016/j.ijplas.2022.103430 ↗

40. McDowell DL (2010) A perspective on trends in multiscale plasticity. Int J Plast 26(9):1280–130910.1016/j.ijplas.2010.02.008 ↗

41. Benner P, Gugercin S, Willcox K (2015) A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Rev 57(4):483–53110.1137/130932715 ↗

42. Hesthaven JS, Pagliantini C, Rozza G (2022) Reduced basis methods for time-dependent problems. Acta Numer 31:265–34510.1017/S0962492922000058 ↗

43. Xia D, Oskay C (2024) Proper orthogonal decomposition assisted eigendeformation-based mathematical homogenization method for modeling cracks in 3D polycrystalline microstructures. Comput Methods Appl Mech Eng 418:116508

44. Nasirov A, Zhang X, Wagner D, Yeratapally SR, Oskay C (2024) Achieving high efficiency in reduced order modeling for large scale polycrystal plasticity simulations. Finite Elem Anal Des 228:10405310.1016/j.finel.2023.104053 ↗

45. Menasche DB, Musinski WD, Obstalecki M, Shah MN, Donegan SP, Bernier JV, Kenesei P, Park J-S, Shade PA (2021) AFRL additive manufacturing modeling series: challenge 4, in situ mechanical test of an IN625 sample with concurrent high-energy diffraction microscopy characterization. Integr Mater Manuf Innov 10(3):338–34710.1007/s40192-021-00218-3 ↗

46. Chapman MG, Shah MN, Donegan SP, Scott JM, Shade PA, Menasche D, Uchic MD (2021) AFRL additive manufacturing modeling series: challenge 4, 3D reconstruction of an IN625 high-energy diffraction microscopy sample using multi-modal serial sectioning. Integr Mater Manuf Innov 10:129–14110.1007/s40192-021-00212-9 ↗

47. Tran A, Furlan JM, Pagalthivarthi KV, Visintainer RJ, Wildey T, Wang Y (2019) WearGP: a computationally efficient machine learning framework for local erosive wear predictions via nodal Gaussian processes. Wear 422:9–2610.1016/j.wear.2018.12.081 ↗

48. Casenave F, Akkari N, Bordeu F, Rey C, Ryckelynck D (2020) A nonintrusive distributed reduced-order modeling framework for nonlinear structural mechanics - Application to elastoviscoplastic computations. Int J Numer Meth Eng 121(1):32–5310.1002/nme.6187 ↗

49. Fritzen F, Kunc O (2018) Two-stage data-driven homogenization for nonlinear solids using a reduced order model. Eur J Mech A/Solids 69:201–22010.1016/j.euromechsol.2017.11.007 ↗

50. Daniel T, Casenave F, Akkari N, Ketata A, Ryckelynck D (2022) Physics-informed cluster analysis and a priori efficiency criterion for the construction of local reduced-order bases. J Comput Phys 458:11112010.1016/j.jcp.2022.111120 ↗

51. Huang D, Fuhg JN, Weißenfels C, Wriggers P (2020) A machine learning based plasticity model using proper orthogonal decomposition. Comput Methods Appl Mech Eng 365:11300810.1016/j.cma.2020.113008 ↗

52. Fauque J, Ramière I, Ryckelynck D (2018) Hybrid hyper-reduced modeling for contact mechanics problems. Int J Numer Meth Eng 115(1):117–13910.1002/nme.5798 ↗

53. Buljak V, Maier G (2011) Proper orthogonal decomposition and radial basis functions in material characterization based on instrumented indentation. Eng Struct 33(2):492–50110.1016/j.engstruct.2010.11.006 ↗

54. Guo M, Hesthaven JS (2019) Data-driven reduced order modeling for time-dependent problems. Comput Methods Appl Mech Eng 345:75–9910.1016/j.cma.2018.10.029 ↗

55. Tu JH (2013) Dynamic mode decomposition: Theory and applications, Ph.D. thesis, Princeton University

56. Kutz JN, Brunton SL, Brunton BW, Proctor JL (2016) Dynamic mode decomposition: data-driven modeling of complex systems, SIAM10.1137/1.9781611974508 ↗

57. Peirce D, Asaro R, Needleman A (1982) An analysis of nonuniform and localized deformation in ductile single crystals. Acta Metall 30(6):1087–111910.1016/0001-6160(82)90005-0 ↗

58. Kalidindi SR, Bronkhorst CA, Anand L (1992) Crystallographic texture evolution in bulk deformation processing of FCC metals. J Mech Phys Solids 40(3):537–56910.1016/0022-5096(92)80003-9 ↗

59. Biffle JH (1993) JAC3D – A three-dimensional finite element computer program for the nonlinear quasi-static response of solids with the conjugate gradient method; yucca mountain site characterization project, Tech. rep., Sandia National Lab, Albuquerque, NM (United States)10.2172/138710 ↗

60. Lee M, Lim H, Adams B, Hirth J, Wagoner R (2010) A dislocation density-based single crystal constitutive equation. Int J Plast 26(7):925–93810.1016/j.ijplas.2009.11.004 ↗

61. Aragon NK, Rezwan AA, Montes de Oca Zapiain D, Lim H (2024) Investigating the orientation dependence of local fields around spherical defects using crystal plasticity simulations. J Mater Res Technol 33:235–24310.1016/j.jmrt.2024.09.029 ↗

62. Owen SJ, Staten ML, Sorensen MC (2012) Parallel hex meshing from volume fractions, in: Proceedings of the 20th international meshing roundtable, Springer, 161–17810.1007/978-3-642-24734-7_9 ↗

63. Owen SJ (2012) Parallel smoothing for grid-based methods., Tech. rep., Sandia National Laboratories, Albuquerque, NM, and Livermore, CA

64. Lim H, Abdeljawad F, Owen SJ, Hanks BW, Foulk JW, Battaile CC (2016) Incorporating physically-based microstructures in materials modeling: bridging phase field and crystal plasticity frameworks. Modell Simul Mater Sci Eng 24(4):045016

65. Owen SJ, Brown JA, Ernst CD, Lim H, Long KN (2017) Hexahedral mesh generation for computational materials modeling. Proc Eng 203:167–17910.1016/j.proeng.2017.09.803 ↗

66. Lim H, Battaile CC, Bishop JE, Foulk JW III (2019) Investigating mesh sensitivity and polycrystalline RVEs in crystal plasticity finite element simulations. Int J Plast 121:101–11510.1016/j.ijplas.2019.06.001 ↗

67. Peherstorfer B (2022) Breaking the Kolmogorov barrier with nonlinear model reduction. Not Am Math Soc 69(5):725–733

68. Ohlberger M, Rave S (2015) Reduced basis methods: Success, limitations and future challenges, arXiv preprint arXiv:1511.02021

69. Cohen A, DeVore R (2016) Kolmogorov widths under holomorphic mappings. IMA J Numer Anal 36(1):1–12

70. Chen W, Hesthaven JS, Junqiang B, Qiu Y, Yang Z, Tihao Y (2018) Greedy nonintrusive reduced order model for fluid dynamics. AIAA J 56(12):4927–494310.2514/1.J056161 ↗

71. Behere A, Rajaram D, Puranik TG, Kirby M, Mavris DN (2021) Reduced order modeling methods for aviation noise estimation. Sustainability 13(3):112010.3390/su13031120 ↗

72. Golub GH, Van Loan CF (2013) Matrix computations, Johns Hopkins University Press10.56021/9781421407944 ↗

73. Benner P, Schilders W, Grivet-Talocia S, Quarteroni A, Rozza G, Miguel Silveira L (2020) Model Order Reduction: Volume 2: Snapshot-Based Methods and Algorithms, De Gruyter

74. Frangos M, Marzouk Y, Willcox K, van Bloemen Waanders B (2010) Surrogate and reduced-order modeling: a comparison of approaches for large-scale statistical inverse problems. In: Large-scale inverse problems and quantification of uncertainty, Wiley, pp 123–14910.1002/9780470685853.ch7 ↗

75. Álvarez MA, Rosasco L, Lawrence ND (2012) Kernels for vector-valued functions: a review. Found Trends Mach Learn 4(3):195–26610.1561/2200000036 ↗

76. Shahriari B, Swersky K, Wang Z, Adams RP, de Freitas N (2016) Taking the human out of the loop: AA review of Bayesian optimization. Proc IEEE 104(1):148–17510.1109/JPROC.2015.2494218 ↗

77. Quiñonero-Candela J, Rasmussen CE (2005) A unifying view of sparse approximate Gaussian process regression, Journal of Machine Learning Research 6 1939–1959

78. Quiñonero-Candela J, Rasmussen CE, Williams CK (2007) Approximation methods for Gaussian process regression, Large-scale kernel machines 203–22410.7551/mitpress/7496.003.0011 ↗

79. Titsias M (2009) Variational learning of inducing variables in sparse Gaussian processes. In: Proceedings of the twelfth international conference on artificial intelligence and statistics, PMLR 5, pp 567–574

80. Titsias MK (2009) Variational model selection for sparse gaussian process regression, Report, University of Manchester, UK

81. Rasmussen CE (2006) Gaussian processes in machine learning, MIT Press10.7551/mitpress/3206.001.0001 ↗

82. Rahimi A, Recht B (2007) Random features for large-scale kernel machines, Advances in neural information processing systems 20

83. Ton J-F, Flaxman S, Sejdinovic D, Bhatt S (2018) Spatial mapping with gaussian processes and nonstationary Fourier features. Sp Stat 28:59–7810.1016/j.spasta.2018.02.002 ↗

84. Martinsson P-G, Tropp JA (2020) Randomized numerical linear algebra: foundations and algorithms. Acta Num 29:403–57210.1017/S0962492920000021 ↗

85. Tran A (2021) Scalable$$^3$$-BO: Big Data meets HPC - A scalable asynchronous parallel high-dimensional Bayesian optimization framework on supercomputers. In: Proceedings of the ASME 2021 IDETC/CIE, Vol. Volume 1: 41th Computers and Information in Engineering Conference of International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, American Society of Mechanical Engineers10.1115/DETC2021-70828 ↗

86. Man C-S (2022) Crystallographic texture and group representations, Springer10.1007/978-94-024-2158-3 ↗

87. Bonilla EV, Chai KM, Williams C (2007) Multi-task Gaussian process prediction, Advances in neural information processing systems 153–160

88. Bui-Thanh T, Willcox K, Ghattas O (2008) Model reduction for large-scale systems with high-dimensional parametric input space. SIAM J Sci Comput 30(6):3270–328810.1137/070694855 ↗

89. Binev P, Cohen A, Dahmen W, DeVore R, Petrova G, Wojtaszczyk P (2011) Convergence rates for greedy algorithms in reduced basis methods. SIAM J Math Anal 43(3):1457–147210.1137/100795772 ↗

90. Buffa A, Maday Y, Patera AT, Prud’homme C, Turinici G (2012) A priori convergence of the greedy algorithm for the parametrized reduced basis method. ESAIM Math Modell Num Anal 46(3):595–60310.1051/m2an/2011056 ↗

91. Chellappa S, Feng L, Benner P (2022) An adaptive sampling approach for the reduced basis method. In: Realization and model reduction of dynamical systems: a festschrift in honor of the 70th birthday of Thanos Antoulas, Springer, pp 137–15510.1007/978-3-030-95157-3_8 ↗

92. Borggaard J, Pond KR, Zietsman L (2014) Parametric reduced order models using adaptive sampling and interpolation. IFAC Proc Vol 47(3):7773–777810.3182/20140824-6-ZA-1003.02664 ↗

93. Tran A, Lim H (2023) An asynchronous parallel high-throughput model calibration framework for crystal plasticity finite element constitutive models, Computational Mechanics10.2172/2431545 ↗

94. Bunge H-J (1982) Texture analysis in materials science: Mathematical methods, Elsevier10.1016/B978-0-408-10642-9.50019-2 ↗

95. Dahms M, Bunge H-J (1989) The iterative series-expansion method for quantitative texture analysis. I. general outline. J Appl Crystallogr 22(5):439–44710.1107/S0021889889005261 ↗

96. Dahms M (1992) The iterative series-expansion method for quantitative texture analysis ii. applications,. J Appl Crystallogr 25(2):259–26710.1107/S0021889891012499 ↗

97. Kostelec PJ, Rockmore DN (2008) FFTs on the rotation group. J Fourier Anal Appl 14:145–17910.1007/s00041-008-9013-5 ↗

98. Hielscher R, Schaeben H (2008) A novel pole figure inversion method: specification of the MTEX algorithm. J Appl Crystallogr 41(6):1024–103710.1107/S0021889808030112 ↗

99. Hielscher R, Mainprice D, Schaeben H (2010) Material behavior: texture and anisotropy. In: Handbook of geomathematics. Springer, Berlin, pp 973–100310.1007/978-3-642-01546-5_33 ↗

100. Callahan PG, Echlin M, Pollock TM, Singh S, De Graef M (2017) Three-dimensional texture visualization approaches: theoretical analysis and examples. J Appl Crystallogr 50(2):430–44010.1107/S1600576717001157 ↗