Towards surrogate modeling of material microstructures through the processing variables. (English) Zbl 1411.74065
Summary: In order to obtain high-performance materials, it is of significant importance to be able to depict the material microstructure corresponding to given values of processing variables in the manufacturing process. Conventional approaches require a knowledge of the internal mechanisms of the evolution in order to numerically simulate the microstructures. This work focuses instead on establishing a surrogate model in order to parameterize microstructures of Representative Volume Elements (RVE) using processing variables. The surrogate model requires a set of RVE microstructure snapshots generated experimentally or numerically. By using the Proper Orthogonal Decomposition (POD) method, the parametric space is developed using a series of approximated response surfaces of the POD projection coefficients. Thereafter, RVE microstructures may be parameterized for any given value of the processing variables. In addition, for the purpose of scaling down the storage requirement due to a high quality digital representation, the snapshots are given a bi-level reduced order epresentation in terms of the extracted common spatial and parametric bases. We showcase the approach by parameterizing Voronoi-simulated RVE microstructures under both uniaxial and biaxial conceptional compressions.
MSC:
| 74S30 | Other numerical methods in solid mechanics (MSC2010) |
| 74M25 | Micromechanics of solids |
Keywords:
microstructure parameterization; processing variables; model reduction; data-driven models; moving least squares; separation of variablesReferences:
| [1] | Engler, O.; Hirsch, J., Texture control by thermomechanical processing of aa6xxx almgsi sheet alloys for automotive applicationsa review, Mater. Sci. Eng. A, 336, 1-2, 249-262 (2002) |
| [2] | Matsuo, M., Texture control in the production of grain oriented silicon steels, ISIJ Int., 29, 10, 809-827 (1989) |
| [3] | Sebald, R.; Gottstein, G., Modeling of recrystallization textures: interaction of nucleation and growth, Acta Mater., 50, 6, 1587-1598 (2002) |
| [4] | Engler, O.; Löchte, L.; Hirsch, J., Through-process simulation of texture and properties during the thermomechanical processing of aluminium sheets, Acta Mater., 55, 16, 5449-5463 (2007) |
| [5] | Schäfer, C.; Song, J.; Gottstein, G., Modeling of texture evolution in the deformation zone of second-phase particles, Acta Mater., 57, 4, 1026-1034 (2009) |
| [6] | Sidor, S. J.; Petrov, R. H.; Kestens, L. A.I., Modeling the crystallographic texture changes in aluminum alloys during recrystallization, Acta Mater., 59, 14, 5735-5748 (2009) |
| [7] | Nygards, M.; Gudmundson, P., Three-dimensional periodic voronoi grain models and micromechanical fe-simulations of a two-phase steel, Comput. Mater. Sci., 24, 4, 513-519 (2002) |
| [8] | Nygards, M.; Gudmundson, P., Micromechanical modeling of ferritic/pearlitic steels, Mater. Sci. Eng. A, 325, 1-2, 435-443 (2002) |
| [9] | Fritzen, F.; Bhlke, T.; Schnack, E., Periodic three-dimensional mesh generation for crystalline aggregates based on voronoi tessellations, Comput. Mech., 43, 5, 701-713 (2009) |
| [10] | Fritzen, F.; Bhlke, T., Periodic three-dimensional mesh generation for particle reinforced composites with application to metal matrix composites, Int. J. Solids Struct., 48, 5, 706-718 (2011) · Zbl 1236.74058 |
| [11] | Sonon, B.; François, B.; Massart, T. J., A unified level set based methodology for fast generation of complex microstructural multi-phase rves, Comput. Methods Appl. Mech. Eng., 223-224, 103-122 (2012) |
| [12] | Xu, Y.; Zhang, W., Numerical modelling of oxidized microstructure and degraded properties of 2d c/sic composites in air oxidizing environments below 800 °C, Mater. Sci. Eng. A, 528, 27, 7974-7982 (2011) |
| [13] | Mishnaevsky Jr., L., Automatic voxel-based generation of 3d microstructural fe models and its application to the damage analysis of composites, Mater. Sci. Eng.: A, 407, 1-2, 11-23 (2005) |
| [14] | Chawla, N.; Sidhu, R.; Ganesh, V., Three-dimensional visualization and microstructure-based modeling of deformation in particle-reinforced composites, Acta Mater., 54, 6, 1541-1548 (2006) |
| [15] | Xia, L.; Raghavan, B.; Breitkopf, P.; Zhang, W., Numerical material representation using proper orthogonal decomposition and diffuse approximation, Appl. Math. Comput., 224, 450-462 (2013) · Zbl 1334.74099 |
| [16] | Guessasma, S.; Babin, P.; Della Valle, G.; Dendieve, R., Relating cellular structure of open solid food foams to their young’s modulus: Finite element calculation, Int. J. Solids Struct., 45, 10, 2881-2896 (2008) · Zbl 1169.74307 |
| [17] | Xu, Y.; Zhang, W., A strain energy model for the prediction of the effective coefficient of thermal expansion of composite materials, Comput. Mater. Sci., 53, 1, 241-250 (2012) |
| [18] | Zeman, J.; Sejnoha, M., Numerical evaluation of effective elastic properties of graphite fiber tow impregnated by polymer matrix, J. Mech. Phys. Solids, 49, 1, 69-90 (2001) · Zbl 1010.74052 |
| [19] | Xia, L.; Breitkopf, P., A reduced multiscale model for nonlinear structural topology optimization, Comput. Methods Appl. Mech. Eng., 280, 117-134 (2014) · Zbl 1423.74771 |
| [20] | Fritzen, F.; Xia, L.; Leuschner, M.; Breitkopf, P., Topology optimization of multiscale elastoviscoplastic structures, Int. J. Numer. Methods Eng., 106, 430-453 (2016) · Zbl 1352.74239 |
| [21] | Fullwood, D. T.; Niezgoda, S. R.; Adams, B. L.; Kalidindi, S. R., Microstructure sensitive design for performance optimization, Progr. Mater. Sci., 55, 6, 477-562 (2010) |
| [22] | Torquato, S., Optimal design of heterogeneous materials, Annu. Rev. Mater. Res., vol. 40, 101-129 (2010) |
| [23] | Queipo, N. B.; Haftka, R. T.; Shyy, W.; Goel, T.; Vaidyanathan, R.; Tucker, P. K., Surrogate-based analysis and optimization, Progr. Aerosp. Sci., 41, 1, 1-28 (2005) |
| [24] | Forrester, A.; Keane, A., Recent advances in surrogate-based optimization, Progr. Aerosp. Sci., 45, 1-3, 50-79 (2009) |
| [25] | Sundararaghavan, V.; Zabaras, N., A dynamic material library for the representation of single-phase polyhedral microstructures, Acta Mater., 52, 14, 4111-4119 (2004) |
| [26] | Ganapathysubramanian, B.; Zabaras, N., Modeling diffusion in random heterogeneous media: data-driven models, stochastic collocation and the variational multiscale method, J. Comput. Phys., 226, 1, 326-353 (2007) · Zbl 1124.65007 |
| [27] | Sirovich, L., Turbulence and the dynamics of coherent structures; part i: coherent structures, Q. Appl. Math., 45, 3, 561-571 (1987) · Zbl 0676.76047 |
| [28] | Newman, A., Model Reduction via the Karhunen-Loeve Expansion Part I: An Exposition, Technical Report (1996) |
| [29] | Nayroles, B.; Touzot, G.; Villon, P., Generalizing the finite element method: diffuse approximation and diffuse elements, Comput. Mech., 10, 5, 307-318 (1992) · Zbl 0764.65068 |
| [30] | Filomeno Coelho, R.; Breitkopf, P.; Knopf-Lenoir, C., Model reduction for multidisciplinary optimization - application to a 2d wing, Struct. Multidiscip. Opt., 37, 1, 29-48 (2008) |
| [31] | Filomeno Coelho, R.; Breitkopf, P.; Knopf-Lenoir, C.; Villon, P., Bi-level model reduction for coupled problems, Struct. Multidiscip. Opt., 39, 4, 401-418 (2009) · Zbl 1274.74225 |
| [32] | Filomeno Coelho, R.; Lebon, J.; Bouillard, P., Hierarchical stochastic metamodels based on moving least squares and polynomial chaos expansion, Struct. Multidiscip. Opt., 43, 5, 707-729 (2011) · Zbl 1274.74267 |
| [33] | Ghosh, S.; Dimiduk, D., Computational Methods for Microstructure-Property Relationships (2011), Springer: Springer New York |
| [34] | Breitkopf, P.; Rassineux, A.; P., V., An introduction to moving least squares meshfree methods, Revue Européenne des Éléments, 11, 7-8, 825-867 (2002) · Zbl 1120.74856 |
| [35] | Alexa, M.; Behr, J.; Cohen-Or, D.; Fleishman, S.; Levin, D.; Silva, C. T., Computing and rendering point set surfaces, IEEE Trans. Vis. Comput. Graph., 9, 1, 3-15 (2003) |
| [36] | Law, T.; Itoh, H.; Seki, H., Image filtering, edge detection, and edge tracing using fuzzy reasoning, IEEE Trans. Pattern Anal. Mach. Intell., 18, 5, 481-491 (1996) |
| [37] | Johnson, M.; Moore, L.; Ylvisaker, D., Minimax and maximin distance designs, J. Stat. Plann. Inference, 26, 2, 131-148 (1990) |
| [38] | McKay, M.; Beckman, R.; Conover, W., Comparison of three methods for selecting values of input variables in the analysis of output from a computer code., Technometrics, 21, 2, 239-245 (1979) · Zbl 0415.62011 |
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.
