A POD-Based Parameterization Model for Material Microstructure Representation and Its Application to Optimal Design of Material Effective Mechanical Properties

GUO Zhi-wen; XIAO Man-yu; XIA Liang

doi:10.21656/1000-0887.370279

Volume 38 Issue 7

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2017 > 38(7): 727-742

GUO Zhi-wen, XIAO Man-yu, XIA Liang. A POD-Based Parameterization Model for Material Microstructure Representation and Its Application to Optimal Design of Material Effective Mechanical Properties[J]. Applied Mathematics and Mechanics, 2017, 38(7): 727-742. doi: 10.21656/1000-0887.370279

Citation:

PDF( 3163 KB)

A POD-Based Parameterization Model for Material Microstructure Representation and Its Application to Optimal Design of Material Effective Mechanical Properties

doi: 10.21656/1000-0887.370279

¹Department of Applied Mathematics, School of Natural and Applied Sciences,Northwestern Polytechnical University, Xi’an 710129, P.R.China;²Multiscale Laboratory of Modeling and Simulation(CNRS UMR 8208),University Paris-Est, Marne-la-Vallée 77454, France;³State Key Laboratory of Digital Manufacturing Equipment & Technology(Huazhong University of Science and Technology); School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, P.R.China

Funds: The National Science Fund for Young Scholars of China(11302173)

Received Date: 2016-09-13
Rev Recd Date: 2016-10-22
Publish Date: 2017-07-15

Abstract

Abstract

With the increasing computing capability, numerical material simulation based on material microstructure images has attracted interest of more and more researchers. Within this context, an efficient numerical material parameterization model was proposed for the representation of material microstructures. First, the eigenvalue analysis of the material microstructure image data was carried out through the proper orthogonal decomposition (POD) to extract a common POD basis. The material microstructure image can be represented as a linear combination of the retained POD basis. Then, response surfaces of the POD projection coefficients with respect to the controlling parameters were built with the method of moving least squares. By means of this numerical parameterization model, the corresponding material microstructure image for arbitrary input controlling parameters can be reconstructed. Application of this model was demonstrated in view of a set of 2phase composite material snapshots. This parameterized material microstructure representation model can also been applied to the optimal design of material effective mechanical properties.
- material microstructure,
- proper orthogonal decomposition,
- response surface,
- parameterization model,
- surrogate model,
- homogenization,
- optimal design

FullText(HTML)

References(46)

References

[1]	Sonon B, Franois B, Massart T J. A unified level set based methodology for fast generation of complex microstructural multi-phase RVEs[J]. Computer Methods in Applied Mechanics and Engineering,2012,223/224: 103-122.
[2]	XU Ying-jie, ZHANG Wei-hong. Numerical modeling of oxidized microstructure and degraded properties of 2D C/SiC composites in air oxidizing environments below 800 ℃[J]. Materials Science & Engineering: A,2011,528(27): 7974-7982.
[3]	任淮辉, 李旭东. 三维材料微结构设计与数值模拟[J]. 物理学报, 2009,58(6): 4041-4052.(REN Huai-hui, LI Xu-dong. 3D material microstructures design and numerical simulation [J]. Acta Physica Sinica,2009,58(6): 4041-4052.(in Chinese))
[4]	Guessasma S, Babin P, Della Valle G, et al. Relating cellular structure of open solid food foams to their Young’s modulus: finite element calculation[J]. International Journal of Solids and Structures,2008,45(10): 2881-2896.
[5]	XU Ying-jie, ZHANG Wei-hong. A strain energy model for the prediction of the effective coefficient of thermal expansion of composite materials[J]. Computational Materials Science,2012,53(1): 241-250.
[6]	Feyel F, Chaboche J L. FE2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials[J]. Computer Methods in Applied Mechanics and Engineering,2000,183(3/4): 309-330.
[7]	Smit R J M, Brekelmans W A M, Meijer H E H. Prediction of the mechanical behavior of nonlinear heterogeneous systems by multi-level finite element modeling[J]. Computer Methods in Applied Mechanics and Engineering,1998,155(1/2): 181-192.
[8]	Ibrahimbegovic A, Papadrakakis M. Multi-scale models and mathematical aspects in solid and fluid mechanics[J]. Computer Methods in Applied Mechanics and Engineering,2010,199(21/22): 1241.
[9]	Fullwood D T, Niezgoda S R, Adams B L, et al. Microstructure sensitive design for performance optimization[J]. Progress in Materials Science,2010,55(6): 477-562.
[10]	Torquato S. Optimal design of heterogeneous materials[J]. Annual Review of Materials Research,2010,40: 101-129.
[11]	Michel J C, Moulinec H, Suquet P. Effective properties of composite materials with periodic microstructure: a computational approach[J]. Computer Methods in Applied Mechanics and Engineering,1999,172(1/4): 109-143.
[12]	Mishnaevsky Jr L L. Automatic voxel-based generation of 3D microstructural FE models and its application to the damage analysis of composites[J]. Materials Science and Engineering: A,2005,407(1/2): 11-23.
[13]	Landi G, Niezgoda S R, Kalidindi S R. Multi-scale modeling of elastic response of three-dimensional voxel-based microstructure datasets using novel DFT-based knowledge systems [J]. Acta Materialia,2010,58(7): 2716-2725.
[14]	Mishnaevsky Jr L. Micromechanical analysis of nanocomposites using 3D voxel based material model[J]. Composites Science and Technology,2012,72(10): 1167-1177.
[15]	Legrain G, Chevaugeon N, Dréau K. High order X-FEM and levelsets for complex microstructures: uncoupling geometry and approximation[J]. Computer Methods in Applied Mechanics and Engineering,2012,241/244: 172-189.
[16]	Lian W D, Legrain G, Cartraud P. Image-based computational homogenization and localization: comparison between X-FEM/levelset and voxel-based approaches[J]. Computational Mechanics,2013,51(3): 279-293.
[17]	Engler O, Hirsch J. Texture control by thermomechanical processing of AA6 xxx Al-Mg-Si sheet alloys for automotive applications a review[J]. Materials Science and Engineering,2002,336(1/2): 249-262.
[18]	CHEN Yong-jin, ZHANG Bin, DING Qing-qing, et al. Microstructure evolution and crystallography of the phase-change material TiSbTe films annealed in situ[J]. Journal of Alloys and Compounds,2016,678: 185-192.
[19]	顾善群, 李金焕, 王海洋, 等. 石墨烯/纳米银复合材料的制备、微结构及其导电性能[J]. 复合材料学报, 2015,32(4): 1061-1066.(GU Shan-qun, LI Jin-huan, WANG Hai-yang, et al. Preparation of grapheme/nano-Ag composite, microstructure and electrical property[J]. Acta Materiae Composite Sinica,2015,32(4): 1061-1066.(in Chinese))
[20]	Engler O, Lchte L, Hirsch J. Through-process simulation of texture and properties during the thermomechanical processing of aluminium sheets[J]. Acta Materialia,2007,55(16): 5449-5463.
[21]	Kavoosi V, Abbasi S M, Ghazi Mirsaed S M, et al. Influence of cooling rate on the solidification behavior and microstructure of IN738LC superalloy[J]. Journal of Alloys and Compounds,2016,680: 291-300.
[22]	Wynne B P, Gorley M J, Zheng P F, et al. An analysis of the microstructure of spark plasma sintered and hot isostatically pressed V—4Cr—4Ti—1.8Y—0.4Ti₃SiC₂alloy and its thermal stability[J]. Journal of Alloys and Compounds,2016,680: 506-511.
[23]	Forrester A I J, Keane A J. Recent advances in surrogate-based optimization[J]. Progress in Aerospace Sciences,2009,45(1/3): 50-79.
[24]	Coelho R F, Breitkopf P, Knopf-Lenoir C. Model reduction for multidisciplinary optimization-application to a 2D wing[J]. Structural and Multidisciplinary Optimization,2008,37(1): 29-48.
[25]	Berkooz G, Holmes P, Lumley J L. The proper orthogonal decomposition in the analysis of turbulent flows[J]. Annual Review of Fluid Mechanics,1993,25: 539-575.
[26]	Willcox K, Peraire J. Balanced model reduction via the proper orthogonal decomposition[J]. AIAA Journal,2002,40(11): 2323-2330.
[27]	Hall K C, Thomas J P, Dowell E H. Proper orthogonal decomposition technique for transonic unsteady aerodynamic flows[J]. AIAA Journal,2000,38(10): 1853-1862.
[28]	Kim T, Bussoletti J E. An optimal reduced-order aeroelastic modeling based on a response-based modal analysis of unsteady CFD models[C]// 〖STBX〗19th AIAA Applied Aerodynamics Conference, Fluid Dynamics and Co-Located Conferences.Anaheim, CA, 2001.
[29]	Thomas J P, Dowell E H, Hall K C. Three-dimensional transonic aeroelasticity using proper orthogonal decomposition-based reduced-order models[J]. Journal of Aircraft,2003,40(3): 544-551.
[30]	Lieu T, Lesoinne M. Parameter adaptation of reduced order models for three-dimensional flutter analysis[C]//〖STBX〗42nd AIAA Aerospace Sciences Meeting and Exhibit.Reno, Nevada, 2004.
[31]	XIAO Man-yu, Breitkopf P, Coelho R F, et al. Model reduction by CPOD and Kriging: application to the shape optimization of an intake port[J]. Structural and Multidisciplinary Optimization,2010,41(4): 555-574.
[32]	XIAO Man-yu, Breitkopf P, Coelho R F, et al. Constrained proper orthogonal decomposition based on QR -factorization for aerodynamical shape optimization[J]. Applied Mathematics and Computation,2013,223: 254-263.
[33]	Raghavan B, XIA Liang, Breitkopf P, et al. Towards simultaneous reduction of both input and output spaces for interactive simulation based structural design[J]. Computer Methods in Applied Mechanics and Engineering,2013,265: 174-185.
[34]	XIA Liang, Raghavan B, Breitkopf P, et al. Numerical material representation using proper orthogonal decomposition and diffuse approximation[J]. Applied Mathematics and Computation,2013,224: 450-462.
[35]	Kersaudy P, Sudret B, Varsier N, et al. A new surrogate modeling technique combining Kriging and polynomial chaos expansions—application to uncertainty analysis in computational dosimetry[J]. Journal of Computational Physics,2015,286: 103-117.
[36]	Pardo-Igúzquiza E, Chica-Olmo M, Luque-Espinar J A, et al. Compositional cokriging for mapping the probability risk of groundwater contamination by nitrates[J]. Science of the Total Environment,2015,532: 162-175.
[37]	Lancaster P, Salkauskas K. Surfaces generatedby moving least squares methods[J]. Mathematics of Computation,1981,37: 141-158.
[38]	Belytschko T, Lu Y Y, Gu L. Element-free Galerkin methods[J]. International Journal for Numerical Methods in Engineering,1994,37(2): 229-256.
[39]	曾清红, 卢德唐. 基于移动最小二乘法的曲线曲面拟合[J]. 工程图学学报, 2004,25(1): 84-89.(ZENG Qing-hong, LU De-tang. Curve and surface fitting based on moving least-squares methods[J]. Journal of Engineering Graphics,2004,25(1): 84-89.(in Chinese))
[40]	单权. 纤维增强复合材料界面相微结构优化设计[D]. 硕士学位论文. 哈尔滨: 哈尔滨工程大学, 2009.(SHAN Quan. Interphase microstructure optimization of carbon fiber reinfored composite materials[D]. Master Thesis. Harbin: Harbin Engineering University, 2009.(in Chinese))
[41]	单豪良. 基于胞体模型的颗粒增强复合材料耦合场数值模拟研究[D]. 硕士学位论文. 昆明: 昆明理工大学, 2009.(SHAN Hao-liang. Numerical simulation of particle reinforced composite coupling field based on cell body model[D]. Master Thesis. Kunming: Kunming University of Science and Technology, 2009.(in Chinese))
[42]	Nguyen V P, Lloberas-Valls O, Stroeven M, et al. On the existence of representative volumes for softening quasi-brittle materials—a failure zone averaging scheme[J]. Computer Methods in Applied Mechanics and Engineering,2010,199(45/48): 3028-3038.
[43]	Suquet P. Elements of homogenization theory for inelastic solid mechanics[J]. Lecture Note in Physics,1987,272: 193-278.
[44]	汤亚男. 基于均匀化理论的材料微结构拓扑优化研究[D]. 硕士学位论文. 湘潭: 湘潭大学, 2011.(TANG Ya-nan. Research of topology optimization design of microstructure for material based on homogenization method[D]. Master Thesis. Xiangtan: Xiangtan University, 2011.(in Chinese))
[45]	Lukkassen D. Some engineering and mathematic aspects on the homogenization method[J]. Composites Engineering,1995,5(5): 519-531.
[46]	赵继俊. 优化技术与MATLAB优化工具箱[M]. 北京: 机械工业出版社, 2011: 173-181.(ZHAO Ji-jun. Optimization Technology and MATLAB Optimization Toolbox [M]. Beijing: China Machine Press, 2011: 173-181.(in Chinese))