Abstract
The different elastic properties of tension and compression are obvious in many engineering materials, especially new materials. Materials with this characteristic, such as graphite, ceramics, and composite materials, are called bi-modulus materials. Their mechanical properties such as Young’s modulus have randomness in tension and compression due to different porosity, microstructure, etc. To calibrate the mechanical properties of bi-modulus materials by bridging finite element method (FEM) simulation results and scarce experimental data, the paper presents a data-fusion computational method. The FEM simulation is implemented based on parametric variational principle (PVP), while the experimental result is obtained by digital image correlation (DIC) technology. To deal with scarce experimental data, maximum entropy principle (MEP) is employed for the uncertainty quantification (UQ) and calibration of material parameters and responses, which can retain the original probabilistic property of a priori data. The non-parametric p-box is used as a constraint for data fusion. The method presented in this paper can quantify the mechanical properties of materials with high uncertainty, which is verified by a typical example of bi-modulus graphite. It is possible to find applications in the real-time estimation of structural reliability by combining with digital twin technology in the future.
Issue Section:
Research Papers
References
1.
Khan
, K.
, Patel
, B. P.
, and Nath
, Y.
, 2015
, “Free and Forced Vibration Characteristics of Bimodular Composite Laminated Circular Cylindrical Shells
,” Compos. Struct.
, 126
, pp. 386
–397
. 2.
Cai
, K.
, Gao
, Z.
, and Shi
, J.
, 2014
, “Topology Optimization of Continuum Structures With Bi-Modulus Materials
,” Eng. Optim.
, 46
(2
), pp. 244
–260
. 3.
Huang
, X.
, Li
, B.
, Hong
, W.
, Cao
, Y.-P.
, and Feng
, X.-Q.
, 2016
, “Effects of Tension–Compression Asymmetry on the Surface Wrinkling of Film–Substrate Systems
,” J. Mech. Phys. Solids
, 94
, pp. 88
–104
. 4.
Hatami-Marbini
, H.
, and Rohanifar
, M.
, 2019
, “Stiffness of Bi-Modulus Hexagonal and Diamond Honeycombs
,” J. Mech. Sci. Technol.
, 33
(4
), pp. 1703
–1709
. 5.
Qiu
, Y.
, Shen
, W.
, Yan
, R.
, Li
, X.
, Ye
, Z.
, Li
, M.
, Liu
, K.
, and Qin
, K.
, 2022
, “An Improved Numerical Method for Calculating Mechanical Properties of Bi-Modulus Sandwich Composite Structures
,” Ocean Eng.
, 250
, p. 110998
. 6.
Du
, Z.
, Zhang
, G.
, Guo
, T.
, Tang
, S.
, and Guo
, X.
, 2020
, “Tension-Compression Asymmetry at Finite Strains: A Theoretical Model and Exact Solutions
,” J. Mech. Phys. Solids
, 143
, p. 104084
. 7.
Cost
, J. R.
, Janowski
, K. R.
, and Rossi
, R. C.
, 1968
, “Elastic Properties of Isotropic Graphite
,” Philos. Mag. J. Theor. Exp. Appl. Phys.
, 17
(148
), pp. 851
–854
.8.
Olasov
, L. R.
, Zeng
, F. W.
, Spicer
, J. B.
, Gallego
, N. C.
, and Contescu
, C. I.
, 2019
, “Modeling the Effects of Oxidation-Induced Porosity on the Elastic Moduli of Nuclear Graphites
,” Carbon
, 141
, pp. 304
–315
. 9.
Faris
, F.
, Green
, L.
, and Smith
, C.
, 1952
, “The Thermal Dependence of the Elastic Moduli of Polycrystalline Graphite
,” J. Appl. Phys.
, 23
(1
), pp. 89
–95
. 10.
Green
, L.
, 1953
, “High-Temperature Compression Testing of Graphite
,” ASME J. Appl. Mech.
, 20
(2
), pp. 289
–294
. 11.
Zhao
, J.
, Gu
, W.
, and Yao
, W.
, 2021
, “Elastoplastic Analysis and Experimental Study of Simply Supported Graphite Beams With Different Moduli
,” Sci. Technol. Eng.
, 21
(3
), pp. 1116
–1122
. (in Chinese)
.12.
Hart
, P. E.
, 1972
, “The Effect of Pre-Stressing on the Thermal Expansion and Young’s Modulus of Graphite
,” Carbon
, 10
(2
), pp. 233
–236
. 13.
Samoilov
, V. M.
, and Ostronov
, B. G.
, 2004
, “Effect of Grain Size on the Modulus of Elasticity and Strength of Synthetic Graphites
,” Inorg. Mater.
, 40
(4
), pp. 359
–363
. 14.
Albers
, T. L.
, 2009
, “High-Temperature Properties of Nuclear Graphite
,” ASME J. Eng. Gas Turbines Power
, 131
(6
), p. 064501
. 15.
Malmstrom
, C.
, Keen
, R.
, and Green
, L.
, 1951
, “Some Mechanical Properties of Graphite at Elevated Temperatures
,” J. Appl. Phys.
, 22
(5
), pp. 593
–600
. 16.
Zhang
, C.
, He
, Z.
, Gao
, Y.
, Tang
, H.
, Qi
, W.
, Song
, J.
, and Zhou
, X.
, 2018
, “The Effect of Molten FLiNaK Salt Infiltration on the Strength of Graphite
,” J. Nucl. Mater.
, 512
, pp. 37
–45
. 17.
Park
, S.
, Kim
, J.
, Jeon
, K.-J.
, and Yoon
, S.-H.
, 2016
, “Characterization on the Expanding Nature of Graphite in Microwave-Irradiated Exfoliation
,” J. Nanosci. Nanotechnol.
, 16
(5
), pp. 4450
–4455
. 18.
Qiu
, Z.
, Ma
, L.
, and Wang
, X.
, 2009
, “Non-Probabilistic Interval Analysis Method for Dynamic Response Analysis of Nonlinear Systems With Uncertainty
,” J. Sound Vib.
, 319
(1–2
), pp. 531
–540
. 19.
Hawkins-Daarud
, A.
, Prudhomme
, S.
, van der Zee
, K. G.
, and Oden
, J. T.
, 2013
, “Bayesian Calibration, Validation, and Uncertainty Quantification of Diffuse Interface Models of Tumor Growth
,” J. Math. Biol.
, 67
(6–7
), pp. 1457
–1485
. 20.
Luo
, Y.
, Xing
, J.
, Kang
, Z.
, Zhan
, J.
, and Li
, M.
, 2020
, “Uncertainty of Membrane Wrinkling Behaviors Considering Initial Thickness Imperfections
,” Int. J. Solids Struct.
, 191
, pp. 264
–277
. 21.
Guo
, X.
, Du
, Z.
, Liu
, C.
, and Tang
, S.
, 2021
, “A New Uncertainty Analysis-Based Framework for Data-Driven Computational Mechanics
,” ASME J. Appl. Mech.
, 88
(11
), p. 111003
. 22.
Bai
, Y.
, Wong
, M. S.
, Shi
, W.-Z.
, Wu
, L.-X.
, and Qin
, K.
, 2015
, “Advancing of Land Surface Temperature Retrieval Using Extreme Learning Machine and Spatio-Temporal Adaptive Data Fusion Algorithm
,” Remote Sens.
, 7
(4
), pp. 4424
–4441
. 23.
Prudencio
, E. E.
, Bauman
, P. T.
, Faghihi
, D.
, Ravi-Chandar
, K.
, and Oden
, J. T.
, 2015
, “A Computational Framework for Dynamic Data-Driven Material Damage Control, Based on Bayesian Inference and Model Selection
,” Int. J. Numer. Methods Eng.
, 102
(3–4
), pp. 379
–403
. 24.
Peng
, X.
, Liu
, Z.
, Xu
, X.
, Li
, J.
, Qiu
, C.
, and Jiang
, S.
, 2018
, “Nonparametric Uncertainty Representation Method With Different Insufficient Data From Two Sources
,” Struct. Multidiscip. Optim.
, 58
(5
), pp. 1947
–1960
. 25.
Guel
, N.
, Hamam
, Z.
, Godin
, N.
, Reynaud
, P.
, Caty
, O.
, Bouillon
, F.
, and Paillassa
, A.
, 2020
, “Data Merging of AE Sensors With Different Frequency Resolution for the Detection and Identification of Damage in Oxide-Based Ceramic Matrix Composites
,” Materials
, 13
(20
), p. 4691
. 26.
Jha
, P. K.
, Cao
, L.
, and Oden
, J. T.
, 2020
, “Bayesian-Based Predictions of COVID-19 Evolution in Texas Using Multispecies Mixture-Theoretic Continuum Models
,” Comput. Mech.
, 66
(5
), pp. 1055
–1068
. 27.
Pepper
, N.
, Montomoli
, F.
, and Sharma
, S.
, 2021
, “Data Fusion for Uncertainty Quantification With Non-Intrusive Polynomial Chaos
,” Comput. Methods Appl. Mech. Eng.
, 374
, p. 113577
. 28.
Cai
, K.
, Luo
, Z.
, and Wang
, Y.
, 2015
, “Topology Optimization for Human Proximal Femur Considering Bi-Modulus Behavior of Cortical Bones,” Advances in Global Optimization
, D.
Gao
, N.
Ruan
, and W.
Xing
, eds., Springer
, New York
, pp. 263
–270
.29.
Briccola
, D.
, Bruggi
, M.
, and Taliercio
, A.
, 2019
, “Analysis of 3D No-Tension Masonry-Like Walls
,” J. Mech. Mater. Struct.
, 13
(5
), pp. 631
–646
. 30.
Lu
, M.
, Zhang
, L.
, Yan
, Z.
, and Wu
, J.
, 2021
, “Nonlinear Analysis of Structures Made of No-Tension/Compression Materials Using an Efficient Projection-Contraction Algorithm
,” Comput. Struct.
, 244
, p. 106432
. 31.
Zhang
, L.
, Zhang
, H.
, Wu
, J.
, Yan
, B.
, and Lu
, M.
, 2016
, “Parametric Variational Principle for Bi-Modulus Materials and Its Application to Nacreous Bio-Composites
,” Int. J. Appl. Mech.
, 8
(6
), p. 1650082
. 32.
Zhang
, L.
, Dong
, K.
, Lu
, M.
, and Zhang
, H.
, 2020
, “A Wrinkling Model for Pneumatic Membranes and the Complementarity Computational Framework
,” Comput. Mech.
, 65
(1
), pp. 119
–134
. 33.
Shannon
, C. E.
, 1948
, “A Mathematical Theory of Communication
,” Bell Syst. Tech. J.
, 27
(3
), pp. 379
–423
. 34.
Jaynes
, E. T.
, 1957
, “Information Theory and Statistical Mechanics
,” Phys. Rev.
, 106
(4
), pp. 620
–630
. 35.
Jaynes
, E. T.
, 1982
, “On the Rationale of Maximum-Entropy Methods
,” Proc. IEEE
, 70
(9
), pp. 939
–952
. 36.
Gaymann
, A.
, Pietropaoli
, M.
, Crespo
, L. G.
, Kenny
, S. P.
, and Montomoli
, F.
, 2018
, “Random Variable Estimation and Model Calibration in the Presence of Epistemic and Aleatory Uncertainties
,” Sae Int. J. Mater. Manuf.
, 11
(4
), pp. 453
–466
. 37.
Massart
, P.
, 1990
, “The Tight Constant in the Dvoretzky-Kiefer-Wolfowitz Inequality
,” Ann. Probab.
, 18
(3
), pp. 1269
–1283
. 38.
Tsang
, D. K. L.
, and Marsden
, B. J.
, 2006
, “The Development of a Stress Analysis Code for Nuclear Graphite Components in Gas-Cooled Reactors
,” J. Nucl. Mater.
, 350
(3
), pp. 208
–220
. 39.
Luo
, P.
, Chao
, Y.
, Sutton
, M.
, and Peters
, W.
, 1993
, “Accurate Measurement of 3-Dimensional Deformations in Deformable and Rigid Bodies Using Computer Vision
,” Exp. Mech.
, 33
(2
), pp. 123
–132
. 40.
Bessa
, M. A.
, Bostanabad
, R.
, Liu
, Z.
, Hu
, A.
, Apley
, D. W.
, Brinson
, C.
, Chen
, W.
, and Liu
, W. K.
, 2017
, “A Framework for Data-Driven Analysis of Materials Under Uncertainty: Countering the Curse of Dimensionality
,” Comput. Methods Appl. Mech. Eng.
, 320
, pp. 633
–667
. 41.
Kingma
, D.
, and Ba
, J.
, 2015
, “Adam: A Method for Stochastic Optimization
,” The 3rd International Conference for Learning Representations
, San Diego, CA
, May 7–9
.42.
Byrd
, R. H.
, Lu
, P.
, Nocedal
, J.
, and Zhu
, C.
, 1995
, “A Limited Memory Algorithm for Bound Constrained Optimization
,” Siam J. Sci. Comput.
, 16
(5
), pp. 1190
–1208
. 43.
Zohdi
, T. I.
, 2020
, “A Machine-Learning Framework for Rapid Adaptive Digital-Twin Based Fire-Propagation Simulation in Complex Environments
,” Comput. Meth. Appl. Mech. Eng.
, 363
, p. 112907
. 44.
Zohdi
, T. I.
, 2021
, “A Digital Twin Framework for Machine Learning Optimization of Aerial Fire Fighting and Pilot Safety
,” Comput. Meth. Appl. Mech. Eng.
, 373
, p. 113446
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