Analysis of Rectangular Orthotropic Membranes for Mechanical Properties Identification through Load-Displacement Data
Publication: Journal of Engineering Mechanics
Volume 147, Issue 6
Abstract
In this paper, an innovative procedure is introduced for the identification of the mechanical properties of orthotropic membranes based on load-displacement data. To this end, novel functional forms of the displacement components for rectangular membranes are appropriately introduced. Unknown coefficients of these displacement functions are determined, minimizing the total potential energy of the membrane. The energy method is then combined with an optimization procedure to estimate the elastic constants of the membranes in a straightforward manner. Specifically, a genetic algorithm is used to minimize a properly defined objective function directly related to the sought mechanical properties and computed based on known load-displacement data of the membrane under uniformly distributed load. Numerous applications are reported to demonstrate the efficiency and accuracy of the proposed identification procedure in capturing properties of the membranes. Further, several numerical applications are presented to show the reliability of the proposed displacement field functions by comparing results with finite-element model data, as well as analytical solutions when available. Notably, considering the increasing use of membrane elements in many engineering applications, results suggest that the proposed procedure may represent an accurate and appealing alternative approach for determining membrane mechanical properties, whose characteristics are still difficult to estimate using commonly employed techniques.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request. (MATLAB code for the identification procedure.)
Acknowledgments
This work has been supported by the REvivED water (Low energy solutions for drinking water production by a revival of electrodialysis systems) project—Horizon 2020 program, Grant Agreement No. 685579. A. Di Matteo and A. Pirrotta gratefully acknowledge the support received from the Italian Ministry of University and Research through the PRIN 2017 funding scheme [Project 2017J4EAYB 002—Multiscale Innovative Materials and Structures (MIMS)].
References
Aernouts, J., I. Couckuyt, K. Crombecq, and J. J. J. Dirckx. 2010. “Elastic characterization of membranes with a complex shape using point indentation measurements and inverse modeling.” Int. J. Eng. Sci. 48 (6): 599–611. https://doi.org/10.1016/j.ijengsci.2010.02.001.
Andrade-Campos, A., R. De-Carvalho, and R. A. F. Valente. 2012. “Novel criteria for determination of material model parameters.” Int. J. Mech. Sci. 54 (1): 294–305. https://doi.org/10.1016/j.ijmecsci.2011.11.010.
Baker, R. W. 2012. Membrane technology and applications. Chichester, UK: Wiley.
Battaglia, G., A. Di Matteo, G. Micale, and A. Pirrotta. 2018. “Vibration-based identification of mechanical properties of orthotropic arbitrarily shaped plates: Numerical and experimental assessment.” Composites, Part B 150 (Oct): 212–225. https://doi.org/10.1016/j.compositesb.2018.05.029.
Battaglia, G., L. Gurreri, G. Airòfarulla, A. Cipollina, A. Pirrotta, G. Micale, and M. Ciofalo. 2019. “Membrane deformation and its effects on flow and mass transfer in the electromembrane processes.” Int. J. Mol. Sci. 20 (8): 1840. https://doi.org/10.3390/ijms20081840.
Bouzidi, R., and A. Le Van. 2004. “Numerical solution of hyperelastic membranes by energy minimization.” Comput. Struct. 82 (23–26): 1961–1969. https://doi.org/10.1016/j.compstruc.2004.03.057.
Brighenti, R., A. Carpinteri, and S. Vantadori. 2006. “A genetic algorithm applied to optimisation of patch repairs for cracked plates.” Comput. Methods Appl. Mech. Eng. 196 (1–3): 466–475. https://doi.org/10.1016/j.cma.2006.07.004.
Cao, J., and J. Lin. 2008. “A study on formulation of objective functions for determining material models.” Int. J. Mech. Sci. 50 (2): 193–204. https://doi.org/10.1016/j.ijmecsci.2007.07.003.
Chen, D., and Y. Li. 2020. “A development on multimodal optimization technique and its application in structural damage detection.” Appl. Soft Comput. J. 91 (Jun): 106264. https://doi.org/10.1016/j.asoc.2020.106264.
Chiozzi, A., G. Milani, and A. Tralli. 2017. “Fast kinematic limit analysis of FRP-reinforced masonry vaults. I: General genetic algorithm-NURBS-based formulation.” J. Eng. Mech. 143 (9): 04017071. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001267.
Cottone, G., G. Fileccia Scimemi, and A. Pirrotta. 2014. “α-stable distributions for better performance of ACO in detecting damage on not well spaced frequency systems.” Probab. Eng. Mech. 35 (Jan): 29–36. https://doi.org/10.1016/j.probengmech.2013.10.007.
Davis, F. M., Y. Luo, S. Avril, A. Duprey, and J. Lu. 2016. “Local mechanical properties of human ascending thoracic aneurysms.” J. Mech. Behav. Biomed. Mater. 61 (Aug): 235–249. https://doi.org/10.1016/j.jmbbm.2016.03.025.
Delfani, M. R. 2018. “Nonlinear elasticity of monolayer hexagonal crystals: Theory and application to circular bulge test.” Eur. J. Mech. A. Solids 68 (Mar–Apr): 117–132. https://doi.org/10.1016/j.euromechsol.2017.09.012.
Di Matteo, A., F. Lo Iacono, G. Navarra, and A. Pirrotta. 2014. “Direct evaluation of the equivalent linear damping for TLCD systems in random vibration for pre-design purposes.” Int. J. Non Linear Mech. 63 (Jul): 19–30. https://doi.org/10.1016/j.ijnonlinmec.2014.03.009.
Du, C., W. Zhao, S. Jiang, and X. Deng. 2020. “Dynamic XFEM-based detection of multiple flaws using an improved artificial bee colony algorithm.” Comput. Methods Appl. Mech. Eng. 365 (Jun): 112995. https://doi.org/10.1016/j.cma.2020.112995.
Ehsani, A., and J. Rezaeepazhand. 2016. “Stacking sequence optimization of laminated composite grid plates for maximum buckling load using genetic algorithm.” Int. J. Mech. Sci. 119 (Dec): 97–106. https://doi.org/10.1016/j.ijmecsci.2016.09.028.
Fries, T. P., and D. Schöllhammer. 2020. “A unified finite strain theory for membranes and ropes.” Comput. Methods Appl. Mech. Eng. 365 (Jun): 113031. https://doi.org/10.1016/j.cma.2020.113031.
Harb, N., N. Labed, M. Domaszewski, and F. Peyraut. 2011. “A new parameter identification method of soft biological tissue combining genetic algorithm with analytical optimization.” Comput. Methods Appl. Mech. Eng. 200 (1–4): 208–215. https://doi.org/10.1016/j.cma.2010.08.005.
Hwang, S. F., J. C. Wu, and R. S. He. 2009. “Identification of effective elastic constants of composite plates based on a hybrid genetic algorithm.” Compos. Struct. 90 (2): 217–224. https://doi.org/10.1016/j.compstruct.2009.03.021.
Jayyosi, C., K. Bruyère-Garnier, and M. Coret. 2017. “Geometry of an inflated membrane in elliptic bulge tests: Evaluation of an ellipsoidal shape approximation by stereoscopic digital image correlation measurements.” Med. Eng. Phys. 48 (Oct): 150–157. https://doi.org/10.1016/j.medengphy.2017.06.020.
Khodadadian, A., N. Noii, M. Parvizi, M. Abbaszadeh, T. Wick, and H. Clemens. 2020. “A Bayesian estimation method for variational phase-field fracture problems.” Comput. Mech. 66: 827–849. https://doi.org/10.1007/s00466-020-01876-4.
Kiris, A., and E. Inan. 2008. “On the identification of microstretch elastic moduli of materials by using vibration data of plates.” Int. J. Eng. Sci. 46 (6): 585–597. https://doi.org/10.1016/j.ijengsci.2008.01.001.
Kleuter, B., A. Menzel, and P. Steinmann. 2007. “Generalized parameter identification for finite viscoelasticity.” Comput. Methods Appl. Mech. Eng. 196 (35–36): 3315–3334. https://doi.org/10.1016/j.cma.2007.03.010.
Kydoniefs, A. D. 1995. “On finite deformations of elastic membranes.” Int. J. Eng. Sci. 33 (15): 2221–2238. https://doi.org/10.1016/0020-7225(95)00067-8.
Larson, M. D., C. J. Simonson, R. W. Besant, and P. W. Gibson. 2007. “The elastic and moisture transfer properties of polyethylene and polypropylene membranes for use in liquid-to-air energy exchangers.” J. Membr. Sci. 302 (1–2): 136–149. https://doi.org/10.1016/j.memsci.2007.06.050.
Li, D., Z. L. Zheng, C. Y. Liu, G. X. Zhang, Y. S. Lian, Y. Tian, Y. Xiao, and X. M. Xie. 2017. “Dynamic response of rectangular prestressed membrane subjected to uniform impact load.” Arch. Civ. Mech. Eng. 17 (3): 586–598. https://doi.org/10.1016/j.acme.2017.01.006.
Liu, G. R., X. Han, and K. Y. Lam. 2002. “A combined genetic algorithm and nonlinear least squares method for material characterization using elastic waves.” Comput. Methods Appl. Mech. Eng. 191 (17–18): 1909–1921. https://doi.org/10.1016/S0045-7825(01)00359-0.
Maier-Schneider, D., J. Maibach, and E. Obermeier. 1995. “A new analytical solution for the load-deflection of square membranes.” J. Microelectromech. Syst. 4 (4): 238–241. https://doi.org/10.1109/84.475551.
Maletta, C., and L. Pagnotta. 2004. “On the determination of mechanical properties of composite laminates using genetic algorithms.” Int. J. Mech. Mater. Des. 1 (2): 199–211. https://doi.org/10.1007/s10999-004-1731-5.
Martins, J. M. P., A. Andrade-Campos, and S. Thuillier. 2018. “Comparison of inverse identification strategies for constitutive mechanical models using full-field measurements.” Int. J. Mech. Sci. 145 (Sep): 330–345. https://doi.org/10.1016/j.ijmecsci.2018.07.013.
Maruthoor, S., A. Ajayakumar, T. Fuchs, O. Jakovlev, H. Reinecke, and J. Wilde. 2013. “Mechanical characterization of polycrystalline and amorphous silicon carbide thin films using bulge test.” J. Microelectromech. Syst. 22 (1): 140–146. https://doi.org/10.1109/JMEMS.2012.2218577.
Matouš, K., M. Lepš, J. Zeman, and M. Šejnoha. 2000. “Applying genetic algorithms to selected topics commonly encountered in engineering practice.” Comput. Methods Appl. Mech. Eng. 190 (13–14): 1629–1650. https://doi.org/10.1016/S0045-7825(00)00192-4.
Noii, N., and I. Aghayan. 2019. “Characterization of elastic-plastic coated material properties by indentation techniques using optimisation algorithms and finite element analysis.” Int. J. Mech. Sci. 152 (Mar): 465–480. https://doi.org/10.1016/j.ijmecsci.2019.01.010.
Noii, N., F. Aldakheel, T. Wick, and P. Wriggers. 2020. “An adaptive global–local approach for phase-field modeling of anisotropic brittle fracture.” Comput. Methods Appl. Mech. Eng. 361 (Apr): 112744. https://doi.org/10.1016/j.cma.2019.112744.
Pabst, O., M. Schiffer, E. Obermeier, T. Tekin, K. D. Lang, and H. D. Ngo. 2012. “Measurement of Young’s modulus and residual stress of thin SiC layers for MEMS high temperature applications.” Microsyst. Technol. 18 (7–8): 945–953. https://doi.org/10.1007/s00542-011-1419-3.
Pan, J. Y., P. Lin, F. Maseeh, and S. D. Senturia. 1990. “Verification of FEM analysis of load-deflection methods for measuring mechanical properties of thin films.” In Proc., IEEE 4th Technical Digest on Solid-State Sensor and Actuator Workshop, 70–73. New York: IEEE. https://doi.org/10.1109/solsen.1990.109823.
Perez, R. E., and K. Behdinan. 2007. “Particle swarm approach for structural design optimization.” Comput. Struct. 85 (19–20): 1579–1588. https://doi.org/10.1016/j.compstruc.2006.10.013.
Rixen, D., and M. Geradin. 1997. Mechanical vibrations: Theory and application to structural dynamics. Chichester, UK: Wiley.
Seide, P. 1977. “Large deflections of rectangular membranes under uniform pressure.” Int. J. Non Linear Mech. 12 (6): 397–406. https://doi.org/10.1016/0020-7462(77)90040-3.
Smith, C., A. Kanvinde, and G. Deierlein. 2017. “Calibration of continuum cyclic constitutive models for structural steel using particle swarm optimization.” J. Eng. Mech. 143 (5): 04017012. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001214.
Szilard, R. 2004. Theories and applications of plate analysis: Classical, numerical and engineering methods. Hoboken, NJ: Wiley.
Tabata, O., K. Kawahata, S. Sugiyama, and I. Igarashi. 1989. “Mechanical property measurements of thin films using load-deflection of composite rectangular membranes.” Sens. Actuators 20 (1–2): 135–141. https://doi.org/10.1016/0250-6874(89)87111-2.
Tam, J. H. 2020. “Identification of elastic properties utilizing non-destructive vibrational evaluation methods with emphasis on definition of objective functions: A review.” Struct. Multidiscip. Optim. 61 (Apr): 1677–1710. https://doi.org/10.1007/s00158-019-02433-1.
Timoshenko, S., and S. Woinowsky-Krieger. 1959. Theory of plates and shells. New York: McGraw-Hill.
Tinoco, H., J. Holzer, T. Pikálek, Z. Buchta, J. Lazar, A. Chlupová, T. Kruml, and P. Hutař. 2019. “Determination of elastic parameters of Si3N4 thin films by means of a numerical approach and bulge tests.” Thin Solid Films 672 (Feb): 66–74. https://doi.org/10.1016/j.tsf.2018.12.039.
Tonge, T. K., L. S. Atlan, L. M. Voo, and T. D. Nguyen. 2013. “Full-field bulge test for planar anisotropic tissues: Part I-Experimental methods applied to human skin tissue.” Acta Biomater. 9 (4): 5913–5925. https://doi.org/10.1016/j.actbio.2012.11.035.
Valdés, J. G., J. Miquel, and E. Oñate. 2009. “Nonlinear finite element analysis of orthotropic and prestressed membrane structures.” Finite Elem. Anal. Des. 45 (6–7): 395–405. https://doi.org/10.1016/j.finel.2008.11.008.
Ventsel, E., and T. Krauthammer. 2001. Thin plates and shells. New York: CRC Press.
Vlassak, J. J., and W. D. Nix. 1992. “A new bulge test technique for the determination of Young’s modulus and Poisson’s ratio of thin films.” J. Mater. Res. 7 (12): 3242–3249. https://doi.org/10.1557/JMR.1992.3242.
Walmsley, B. A., Y. Liu, X. Z. Hu, M. B. Bush, J. M. Dell, and L. Faraone. 2007. “Poisson’s ratio of low-temperature PECVD silicon nitride thin films.” J. Microelectromech. Syst. 16 (3): 622–627. https://doi.org/10.1109/JMEMS.2007.893518.
Wang, K., A. A. Abdalla, M. A. Khaleel, N. Hilal, and M. K. Khraisheh. 2017. “Mechanical properties of water desalination and wastewater treatment membranes.” Desalination 401 (Jan): 190–205. https://doi.org/10.1016/j.desal.2016.06.032.
Yokoyama, T., and K. Nakai. 2007. “Evaluation of in-plane orthotopic elastic constants of paper and paperboard.” In Vol. 3 of Proc., SEM Annual Conf. and Exposition on Experimental and Applied Mechanics 2007, 1505–1511. Red Hook, NY: Curran Associates.
Yokoyama, T., K. Nakai, and T. Inagaki. 2009. “Orientation dependence of in-plane tensile properties of paper: Experiments and theories.” J. Jpn. Soc. Exp. Mech. 9 (Special Issue): 86–91. https://doi.org/10.11395/jjsem.9.s86.
Yoshihara, H., and M. Yoshinobu. 2014. “Effects of specimen configuration and measurement method of strain on the characterization of tensile properties of paper.” J. Wood Sci. 60 (4): 287–293. https://doi.org/10.1007/s10086-014-1398-y.
Youssef, H., A. Ferrand, P. Calmon, P. Pons, and R. Plana. 2010. “Methods to improve reliability of bulge test technique to extract mechanical properties of thin films.” Microelectron. Reliab. 50 (9–11): 1888–1893. https://doi.org/10.1016/j.microrel.2010.07.013.
Zheng, Z., W. Sun, X. Suo, L. L. P. Wong, Z. Sun, and J. T. W. Yeow. 2015. “A novel deflection shape function for rectangular capacitive micromachined ultrasonic transducer diaphragms.” Sens. Bio-Sens. Res. 5 (Sep): 62–70. https://doi.org/10.1016/j.sbsr.2015.07.006.
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Journal of Engineering Mechanics
Volume 147 • Issue 6 • June 2021
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© 2021 American Society of Civil Engineers.
History
Received: Aug 24, 2020
Accepted: Dec 22, 2020
Published online: Mar 17, 2021
Published in print: Jun 1, 2021
Discussion open until: Aug 17, 2021
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