Home / Regular Issue / JST Vol. 31 (6) Oct. 2023 / JST-4080-2022


Numerical Analysis and Validation of Characterization of Polydimethylsiloxane Using Hyper-elastic Constitutive Models

Sana Zulfiqar, Abdullah Aziz Saad, Zulkifli Ahmad, Feizal Yusof and Zuraihana Bachok

Pertanika Journal of Science & Technology, Volume 31, Issue 6, October 2023

DOI: https://doi.org/10.47836/pjst.31.6.23

Keywords: Characterization of material, FEM analysis, hyper-elastic material models, material parameters, polydimethylsiloxane

Published on: 12 October 2023

The most researched elastomer in recent years is polydimethylsiloxane (PDMS), which has several uses in various engineering industries. One of the PDMS’s key characteristics is its hyper-elasticity nature, which enables the production of sensors, flexible electrical circuits, transducers, and antennas. This study used the hyper-elastic constitutive models to predict the mechanical behavior of incompressible, isotropic, and hyper-elastic material PDMS under uniaxial tension. These models are curve-fitting tools that consist of strain energy density and stress functions. To pursue the analysis, a new formulation of PDMS substrate was proposed, and a tensile test was performed to evaluate its stress-strain behavior. The experimental data was implemented on various hyper-elastic models using Abaqus, like Mooney-Rivlin, Yeoh, Ogden, and reduced polynomial models. The goodness of fit of every model was evaluated by calculating R2 values. Consequently, among these models, the reduced polynomial model with 6 material constants possessed the highest R2 value (0.9936) and was considered the best-fit model among the other models. Furthermore, the material constants of this model were applied to the 3D dumbbell-shaped model of PDMS in Abaqus for its validation. The boundary conditions were applied on the model similar to the experimental setup, as 33 mm displacement on one end and the other was fixed with all DOF. For mesh quality and mesh sensitivity of the material, various mesh sizes with the linear formulation (C3D8RH) were utilized, and the best mesh size was selected to evaluate very close results with the experimental.

  • Akther, F., Yakob, S. B., Nguyen, N. T., & Ta, H. T. (2020). Surface modification techniques for endothelial cell seeding in PDMS microfluidic devices. Biosensors, 10(11), Article 182. https://doi.org/10.3390/bios10110182

  • Ali, A., Hosseini, M., & Sahari, B. B. (2010). A review of constitutive models for rubber-like materials. American Journal of Engineering and Applied Sciences, 3(1), 232-239. https://doi.org/10.3844/ajeassp.2010.232.239

  • Anssari-Benam, A., & Bucchi, A. (2021). A generalised neo-Hookean strain energy function for application to the finite deformation of elastomers. International Journal of Non-Linear Mechanics, 128, Article 103626. https://doi.org/https://doi.org/10.1016/j.ijnonlinmec.2020.103626

  • ASTM D412-16. (2021). Standard test methods for vulcanized rubber and thermoplastic elastomers-tension. ASTM International. https://doi.org/10.1520/D0412-16R21

  • Aziz, N. A., Saad, A. A., Ahmad, Z., Zulfiqar, S., Ani, F. C., & Samsudin, Z. (2020). Chapter 8 - Stress analysis of stretchable conductive polymer for electronics circuit application. In A. S. H. Makhlouf & M. Aliofkhazraei (Eds.), Handbook of Materials Failure Analysis (pp. 205-224). Butterworth-Heinemann. https://doi.org/https://doi.org/10.1016/B978-0-08-101937-5.00008-7

  • Bashirzadeh, Y., Qian, S., & Maruthamuthu, V. (2018). Non-intrusive measurement of wall shear stress in flow channels. Sensors and Actuators, A: Physical, 271, 118-123. https://doi.org/10.1016/j.sna.2018.01.012

  • Beda, T. (2007). Modeling hyperelastic behavior of rubber: A novel invariant-based and a review of constitutive models. Journal of Polymer Science, Part B: Polymer Physics, 45(13), 1713-1732. https://doi.org/10.1002/polb.20928

  • Beda, T., & Chevalier, Y. (2003). Hybrid continuum model for large elastic deformation of rubber. Journal of Applied Physics, 94(4), 2701-2706. https://doi.org/10.1063/1.1586471

  • Bien-aimé, L. K. M., Blaise, B. B., & Beda, T. (2020). Characterization of hyperelastic deformation behavior of rubber-like materials. SN Applied Sciences, 2(4), Article 648. https://doi.org/10.1007/s42452-020-2355-6

  • Boyce, M. C., & Arruda, E. M. (2000). Constitutive models of rubber elasticity: A review. Rubber Chemistry and Technology, 73(3), 504-523. https://doi.org/10.5254/1.3547602

  • Casanova-Moreno, J., To, J., Yang, C. W. T., Turner, R. F. B., Bizzotto, D., & Cheung, K. C. (2017). Fabricating devices with improved adhesion between PDMS and gold-patterned glass. Sensors and Actuators, B: Chemical, 246, 904-909. https://doi.org/10.1016/j.snb.2017.02.109

  • Chen, Z., Tristano, J. R., & Kwok, W. (2003, September 14-17). Combined laplacian and optimization-based smoothing for quadratic mixed surface meshes. In Proceedings of the 12th International Meshing Roundtable, IMR 2003 (pp. 360-370). Santa Fe, New Mexico, USA.

  • Dassi, F., Kamenski, L., & Si, H. (2016). Tetrahedral mesh improvement using moving mesh smoothing and lazy searching flips. Procedia Engineering, 163, 302-314. https://doi.org/10.1016/j.proeng.2016.11.065

  • Doan, H. G. M., & Mertiny, P. (2020). Creep testing of thermoplastic fiber-reinforced polymer composite tubular coupons. Materials, 13(20), 1-17. https://doi.org/10.3390/ma13204637

  • Faghihi, S., Karimi, A., Jamadi, M., Imani, R., & Salarian, R. (2014). Graphene oxide/poly(acrylic acid)/gelatin nanocomposite hydrogel: Experimental and numerical validation of hyperelastic model. Materials Science and Engineering C, 38(1), 299-305. https://doi.org/10.1016/j.msec.2014.02.015

  • Gómez, F. S., Lorza, R. L., Bobadilla, M. C., & García, R. E. (2017). Improving the process of adjusting the parameters of finite element models of healthy human intervertebral discs by the multi-response surface method. Materials, 10(10), Article 1116. https://doi.org/10.3390/ma10101116

  • Gonzalez, M., Axisa, F., Bulcke, M. Vanden, Brosteaux, D., Vandevelde, B., & Vanfleteren, J. (2008). Design of metal interconnects for stretchable electronic circuits. Microelectronics Reliability, 48(6), 825-832. https://doi.org/10.1016/j.microrel.2008.03.025

  • Guo, Z., & Sluys, L. J. (2006). Application of a new constitutive model for the description of rubber-like materials under monotonic loading. International Journal of Solids and Structures, 43(9), 2799-2819. https://doi.org/10.1016/j.ijsolstr.2005.06.026

  • Hassler, C., Boretius, T., & Stieglitz, T. (2011). Polymers for neural implants. Journal of Polymer Science, Part B: Polymer Physics, 49(1), 18-33. https://doi.org/10.1002/polb.22169

  • Íñiguez-Macedo, S., Lostado-Lorza, R., Escribano-García, R., & Martínez-Calvo, M. A. (2019). Finite element model updating combined with multi-response optimization for hyper-elastic materials characterization. Materials, 12(7), Article 1019. https://doi.org/10.3390/ma12071019

  • Izdihar, K., Razak, H. R. A., Supion, N., Karim, M. K. A., Osman, N. H., & Norkhairunnisa, M. (2021). Structural, mechanical, and dielectric properties of polydimethylsiloxane and silicone elastomer for the fabrication of clinical-grade kidney phantom. Applied Sciences, 11(3), 1-13. https://doi.org/10.3390/app11031172

  • Jewkes, R., Burton, H. E., & Espino, D. M. (2018). Towards additive manufacture of functional, spline-based morphometric models of healthy and diseased coronary arteries: In vitro proof-of-concept using a porcine template. Journal of Functional Biomaterials, 9(1), Article 15. https://doi.org/10.3390/jfb9010015

  • Ju, M. L., Jmal, H., Dupuis, R., & Aubry, E. (2014). A Comparison among polynomial model, reduced polynomial model and Ogden model for polyurethane foam. Material Science and Engineering Technology II, 856, 169-173. https://doi.org/10.4028/www.scientific.net/AMR.856.169

  • Kim, B., Lee, S. B., Lee, J., Cho, S., Park, H., Yeom, S., & Park, S. H. (2012). A comparison among Neo-Hookean model, Mooney-Rivlin model, and Ogden model for Chloroprene rubber. International Journal of Precision Engineering and Manufacturing, 13(5), 759-764. https://doi.org/10.1007/s12541-012-0099-y

  • López-Campos, J. A., Segade, A., Casarejos, E., Fernández, J. R., & Días, G. R. (2019). Hyperelastic characterization oriented to finite element applications using genetic algorithms. Advances in Engineering Software, 133, 52-59. https://doi.org/10.1016/j.advengsoft.2019.04.001

  • Lorza, R. L., Bobadilla, M. C., Calvo, M. Á. M., & Roldán, P. M. V. (2017). Residual stresses with time-independent cyclic plasticity in finite element analysis of welded joints. Metals, 7(4), Article 136. https://doi.org/10.3390/met7040136

  • Ma, Y., & Wang, M. (2021). An efficient method to improve the quality of tetrahedron mesh with MFRC. Scientific Reports, 11(1), Article 22802. https://doi.org/10.1038/s41598-021-02187-1

  • Martin, S., & Bhushan, B. (2017). Transparent, wear-resistant, superhydrophobic and superoleophobic poly(dimethylsiloxane) (PDMS) surfaces. Journal of Colloid and Interface Science, 488, 118-126. https://doi.org/10.1016/j.jcis.2016.10.094

  • Martinez, R. F., Lorza, R. L., Delgado, A. A. S., & Pullaguari, N. O. P. (2018). Optimizing presetting attributes by softcomputing techniques to improve tapered roller bearings working conditions. Advances in Engineering Software, 123, 13-24. https://doi.org/10.1016/j.advengsoft.2018.05.005

  • Martins, P., Peña, E., Calvo, B., Doblaré, M., Mascarenhas, T., Jorge, R. N., & Ferreira, A. (2010). Prediction of nonlinear elastic behaviour of vaginal tissue: Experimental results and model formulation. Computer Methods in Biomechanics and Biomedical Engineering, 13(3), 327-337. https://doi.org/10.1080/10255840903208197

  • Meissner, B., & Matějka, L. (2002). Comparison of recent rubber-elasticity theories with biaxial stress-strain data: The slip-link theory of Edwards and Vilgis. Polymer, 43(13), 3803-3809. https://doi.org/10.1016/S0032-3861(02)00150-7

  • Nunes, L. C. S. (2011). Mechanical characterization of hyperelastic polydimethylsiloxane by simple shear test. Materials Science and Engineering: A, 528(3), 1799-1804. https://doi.org/https://doi.org/10.1016/j.msea.2010.11.025

  • Parthasarathy, V. N., & Kodiyalam, S. (1991). A constrained optimization approach to finite element mesh smoothing. Finite Elements in Analysis and Design, 9(4), 309-320. https://doi.org/10.1016/0168-874X(91)90004-I

  • Pucci, E., & Saccomandi, G. (2002). A note on the gent model for rubber-like materials. Rubber Chemistry and Technology, 75(5), 839-851. https://doi.org/10.5254/1.3547687

  • Ribeiro, J., Fernandes, C. S., & Lima, R. (2018). Numerical simulation of hyperelastic behaviour in aneurysm models. Lecture Notes in Computational Vision and Biomechanics, 27, 937-944. https://doi.org/10.1007/978-3-319-68195-5_102

  • Roh, C., Lee, J., & Kang, C. K. (2016). Physical properties of PDMS (polydimethylsiloxane) microfluidic devices on fluid behaviors: Various diameters and shapes of periodically-embedded microstructures. Materials, 9(10), Article 836. https://doi.org/10.3390/ma9100836

  • Sattarian, M., & Ghassemi, A. (2019). Identifying the poly methyl methacrylate behavior during free thermoforming using experimental tests and numerical simulation. Journal of Theoretical and Applied Mechanics, 57(4), 909-921. https://doi.org/10.15632/jtam-pl/112414

  • Shahzad, M., Kamran, A., Siddiqui, M. Z., & Farhan, M. (2015). Mechanical characterization and FE modelling of a hyperelastic material. Materials Research, 18(5), 918-924. https://doi.org/10.1590/1516-1439.320414

  • Souza, A., Marques, E., Balsa, C., & Ribeiro, J. (2020). Characterization of shear strain on PDMS: Numerical and experimental approaches. Applied Sciences, 10(9), Article 3322. https://doi.org/10.3390/app10093322

  • Subhani, P. M., & Kumar, R. K. (2009). A new stored energy function for rubber like materials for low strains. Mechanics of Advanced Materials and Structures, 16(5), 402-416. https://doi.org/10.1080/15376490902781167

  • Sugihardjo, H., Tavio, T., & Lesmana, Y. (2018). FE model of low grade rubber for modeling housing’s low-cost rubber base isolators. Civil Engineering Journal, 4(1), 24-45. https://doi.org/10.28991/cej-030966

  • SYSTEMES, D. (2021). Mesh Quality Checks. DASSAULT SYSTEMES. https://help.solidworks.com/2021/english/SolidWorks/cworks/c_Mesh_Quality_Checks.htm#:~:text=A good-quality mesh has,Aspect ratio of all elements

  • Tansel, D. Z., Brenneman, J., Fedder, G. K., & Panat, R. (2020). Mechanical characterization of polydimethylsiloxane (PDMS) exposed to thermal histories up to 300 C in a vacuum environment. Journal of Micromechanics and Microengineering, 30(6), Article 67001. https://doi.org/10.1088/1361-6439/ab82f4

  • Wineman, A. (2005). Some results for generalized neo-Hookean elastic materials. International Journal of Non-Linear Mechanics, 40(2), 271-279. https://doi.org/https://doi.org/10.1016/j.ijnonlinmec.2004.05.007

  • Wriggers, P. (2008). Nonlinear Finite Element Methods. Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-540-71001-1

  • Xue, L., Pham, J. T., Iturri, J., & Del Campo, A. (2016). Stick-slip friction of PDMS surfaces for bioinspired adhesives. Langmuir, 32(10), 2428-2435. https://doi.org/10.1021/acs.langmuir.6b00513

  • Yu, Y. S., & Zhao, Y. P. (2009). Deformation of PDMS membrane and microcantilever by a water droplet: Comparison between Mooney-Rivlin and linear elastic constitutive models. Journal of Colloid and Interface Science, 332(2), 467-476. https://doi.org/10.1016/j.jcis.2008.12.054

  • Zulfiqar, S., Saad, A. A., Chek, M. W., Sharif, M. F. M., Samsudin, Z., & Ali, M. Y. T. (2020). Structural and random vibration analysis of LEDs conductive polymer interconnections. IOP Conference Series: Materials Science and Engineering, 815, Article 012003. https://doi.org/10.1088/1757-899X/815/1/012003

  • Zulfiqar, S, Saad, A. A., Ahmad, Z., Yusof, F., & Fakpan, K. (2022). Analysis and characterization of polydimethylsiloxane (PDMS) substrate by using uniaxial tensile test and Mooney-Rivlin Hyper-elastic model. Journal of Advanced Manufacturing Technology, 16(1), 61-72.

  • Zulfiqar, S., Saad, A. A., Ahmad, Z., Yusof, F., & Bachok, Z. (2021). Structural analysis and material characterization of silver conductive ink for stretchable electronics. International Journal of Integrated Engineering, 13(7), 128-135.