Despite wide industrial applications of Bis-GMA polymer, very few studies are available about the material classification, mechanical properties, and behavior of this material. In this study, the compressive behavior of Bis-GMA polymer was studied using different hyperelastic constitutive models through a hybrid experimental-computational process. Standard uniaxial compression tests were conducted to extract the mechanical behavior and structural response of the Bis-GMA polymer. A nano-indentation experiment was used to verify the compressive behavior of Bis-GMA polymer in the form of hyperelastic behavior. The finite element model and real-time simulation of the test incorporating different hyperelastic models were developed in comparison with the experimental finding to obtain the proper type of hyperelastic behavior of Bis-GMA polymer. The results indicate that a second-order polynomial hyperelastic model is the best fit to predict the behavior of Bis-GMA polymer. Next, the validated model was used to determine the true stress-strain curve of the Bis-GMA polymer.

Centre of Advance Manufacturing and Mechanical Engineering Faculty of Engineering University of Malaya Kuala Lumpur 50603 Malaysia

Centre of Advanced Composite Materials Universiti Teknologi Malaysia Johor Bahru 81310 Malaysia

Department of Aerospace Engineering Faculty of Engineering Universiti Putra Malaysia UPM Serdang 43400 Selangor Darul Ehsan Malaysia

Department of Mechanical Engineering Faculty of Engineering University of Malaya Kuala Lumpur 50603 Malaysia

Fatigue and Fracture Laboratory Center of Excellence in Experimental Solid Mechanics and Dynamics School of Mechanical Engineering Iran University of Science and Technology Tehran 16846 Iran

Institute for Nanomaterials Advanced Technologies and Innovation Technical University of Liberec Studentska 2 461 17 Liberec Czech Republic

School of Mechanical Engineering Universiti Teknologi Malaysia Johor Bahru 81310 Malaysia

See more in PubMed

Koloor S.S.R., Khosravani M.R., Hamzah R.I.R., Tamin M.N. FE model-based construction and progressive damage processes of FRP composite laminates with different manufacturing processes. Int. J. Mech. Sci. 2018;141:223–235. doi: 10.1016/j.ijmecsci.2018.03.028. DOI

Douba A., Emiroglu M., Kandil U.F., Reda Taha M.M. Very ductile polymer concrete using carbon nanotubes. Constr. Build. Mater. 2019;196:468–477. doi: 10.1016/j.conbuildmat.2018.11.021. DOI

Arakawa K., Mada T., Todo M., Takahashi J., Ooka S. Impact tensile fracture testing of a brittle polymer. Polym. Test. 2006;25:1095–1100. doi: 10.1016/j.polymertesting.2006.07.006. DOI

Rahimi A.S., Ayatollahi M.R., Torabi A.R. Ductile failure analysis of blunt V-notched epoxy resin plates subjected to combined tension-shear loading. Polym. Test. 2018;70:57–66. doi: 10.1016/j.polymertesting.2018.06.017. DOI

Yang L.M., Shim V.P.W., Lim C.T. A visco-hyperelastic approach to modelling the constitutive behaviour of rubber. Int. J. Impact Eng. 2000;24:545–560. doi: 10.1016/S0734-743X(99)00044-5. DOI

Khalajmasoumi M., Koloor S.S.R., Arefnia A., Ibrahim I.S., Yatim J.M. Hyperelastic Analysis of High Density Polyethylene under Monotonic Compressive Load. Appl. Mech. Mater. 2012;229–231:309–313. doi: 10.4028/www.scientific.net/AMM.229-231.309. DOI

Muhr A.H. Modeling the Stress–strain Behavior of Rubber. Rubber Chem. Technol. 2005;78:391–425. doi: 10.5254/1.3547890. DOI

Elhaouzi F., Nourdine A., Brosseau C., Mdarhri A., El Aboudi I., Zaghrioui M. Hyperelastic Behavior and Dynamic Mechanical Relaxation in Carbon Black-Polymer Composites. Polym. Compos. 2018 doi: 10.1002/pc.25142. DOI

Shin H., Choi J., Cho M. An efficient multiscale homogenization modeling approach to describe hyperelastic behavior of polymer nanocomposites. Compos. Sci. Technol. 2019;175:128–134. doi: 10.1016/j.compscitech.2019.03.015. DOI

Ju M.L., Mezghani S., Jmal H., Dupuis R., Aubry E. Parameter estimation of a hyperelastic constitutive model for the description of polyurethane foam in large deformation. Cell. Polym. 2013;32:21–40. doi: 10.1177/026248931303200102. DOI

Chen Z., Diebels S. Modelling and parameter re-identification of nanoindentation of soft polymers taking into account effects of surface roughness. Comput. Math. Appl. 2012;64:2775–2786. doi: 10.1016/j.camwa.2012.04.010. DOI

Luczynski K.W., Dejaco A., Lahayne O., Jaroszewicz J., Swieszkowski W., Hellmich C. MicroCT/Micromechanics-Based Finite Element Models and Quasi-Static Unloading Tests Deliver Consistent Values for Young’s Modulus of Rapid-Prototyped Polymer-Ceramic Tissue Engineering Scaffold. Comput. Model. Eng. Sci. 2012;87:505–528.

Mathews M., Wang H.-T., Li L. Finite Element Analysis of Nanoindentation and Elastic Behavior of Bi2Te3 Two-Dimensional Nanosheets. ECS J. Solid State Sci. Technol. 2016;5:Q3082–Q3087. doi: 10.1149/2.0151611jss. DOI

Lin D.C., Shreiber D.I., Dimitriadis E.K., Horkay F. Spherical indentation of soft matter beyond the Hertzian regime: Numerical and experimental validation of hyperelastic models. Biomech. Model. Mechanobiol. 2009;8:345–358. doi: 10.1007/s10237-008-0139-9. PubMed DOI PMC

Ehret A.E., Itskov M. A polyconvex hyperelastic model for fiber-reinforced materials in application to soft tissues. J. Mater. Sci. 2007;42:8853–8863. doi: 10.1007/s10853-007-1812-6. DOI

Zhang P., To A.C. Transversely isotropic hyperelastic-viscoplastic model for glassy polymers with application to additive manufactured photopolymers. Int. J. Plast. 2016;80:56–74. doi: 10.1016/j.ijplas.2015.12.012. DOI

Bois P.A.D., Kolling S., Koesters M., Frank T. Material behaviour of polymers under impact loading. Int. J. Impact Eng. 2006;32:725–740. doi: 10.1016/j.ijimpeng.2005.02.007. DOI

Ayoub G., Zaïri F., Fréderix C., Gloaguen J.M., Naït-Abdelaziz M., Seguela R., Lefebvre J.M. Effects of crystal content on the mechanical behaviour of polyethylene under finite strains: Experiments and constitutive modelling. Int. J. Plast. 2011;27:492–511. doi: 10.1016/j.ijplas.2010.07.005. DOI

Ottosen N.S., Ristinmaa M. Hyperelasticity. In: Ottosen N.S., Ristinmaa M., editors. The Mechanics of Constitutive Modeling. Elsevier Science Ltd.; Oxford, UK: 2005. pp. 67–102. DOI

Shannahan L.S. Ph.D. Thesis. Drexel University; Ann Arbor, MI, USA: 2017. A Hybrid Experimental-Computational Approach for the Analysis of Dynamic Fracture.

Perahia D., Grest G.S. From Interfaces to Bulk: Experimental-Computational Studies Across Time and Length Scales of Multi-Functional Ionic Polymers. Clemson Univ.; Clemson, SC, USA: 2017. DOE-Clemson-001. DOI

Meredig B., Wolverton C. A hybrid computational–experimental approach for automated crystal structure solution. Nat. Mater. 2013;12:123–127. doi: 10.1038/nmat3490. PubMed DOI

Tamin M.N., Nor F.M., Wei Keat L. Hybrid Experimental-Computational Approach for Solder/IMC Interface Shear Strength Determination in Solder Joints. IEEE Trans. Compon. Packag. Technol. 2010;33:614–620. doi: 10.1109/TCAPT.2010.2050887. DOI

Khalajmasoumi M., Koloor S.S.R., Arefnia A., Ibrahim I.S., Yatim J.M. Finite element analysis of curvature precast polymer panel for temporary support of tunnels. Appl. Mech. Mater. 2012;229–231:771–777. doi: 10.4028/www.scientific.net/AMM.229-231.771. DOI

Praharaj A.P., Behera D., Bastia T.K. Fabrication and Mechanical Properties of BisGMA/Amine Functionalized Paper Pulp Composites. Int. J. Innov. Res. Sci. Eng. Technol. 2014;3:12719–12723.

MacDonald K., Boyd D. Mechanical loading, an important factor in the evaluation of ion release from bone augmentation materials. Sci. Rep. 2018;8:14225. doi: 10.1038/s41598-018-32325-1. PubMed DOI PMC

Kawanabe K., Tamura J., Yamamuro T., Nakamura T., Kokubo T., Yoshihara S. A new bioactive bone cement consisting of BIS-GMA resin and bioactive glass powder. J. Appl. Biomater. 1993;4:135–141. doi: 10.1002/jab.770040204. PubMed DOI

Sideridou I., Tserki V., Papanastasiou G. Effect of chemical structure on degree of conversion in light-cured dimethacrylate-based dental resins. Biomaterials. 2002;23:1819–1829. doi: 10.1016/S0142-9612(01)00308-8. PubMed DOI

Linden L. Dental polymers. In: Salamone C., editor. Polymeric Materials Encyclopedia. Volume 3D–E. CRC Press; New York, NY, USA: 1996. p. 1839.

Hosseinzadeh-Nik T., Karimzadeh A., Ayatollahi M.R. Bond strength of a nano-composite used for bonding ceramic orthodontic brackets. Mater. Des. 2013;51:902–906. doi: 10.1016/j.matdes.2013.05.002. DOI

Karimzadeh A., Ayatollahi M.R., Hosseinzadeh-Nik T. Effects of a Nano-composite Adhesive on Mechanical Properties of Tooth Enamel After Removing Orthodontics Bracket—An Experimental Study Using Nano-indentation Test. Exp. Mech. 2015;55:1769–1777. doi: 10.1007/s11340-015-0087-0. DOI

Karimzadeh A., Ayatollahi M.R., Bushroa A.R. Effect of dental restorative material type and shade on characteristics of two-layer dental composite systems. Lat. Am. J. Solids Struct. 2016;13:1851–1865. doi: 10.1590/1679-78252562. DOI

Karimzadeh A., Ayatollahi M.R., Hosseinzadeh Nik T. Tribological Properties of Dental Enamel Before and After Orthodontic Bracket Bonding-Debonding by Nano-Scratch Test. J. Mech. 2019;35:279–287. doi: 10.1017/jmech.2017.101. DOI

Karimzadeh A., Ayatollahi M.R., Nikkhooyifar M., Bushroa A.R. Nanomechanical properties and wear resistance of dental restorative materials. Struct. Eng. Mech. 2017;64:819–826. doi: 10.12989/sem.2017.64.6.819. DOI

Kalachandra S., Taylor D., DePorter C., McGrath J. Polymeric materials for composite matrices in biological environments. Polymer. 1993;34:778–782. doi: 10.1016/0032-3861(93)90363-F. DOI

Gajewski V., Pfeifer C., Fróes-Salgado N., Boaro L., Braga R. Monomers Used in Resin Composites: Degree of Conversion, Mechanical Properties and Water Sorption/Solubility. Braz. Dent. J. 2012;23:508–514. doi: 10.1590/S0103-64402012000500007. PubMed DOI

Tiwari A., Polykarpov A. Photocured Materials, Volume 13 of Rsc Smart Materials, Chapter 15: Methacrylate and Epoxy Resins Photocured by Means of Visible Light-Emitting Diodes (LEDs) Royal Society of Chemistry; London, UK: 2014. p. 370.

Barszczewska-Rybarek I.M. Structure–property relationships in dimethacrylate networks based on Bis-GMA, UDMA and TEGDMA. Dent. Mater. 2009;25:1082–1089. doi: 10.1016/j.dental.2009.01.106. PubMed DOI

Floyd C.J.E., Dickens S.H. Network structure of Bis-GMA- and UDMA-based resin systems. Dent. Mater. 2006;22:1143–1149. doi: 10.1016/j.dental.2005.10.009. PubMed DOI

Barszczewska-Rybarek I., Chladek G. Studies on the Curing Efficiency and Mechanical Properties of Bis-GMA and TEGDMA Nanocomposites Containing Silver Nanoparticles. Int. J. Mol. Sci. 2018;19:3937. doi: 10.3390/ijms19123937. PubMed DOI PMC

Emami N., Soderholm K. Young’s modulus and degree of conversion of different combination of light-cure dental resins. Open Dent. J. 2009;3:202–207. doi: 10.2174/1874210600903010202. PubMed DOI PMC

Naumann M., Sterzenbach G., Pröschel P. Evaluation of load testing of postendodontic restorations in vitro: Linear compressive loading, gradual cycling loading and chewing simulation. J. Biomed. Mater. Res. Part. B Appl. Biomater. 2005;74B:829–834. doi: 10.1002/jbm.b.30321. PubMed DOI

Drummond J.L. Degradation, Fatigue, and Failure of Resin Dental Composite Materials. J. Dent. Res. 2008;87:710–719. doi: 10.1177/154405910808700802. PubMed DOI PMC

Ferracane J.L., Greener E.H. The effect of resin formulation on the degree of conversion and mechanical properties of dental restorative resins. J. Biomed. Mater. Res. 1986;20:121–131. doi: 10.1002/jbm.820200111. PubMed DOI

Magne P., Versluis A., Douglas W.H. Effect of luting composite shrinkage and thermal loads on the stress distribution in porcelain laminate veneers. J. Prosthet. Dent. 1999;81:335–344. doi: 10.1016/S0022-3913(99)70278-7. PubMed DOI

Ogden R.W. Non-Linear Elastic Deformations. Dover Publications; New York, NY, USA: 2013.

Arruda E.M., Boyce M.C. A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials. J. Mech. Phys. Solids. 1993;41:389–412. doi: 10.1016/0022-5096(93)90013-6. DOI

Bower A.F. Applied Mechanics of Solids, Chapter 3: Constitutive Equations: Relations between Stress and Strain. CRC Press; Boca Raton, FL, USA: 2009.

Section 22.5.1 of the Abaqus Analysis User’s Guide: Hyperelastic Behavior of Rubberlike Materials. Dassault Systèmes; Providence, RI, USA: 2014. Abaqus 6.14 Online Documentation.

Ogden R.W. Large Deformation Isotropic Elasticity—On the Correlation of Theory and Experiment for Incompressible Rubberlike Solids. Proc. R. Soc. Lond. A Math. Phys. Sci. 1972;326:565–584. doi: 10.1098/rspa.1972.0026. DOI

Yeoh O.H. Characterization of Elastic Properties of Carbon-Black-Filled Rubber Vulcanizates. Rubber Chem. Technol. 1990;63:792–805. doi: 10.5254/1.3538289. DOI

Kilian H.G., Enderle H.F., Unseld K. The use of the van der Waals model to elucidate universal aspects of structure-property relationships in simply extended dry and swollen rubbers. Colloid Polym. Sci. 1986;264:866–876. doi: 10.1007/BF01410637. DOI

Kossa A., Berezvai S. Novel strategy for the hyperelastic parameter fitting procedure of polymer foam materials. Polym. Test. 2016;53:149–155. doi: 10.1016/j.polymertesting.2016.05.014. DOI

Shahzad M., Kamran A., Siddiqui M.Z., Farhan M. Mechanical Characterization and FE Modelling of a Hyperelastic Material. Mater. Res. 2015;18:918–924. doi: 10.1590/1516-1439.320414. DOI

Mishra M., Szlufarska I. Possibility of high-pressure transformation during nanoindentation of SiC. Acta Mater. 2009;57:6156–6165. doi: 10.1016/j.actamat.2009.08.041. DOI

Randolph L.D., Palin W.M., Bebelman S., Devaux J., Gallez B., Leloup G., Leprince J.G. Ultra-fast light-curing resin composite with increased conversion and reduced monomer elution. Dent. Mater. 2014;30:594–604. doi: 10.1016/j.dental.2014.02.023. PubMed DOI

ASTM D695-15 . Standard Test Method for Compressive Properties of Rigid Plastics. ASTM International; West Conshohocken, PA, USA: 2015.

ISO-14577-1 . Metallic Materials—Instrumented Indentation Test for Hardness and Materials Parameters. International Organization for Standardization (ISO); Geneva, Switzerland: 2002. Part 1: Test. Method.

Karimzadeh A., Ayatollahi M.R., Alizadeh M. Finite element simulation of nano-indentation experiment on aluminum 1100. Comput. Mater. Sci. 2014;81:595–600. doi: 10.1016/j.commatsci.2013.09.019. DOI

Greaves G.N., Greer A.L., Lakes R.S., Rouxel T. Poisson’s ratio and modern materials. Nat. Mater. 2011;10:823–837. doi: 10.1038/nmat3134. PubMed DOI

Mott P.H., Roland C.M. Limits to Poisson’s ratio in isotropic materials. Phys. Rev. B. 2009;80:132104–132108. doi: 10.1103/PhysRevB.80.132104. DOI

Nitta K.-H., Yamana M. Rheology. InTech; Rijeka, Croatia: 2012. Chapter 5: Poisson’s Ratio and Mechanical Nonlinearity Under Tensile Deformation in Crystalline Polymers; pp. 113–130.

Karimzadeharani A. Investigation on Orthodontic Bond Strength Using Experimental and Numerical Methods. Iran University of Science and Technology; Tehran, Iran: 2017.

Oliver W.C., Pharr G.M. Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology. J. Mater. Res. 2004;19:3–20. doi: 10.1557/jmr.2004.19.1.3. DOI

Ng T.P., Koloor S.S.R., Djuansjah J.R.P., Abdul Kadir M.R. Assessment of compressive failure process of cortical bone materials using damage-based model. J. Mech. Behav. Biomed. Mater. 2017;66:11. doi: 10.1016/j.jmbbm.2016.10.014. PubMed DOI

Hua Y., Gu L., Watanabe H. Micromechanical analysis of nanoparticle-reinforced dental composites. Int. J. Eng. Sci. 2013;69:69–76. doi: 10.1016/j.ijengsci.2013.04.001. DOI

De Souza Venter S.A., Fávaro S.L., Radovanovic E., Girotto E.M. Hardness and degree of conversion of dental restorative composites based on an organic-inorganic hybrid. Mat. Res. 2013;16:898–902. doi: 10.1590/S1516-14392013005000089. DOI

Hochstetter G., Jimenez A., Cano J.P., Felder E. An attempt to determine the true stress—Strain curves of amorphous polymers by nanoindentation. Tribol. Int. 2003;36:973–985. doi: 10.1016/S0301-679X(03)00107-5. DOI

Haward R.N. The derivation of a strain hardening modulus from true stress–strain curves for thermoplastics. Polymer. 1994;35:3858–3862. doi: 10.1016/0032-3861(94)90268-2. DOI

Lightweight Glass Fiber-Reinforced Polymer Composite for Automotive Bumper Applications: A Review

Hybrid and Synthetic FRP Composites under Different Strain Rates: A Review