An equibiaxial tension test could be necessary to set up hyperelastic material constants for elastomers exactly. Unfortunately, very often, only uniaxial tension experimental data are available. It is possible to use only uniaxial data to compute hyperelastic constants for a hyperelastic model, but the prediction of behavior in different deformation modes (as is equibiaxial or pure shear) will not work correctly with this model. It is quite obvious that there is some relation between uniaxial and equibiaxial behavior for the elastomers. Thus, we could use uniaxial data to predict equibiaxial behavior. If we were able to predict (at least approximately) equibiaxial data, then we could create a hyperelastic model usable for the general prediction of any deformation mode of elastomer. The method of the appropriate processing of experimental data for such prediction is described in the article and is verified by the comparison with the experiment. The presented results include uniaxial and equibiaxial experimental data, the created average curve of both the deformation modes, and the predicted equibiaxial data. Using Student's t-test, a close coincidence of the real and predicted equibiaxial data was confirmed.

Faculty of Technological Studies Uva Wellassa University Kelaniya 11600 Sri Lanka

Faculty of Technology Tomas Bata University in Zlín 760 01 Zlin Czech Republic

Zobrazit více v PubMed

Chaves E.W.V. Notes on Continuum Mechanics. Springer; Dordrecht, The Netherlands: 2013. 694p

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

Martins P.A.L.S., Jorge R.M.N., Ferreira A.J.M. A Comparative Study of Several Material Models for Prediction of Hyperelastic roperties: Application to Silicone-Rubber and Soft Tissues. Strain. 2006;42:135–147. doi: 10.1111/j.1475-1305.2006.00257.x. DOI

Keerthiwansa R., Javořík J., Kledrowetz J., Nekoksa P. Elastomer Testing: The Risk of Using Only Uniaxial Data for Fitting the Mooney-Rivlin Hyperelastic-Material Model. Mater. Tehnol. 2018;52:3–8. doi: 10.17222/mit.2017.085. DOI

Javořík J., Dvořák Z. Equibiaxal Test of Elastomers. KGK Kautsch Gummi Kunstst. 2007;60:608–610.

Keerthiwansa R., Javořík J., Kledrowetz J. Hyperelastic-Material Characterization: A Comparison of Material Constants. Mater. Tehnol. 2020;54:121–123. doi: 10.17222/mit.2019.161. DOI

Seibert H., Scheffer T., Diebels S. Biaxial testing of elastomers: Experimental setup, measurement and experimental optimisation of specimen’s shape. Tech. Mech. 2014;34:72–89.

Ogden R.W. Non-Linear Elastic Deformations. Dover Publications, Inc.; New York, NY, USA: 1984. 544p

Keerthiwansa R., Javorik J., Kledrowetz J., Nekoksa P. Hyperelastic Material Characterization: A Method of Reducing the Error of Using Only Uniaxial Data for Fitting Mooney-Rivlin Curve. Mater. Sci. Forum. 2018;919:292–298. doi: 10.4028/www.scientific.net/MSF.919.292. DOI

Keerthiwansa R., Javořík J., Rusnáková S., Kledrowetz J., Gross P. Hyperelastic Material Characterization: How the Change in Mooney-Rivlin Parameter Values Effect the Model Curve. Mater. Sci. Forum. 2020;914:265–271. doi: 10.4028/www.scientific.net/MSF.994.265. DOI

Brown R. Physical Testing of Rubber. Springer; New York, NY, USA: 2006. 388p. DOI

Smith L.P. The Language of Rubber: An Introduction to the Specification and Testing of Elastomers. Butterworth-Heinemann; Oxford, UK: 1993. 257p

Doman D.A., Cronin D.S., Salisbury C.P. Characterization of polyurethane rubber at high deformation rates. Exp. Mech. 2006;46:367–376. doi: 10.1007/s11340-006-6422-8. DOI

Österlöf R., Wentzel H., Kari L. An efficient method for obtaining the hyperelastic properties of filled elastomers in finite strain applications. Polym. Test. 2015;41:44–54. doi: 10.1016/j.polymertesting.2014.10.008. DOI

Luo H., Zhu Y., Zhao H., Ma L., Zhang J. Equibiaxial Planar Tension Test Method and the Simulation Analysis for Hyperelastic EAP Membrane. Adv. Polym. Technol. 2023;2023:7343992. doi: 10.1155/2023/7343992. DOI

Xiao R. A Review of Cruciform Biaxial Tensile Testing of Sheet Metals. Exp. Tech. 2019;43:501–520. doi: 10.1007/s40799-018-00297-6. DOI

Fujikawa M., Maeda N., Yamabe J., Kodama Y., Koishi M. Determining Stress–Strain in Rubber with In-Plane Biaxial Tensile Tester. Exp. Mech. 2014;54:1639–1649. doi: 10.1007/s11340-014-9942-7. DOI

Marano C., Vangosa F.B., Andena L., Frassine R., editors. Constitutive Models for Rubber XII: Proceedings of the 12th European Conference on Constitutive Models for Rubber (ECCMR 2022) CRC Press; Milano, Italy: 2022. 524p

Beda T. Modeling hyperelastic behavior of rubber: A novel invariant-based and a review of constitutive models. J. Polym. Sci. Part B Polym. Phys. 2007;45:1713–1732. doi: 10.1002/polb.20928. DOI

Mirzapour J. A micro-mechanically-based constitutive model for hyperelastic rubber-like materials considering the topological constraints. Int. J. Solids Struct. 2023;275:112299. doi: 10.1016/j.ijsolstr.2023.112299. DOI

Guo Z., Sluys L.J. Constitutive modelling of hyperelastic rubber-like materials. Heron. 2008;53:109–132.

Kim H.G. A comparative study of hyperelastic and hypoelastic material models with constant elastic moduli for large deformation problems. Acta Mech. 2016;227:1351–1362. doi: 10.1007/s00707-015-1554-5. DOI

Mollaee S., Budgett D.M., Taberner A.J., Nielsen P.M.F. Hyperelastic constitutive model parameters identification using optical-based techniques and hybrid optimisation. Int. J. Mech. Mater. Des. 2024;20:233–249. doi: 10.1007/s10999-023-09673-6. DOI

Rubber, Vulcanized or Thermoplastic—Determination of Tensile Stress-Strain Properties. International Organization for Standardization; Geneva, Switzerland: 2017.

Reuge N., Schmidt F.M., Le Maoult Y., Rachik M. Elastomer biaxial characterization using bubble inflation technique. I: Experimental investigations. Polym. Eng. Sci. 2001;41:522–531. doi: 10.1002/pen.10749. DOI

Sutton M.A., Orteu J.J., Schreier H. Image Correlation for Shape, Motion and Deformation Measurements. Basic Concepts, Theory and Applications. Springer; New York, NY, USA: 2009. 322p. DOI

Ab Ghani A.F., Ali M.B., Dhar Malingam S., Mahmud J. Digital Image Correlation (DIC) Technique in Measuring Strain Using Opensource Platform Ncorr. J. Adv. Res. Appl. Mech. 2016;26:10–21.

Castillo E.R., Allen T., Henry R., Griffith M., Ingham J. Digital image correlation (DIC) for measurement of strains and displacements in coarse, low volume-fraction FRP composites used in civil infrastructure. Compos. Struct. 2019;212:43–57. doi: 10.1016/j.compstruct.2019.01.024. DOI

Khoo S.W., Karuppanan S., Tan C.S. A Review of Surface Deformation and Strain Measurement Using Two-Dimensional Digital Image Correlation. Metrol. Meas. Syst. 2016;23:461–480. doi: 10.1515/mms-2016-0028. DOI

Jerabek M., Major Z., Lang R.W. Strain determination of polymeric materials using digital image correlation. Polym. Test. 2010;29:407–416. doi: 10.1016/j.polymertesting.2010.01.005. DOI

Grytten F., Daiyan H., Polanco-Loria M., Dumoulin S. Use of digital image correlation to measure large-strain tensile properties of ductile thermoplastics. Polym. Test. 2009;28:653–660. doi: 10.1016/j.polymertesting.2009.05.009. DOI

Quanjin M., Rejab M.R.M., Halim Q., Merzuki M.N.M., Darus M.A.H. Experimental investigation of the tensile test using digital image correlation (DIC) method. Mater. Today Proc. 2020;27:757–763. doi: 10.1016/j.matpr.2019.12.072. DOI

Górszczyk J., Malicki K., Zych T. Application of digital image correlation (DIC) method for road material testing. Materials. 2019;12:2349. doi: 10.3390/ma12152349. PubMed DOI PMC