A Simple Method for the Estimation of Hyperelastic Material Properties by Indentation Tests

Jae-Uk Song; Min-Seok Kim; Gu-Hun Jeong; Hyun-Gyu Kim

doi:10.7734/COSEIK.2019.32.5.273

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2019 Vol.32, Issue 5 Next Page

A Simple Method for the Estimation of Hyperelastic Material Properties by Indentation Tests 압입시험을 통하여 초탄성 재료 물성치를 평가하는 단순한 방법

2019. pp. 273-278

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Abstract

In this study, a new simple method for the estimation of hyperelastic material properties by indentation tests is proposed. Among hyperelastic material models, the Yeoh model with three material properties (C₁₀,C₂₀,C₃₀) is adopted to describe the strain energy density in terms of strain invariants. Finite element simulations of the spherical indentation of hyperelastic materials of the Yeoh model with different material properties are performed to establish a database of indentation force-displacement curves. The indentation force-displacement curves are fitted by cubic polynomials, which are approximated as a product of third-order polynomials of (C₁₀,C₂₀,C₃₀). A regression analysis is conducted to determine the coefficients of the equations for the indentation force-displacement curve approximations. A regression equation is used to estimate the hyperelastic material properties. The present method is verified by comparing the estimated material properties with true values.

Keywords

indentation tests

hyperelastic materials

finite element analysis

regression analysis

본 논문에서는 압입시험을 통해서 초탄성 재료 물성치를 평가하는 간단한 방법을 제시하였다. 초탄성 재료 모델 중, 3개의 물성치(C₁₀,C₂₀,C₃₀)를 가지는 Yeoh 모델을 선택하여 주연신률로 표현되는 변형률 에너지 밀도를 적용하였다. Yeoh 물성치를 변화시키며, 구형 압입시험 유한요소해석을 수행하여 압입자 반력-변위 곡선을 획득하였다. 압입자 반력-변위 곡선을 3차 다항식으로 근사하였고, 이 다항식을 물성치(C₁₀,C₂₀,C₃₀)의 3차 곱으로 근사된 3차 다항식으로 표현하였다. 압입자 반력-변위 곡선 근사를 위해 회귀분석을 진행하여 수식들의 계수를 결정하였으며, 이 회귀식을 이용하여 초탄성 재료의 물성치를 평가 하였다. 초탄성 재료 물성치 평가를 수행하고 오차를 비교하여 유효성을 보여 주었다.

키워드

압입시험

초탄성 재료

유한요소해석

회귀 분석

References

Horgan, C.O., Murphy, J.G. (2009) On The Volum -etric Part of Strain-Energy Functions used in the Constitutive Modeling of Slightly Compressible Solid Rubbers, Int. J. Solids &Struct., 46, pp.3078~3085. 10.1016/j.ijsolstr.2009.04.007

10.1016/j.ijsolstr.2009.04.007

Hwang, K.M., Oh, J.S., Lee, H.Y. (2009) Enhanc -ed Spherical Indentation Techniques for Rubber Property Evaluation, Korean Soc. Mech. Eng. A, 33(12), pp.1357~1365. 10.3795/KSME-A.2009.33.12.1357

10.3795/KSME-A.2009.33.12.1357

Hyun, H.C., Lee, J.H., Lee, H. (2008) Mathematical Expressions for Stress-Strain Curve of Metallic Material, Korean Soc. Mech. Eng. A, 32(1), pp.21 ~28. 10.3795/KSME-A.2008.32.1.021

10.3795/KSME-A.2008.32.1.021

Hyun, H.C., Lee, J.H., Kim, M., Lee. H. (2012) A Spherical Indentation Technique for Property Evaluation of Hyperelastic Rubber, J. Mater. Res., 27(20), pp.2677~2690. 10.1557/jmr.2012.241

10.1557/jmr.2012.241

Kim, B., Lee. S.B., Lee. J., Cho. S., Park. H., Yeom. S., Park. S.H. (2012) A Comparison Amo -ng Neo-Hookean Model, Mooney-Rivlin Model, and Ogden Model for Chloroprene Rubber, Int. J. Precis. Eng. &Manuf., 13, pp.759~764. 10.1007/s12541-012-0099-y

10.1007/s12541-012-0099-y

Kim, W.D., Kim. D.J., Kim. W.S., Lee. Y.S. (2003) A Study on the Equi-biaxial Tension Test of Rubber Material, Trans. Korean Soc. Automot. Eng., 11(5), pp.95~104.

Lee, H.J., Kim, K.B., Lee, B.S., Lee, B.S. (2003) Analvsis of True Stress-True Strain Relations through the Modeling of Ball Indentation Test, Korean Soc. Mech. Eng. Spring Conf., pp.2660~665.

Lee, H.Y., Lee, J.H. (2004) Software and Hardware Development of Micro-indenter for Material Property Evaluation of Hyper-Elastic Rubber, Korean Soc. Mech. Eng. A, 28(16), pp.816~825. 10.3795/KSME-A.2004.28.6.816

10.3795/KSME-A.2004.28.6.816

Lee, J.H., Kwon, D. (1997) Evaluation of True Stress- True Strain Curve through Continuous Indentation Test, Korean J. Met. &Mater., 35(12), pp.1616~1625.

Lee, S., Jun, Y., Kim, H.G. (2014) A Study on the Evaluation of Stress-strain Relationships of Materials by Indentation Tests, Korean Soc. Mech. Eng. Fall Conf., pp.2070~7072.

Marckmann, G., Verron, E. (2006) Comparison of Hyperelastic Models for Rubberlike Materials, Rubber Chem. &Technol., 79, pp.835~850. 10.5254/1.3547969

10.5254/1.3547969

Ogden, R.W., Saccomadi, G., Sgura, I. (2004) Fitting Hyperelastic Models to Experimental Data, Comput. Mech., 34, p.484. 10.1007/s00466-004-0593-y

10.1007/s00466-004-0593-y

Wu, Y., Wang, H., Li, A. (2016) Parameter Identifi -cation Methods for Hyperelastic and Hyper -Viscoelastic Models, Appl. Sci., 6(12), p.386. 10.3390/app6120386

10.3390/app6120386

Yeoh, O.H. (1990) Characterization of Elastic Properties of Carbon-black-filled Rubber Vulcan -izates, Rubber Chemistry and Technology, 63, pp.792~805. 10.5254/1.3538289

10.5254/1.3538289

Yeoh, O.H. (1993) Some Forms of the Strain Energy Function for Rubber, Rubber Chem. &Technol., 66, pp.754~771. 10.5254/1.3538343

10.5254/1.3538343

Information

Publisher :Computational Structural Engineering Institute of Korea
Publisher(Ko) :한국전산구조공학회
Journal Title :Journal of the Computational Structural Engineering Institute of Korea
Journal Title(Ko) :한국전산구조공학회 논문집
Volume : 32
No :5
Pages :273-278
Received Date : 2019-04-10
Revised Date : 2019-06-19
Accepted Date : 2019-06-20
DOI :https://doi.org/10.7734/COSEIK.2019.32.5.273

Journal of the Computational Structural Engineering Institute of Korea ISSN:1229-3059(Print) 2287-2302(Online) 한국전산구조공학회 논문집

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