Journal of the Computational Structural Engineering Institute of Korea (한국전산구조공학회논문집)

Computational Structural Engineering Institute of Korea (한국전산구조공학회)
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A Simple Method for the Estimation of Hyperelastic Material Properties by Indentation Tests

압입시험을 통하여 초탄성 재료 물성치를 평가하는 단순한 방법

  • Song, Jae-Uk (Department of Mechanical and Automotive Engineering, Seoul National University of Science and Technology) ;
  • Kim, Min-Seok (Department of Mechanical and Automotive Engineering, Seoul National University of Science and Technology) ;
  • Jeong, Gu-Hun (Department of Mechanical and Automotive Engineering, Seoul National University of Science and Technology) ;
  • Kim, Hyun-Gyu (Department of Mechanical and Automotive Engineering, Seoul National University of Science and Technology)
  • 송재욱 (서울과학기술대학교 기계자동차공학과) ;
  • 김민석 (서울과학기술대학교 기계자동차공학과) ;
  • 정구훈 (서울과학기술대학교 기계자동차공학과) ;
  • 김현규 (서울과학기술대학교 기계자동차공학과)
  • Received : 2019.04.10
  • Accepted : 2019.06.20
  • Published : 2019.10.31
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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 ($C_{10}$, $C_{20}$, $C_{30}$) 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 ($C_{10}$, $C_{20}$, $C_{30}$). 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.

본 논문에서는 압입시험을 통해서 초탄성 재료 물성치를 평가하는 간단한 방법을 제시하였다. 초탄성 재료 모델 중, 3개의 물성치($C_{10}$, $C_{20}$, $C_{30}$)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($C_{10}$, $C_{20}$, $C_{30}$)의 3차 곱으로 근사된 3차 다항식으로 표현하였다. 압입자 반력-변위곡선 근사를 위해 회귀분석을 진행하여 수식들의 계수를 결정하였으며, 이 회귀식을 이용하여 초탄성 재료의 물성치를 평가하였다. 초탄성 재료 물성치 평가를 수행하고 오차를 비교하여 유효성을 보여 주었다.

Keywords

References

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