Estimating material elasticity by spherical indentation load-relaxation tests on viscoelastic samples of finite thickness

Bo Qiang, James F Greenleaf, Michelle Oyen, Xiaoming Zhang

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24 Scopus citations


A two-step viscoelastic spherical indentation method is proposed to compensate for 1) material relaxation and 2) sample thickness. In the first step, the indenter is moved at a constant speed and the reaction force is measured. In the second step, the indenter is held at a constant position and the relaxation response of the material is measured. Then the relaxation response is fit with a multi-exponential function which corresponds to a three-branch general Maxwell model. The relaxation modulus is derived by correcting the finite ramp time introduced in the first step. The proposed model takes into account the sample thickness, which is important for applications in which the sample thickness is less than ten times the indenter radius. The model is validated numerically by finite element simulations. Experiments are carried out on a 10% gelatin phantom and a chicken breast sample with the proposed method. The results for both the gelatin phantom and the chicken breast sample agree with the results obtained from a surface wave method. Both the finite element simulations and experimental results show improved elasticity estimations by incorporating the sample thickness into the model. The measured shear elasticities of the 10% gelatin sample are 6.79 and 6.93 kPa by the proposed finite indentation method at sample thickness of 40 and 20 mm, respectively. The elasticity of the same sample is estimated to be 6.53 kPa by the surface wave method. For the chicken breast sample, the shear elasticity is measured to be 4.51 and 5.17 kPa by the proposed indentation method at sample thickness of 40 and 20 mm, respectively. Its elasticity is measured by the surface wave method to be 4.14 kPa.

Original languageEnglish (US)
Article number5953997
Pages (from-to)1418-1429
Number of pages12
JournalIEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
Issue number7
StatePublished - Jul 2011


ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Acoustics and Ultrasonics
  • Instrumentation

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