TY - JOUR

T1 - Estimating material elasticity by spherical indentation load-relaxation tests on viscoelastic samples of finite thickness

AU - Qiang, Bo

AU - Greenleaf, James

AU - Oyen, Michelle

AU - Zhang, Xiaoming

N1 - Funding Information:
Manuscript received april 18, 2011; accepted april 29, 2011. This study was supported by a research career development award to X. Zhang by Mayo clinic. B. qiang, j. Greenleaf, and X. Zhang are with the department of Physiology and Biomedical Engineering, Mayo clinic college of Medicine, rochester, Mn (e-mail: qiang.bo@mayo.edu). M. oyen is with the department of Engineering, University of cambridge, cambridge, UK. digital object Identifier 10.1109/TUFFc.2011.1961

PY - 2011/7

Y1 - 2011/7

N2 - 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.

AB - 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.

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U2 - 10.1109/TUFFC.2011.1961

DO - 10.1109/TUFFC.2011.1961

M3 - Article

C2 - 21768026

AN - SCOPUS:79960514180

SN - 0885-3010

VL - 58

SP - 1418

EP - 1429

JO - IRE Transactions on Ultrasonic Engineering

JF - IRE Transactions on Ultrasonic Engineering

IS - 7

M1 - 5953997

ER -