Simultaneous estimation of Poisson's ratio and Young's modulus using a single indentation : a finite element study

Abstract

Indentation is commonly used to determine the mechanical properties of different kinds of biological tissues and engineering materials. With the force–deformation data obtained from an indentation test, Young’s modulus of the tissue can be calculated using a linear elastic indentation model with a known Poisson’s ratio. A novel method for simultaneous estimation of Young’s modulus and Poisson’s ratio of the tissue using a single indentation was proposed in this study. Finite element (FE) analysis using 3D models was first used to establish the relationship between Poisson’s ratio and the deformation-dependent indentation stiffness for different aspect ratios (indentor radius/tissue original thickness) in the indentation test. From the FE results, it was found that the deformation-dependent indentation stiffness linearly increased with the deformation. Poisson’s ratio could be extracted based on the deformation-dependent indentation stiffness obtained from the force–deformation data. Young’s modulus was then further calculated with the estimated Poisson’s ratio. The feasibility of this method was demonstrated in virtue of using the indentation models with different material properties in the FE analysis. The numerical results showed that the percentage errors of the estimated Poisson’s ratios and the corresponding Young’s moduli ranged from −1.7% to −3.2% and 3.0% to 7.2%, respectively, with the aspect ratio (indentor radius/tissue thickness) larger than 1. It is expected that this novel method can be potentially used for quantitative assessment of various kinds of engineering materials and biological tissues, such as articular cartilage.