Abstract
Instrumented indentation technique has been increasingly utilized to measure the mechanical properties of soft polymers and biological tissues. However, the indentation behaviors of these materials has not been well understood, especially the parameter identification of their hyperelastic material properties. In this paper, we developed a spherical indentation data analysis method to directly extract the isotropic uniaxial stress-strain relationship of hyperelastic soft materials from the measured spherical indentation load-displacement curves. The proposed method mainly included new measure of indentation stress and strain, which was built based on the Hertz load-displacement relationship and further revised by considering the non-Hertzian effects of neo-Hookean hyperelastic contact problems. Numerical and actual indentation experiments showed the proposed definition of indentation strain can properly evaluate the amount of nonlinear strain for neo-Hookean, Yeoh and Arruda-Boyce hyperelastic materials. Meanwhile, the proposed spherical indentation data analysis method was applicable only in certain deformation range for Yeoh and Arruda-Boyce hyperelastic materials, because their nonlinear material parameters might cause very complicated contact pressure distributions. Building a universal data processing technique for characterizing the hyperelastic mechanical properties of soft materials through indentation experiments still needed further investigations.
Highlights
Instrumented indentation technique[1] has been an important experimental method to measure the mechanical properties of various soft materials including soft elastomers, polymeric gels and biological tissues.[2,3] These materials are “soft” and commonly exhibit nonlinear elastic stress-strain responses under external loadings, which can be well described by the hyperelastic constitutive relationship under finite deformation.[4,5,6,7] The hyperelastic indentation problems involved the coupling interaction of geometric, material and boundary nonlinearity, which make it difficult to be solved analytically.[8]
We proposed a data analysis method for directly extracting the nonlinear stressstrain relationship of hyperelastic soft materials from the spherical indentation load-depth curves
When this relationship was used to process the indentation load-displacement data, the revised function for indentation strain should be intensively defined as the strain field obviously deviated from the prediction of the Hertz model which applied a parabolic to describe the shape of spherical indenter
Summary
Instrumented indentation technique[1] has been an important experimental method to measure the mechanical properties of various soft materials including soft elastomers, polymeric gels and biological tissues.[2,3] These materials are “soft” and commonly exhibit nonlinear elastic stress-strain responses under external loadings, which can be well described by the hyperelastic constitutive relationship under finite deformation.[4,5,6,7] The hyperelastic indentation problems involved the coupling interaction of geometric, material and boundary nonlinearity, which make it difficult to be solved analytically.[8]. The other representative definitions of indentation stress and strain was proposed by Kalidindi et al.,[22] Donohue et al.[23] and Pathak et al.[24] by recasting the Hertzian equation into a different linear relationship between indentation stress and strain: σ This definition of elastic indentation strain can be visualized by idealizing the primary zone of indentation deformation as being equivalent (in an average sense) to compressing by h a cylindrical region of radius a and height 3πa/4. The spherical indentation stress and strain measure above mainly originated from the Hertzian load-displacement relationship was only applicable to linear elastic indentation under small penetration or contact radius. We proposed a data analysis method for directly extracting the nonlinear stressstrain relationship of hyperelastic soft materials from the spherical indentation load-depth curves. The proposed method mainly included novel indentation stress and strain measure, which was developed by considering the non-Hertzian effects associated with spherical indentation of hyperelastic soft materials. The correlations between the extracted spherical indentation stress-strain curves(ISS) and the uniaxial stress-strain curves (USS) of several kinds of hyperelastic soft materials were further analyzed and discussed
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