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Spherical indentation method for determining the constitutive parameters of hyperelastic soft materials

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Abstract

A comprehensive study on the spherical indentation of hyperelastic soft materials is carried out through combined theoretical, computational, and experimental efforts. Four widely used hyperelastic constitutive models are studied, including neo-Hookean, Mooney–Rivlin, Fung, and Arruda–Boyce models. Through dimensional analysis and finite element simulations, we establish the explicit relations between the indentation loads at given indentation depths and the constitutive parameters of materials. Based on the obtained results, the applicability of Hertzian solution to the measurement of the initial shear modulus of hyperelastic materials is examined. Furthermore, from the viewpoint of inverse problems, the possibility to measure some other properties of a hyperelastic material using spherical indentation tests, e.g., locking stretch, is addressed by considering the existence, uniqueness, and stability of the solution. Experiments have been performed on polydimethylsiloxane to validate the conclusions drawn from our theoretical analysis. The results reported in this study should help identify the extent to which the mechanical properties of hyperelastic materials could be measured from spherical indentation tests.

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Acknowledgments

Supports from the National Natural Science Foundation of China (Grant Nos. 11172155, 10972112), Tsinghua University (2012Z02103 and 20121087991) and 973 Program of MOST (2010CB631005) are acknowledged.

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Authors and Affiliations

  1. AML, Department of Engineering Mechanics, Tsinghua University, Beijing, 100084, China

    Man-Gong Zhang, Yan-Ping Cao, Guo-Yang Li & Xi-Qiao Feng

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  1. Man-Gong Zhang
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  2. Yan-Ping Cao
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Correspondence to Yan-Ping Cao.

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Zhang, MG., Cao, YP., Li, GY. et al. Spherical indentation method for determining the constitutive parameters of hyperelastic soft materials. Biomech Model Mechanobiol 13, 1–11 (2014). https://doi.org/10.1007/s10237-013-0481-4

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  • DOI: https://doi.org/10.1007/s10237-013-0481-4

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