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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Indentation has been widely used to characterize the mechanical properties of biopolymers. Besides Hertzian solution, Sneddon's solution is frequently adopted to interpret the indentation data to deduce the elastic properties of biopolymers, e.g., elastic modulus. Sneddon's solution also forms the basis to develop viscoelastic contact models for determining the viscoelastic properties of materials from either conical or flat punch indentation responses. It is worth mentioning that the Sneddon's solution was originally proposed on the basis of linear elastic contact theory. However, in both conical and flat punch indentation of compliant materials, the indented solid may undergo finite deformation. In this case, the extent to which the Sneddon's solution is applicable so far has not been systematically investigated. In this paper, we use the combined theoretical, computational, and experimental efforts to investigate the indentation of hyperelastic compliant materials with a flat punch or a conical tip. The applicability of Sneddon's solutions is examined. Furthermore, we present new models to determine the elastic properties of nonlinear elastic biopolymers.

Determining the mechanical properties of soft matter across different length scales is of great importance in understanding the deformation behavior of compliant materials under various stimuli. A pipette aspiration test is a promising tool for such a purpose. A key challenge in the use of this method is to develop explicit expressions of the relationship between experimental responses and material properties particularly when the tested sample has irregular geometry. A simple scaling relation between the reduced creep function and the aspiration length is revealed in this paper by performing a theoretical analysis on the aspiration creep tests of viscoelastic soft solids with arbitrary surface profile. Numerical experiments have been performed on the tested materials with different geometries to validate the theoretical solution. In order to incorporate the effects of the rise time of the creep pressure, an analytical solution is further derived based on the generalized Maxwell model, which relates the parameters in reduced creep function to the aspiration length. Its usefulness is demonstrated through a numerical example and the analysis of the experimental data from literature. The analytical solutions reported here proved to be independent of the geometric parameters of the system under described conditions. Therefore, they may not only provide insight into the deformation behavior of soft materials in aspiration creep tests but also facilitate the use of this testing method to deduce the intrinsic creep/relaxation properties of viscoelastic compliant materials.

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