A Method to Determine the Constitutive Parameters of Hyperelastic Films Based on Spherical Indentation

An indentation method to determine the properties of hyperelastic thin films is proposed, which is to use a spherical indenter to indent on the film with a small circular hole in the center. During this progress, there exists a maximum indentation load before penetration. Considering geometries of the film and the indenter, the specific form of relationship between the maximum indentation load and the elastic properties of the film is developed for neo-Hookean, Arruda-Boyce, and Ogden hyperelastic constitutive models. On the basis of this relationship, the initial shear modulus of the film can be directly obtained from single data of the maximum load, instead of recording and fitting to indentation curves. Furthermore, other properties of hyperelastic materials are explored from the perspective of the inverse problem. The experiments are performed with natural rubber, silicone rubber, and polydimethylsiloxane (PDMS) films to verify the feasibility of our method, and the optimal radius ratio between the indenter and the hole is concluded from the experimental results.