Strain-stiffening behavior of materials such as rubberlike materials and biological soft tissues is an important phenomenon. In this paper, we proposed a surface Green’s function tensor to describe the strain-stiffening behavior of the stretchable elastomer based on the Gent constitutive model. The surface Green’s function tensor of the Gent constitutive model can be recovered to that of neo-Hookean model, and applied to the indentation problem with a flat-ended cylindrical indenter. The relation between the indentation force and strain-stiffening parameter is analytically derived for equi-biaxial prestretched elastomers. The study shows that the strain-stiffening of the elastomer has a great impact on indentation behaviors, especially for the cases of large prestretches. For a given indentation depth, the indentation force decreases with the increase of the strain-stiffening parameter. For a given stiffening parameter, the indentation force increases with the increase of the prestretches. The proposed surface Green’s function tensor has also potential applications in other fields, such as wetting, cell migration, self-assembly on strain-stiffening materials, etc.
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