Instrumented indentation of a non-equal biaxial prestretched hyperelastic substrate

• We investigate the instrumented indentation of a prestretched hyperelastic substrate.
• The contact region is elliptical with principal axes along the stretching directions.
• We solve the inverse problem of material characterization using instrumented indentation of a prestretched surface.
• Our analysis is supported by finite element calculations and experiments.
• The analysis focuses on spherical indentation, but the results can be extended to all axisymmetric indenters.

The present work investigates the instrumented indentation of a prestretched hyperelastic substrate. The substrate is incompressible and has an elastic energy density which is isotropic in the reference frame. The analysis focuses on spherical indentation, but the results can be extended to all axisymmetric indenters. The substrate is prestretched biaxially, but it is not necessarily equal-biaxial. Due to the non-equal biaxial stretching, the contact region may obtain an elliptical form with principal axes along the stretching directions with the larger axis along the smallest surface stretch. The problem resembles that of the linear contact of an orthotropic substrate; however the problem under investigation is different. Based on the theoretical analysis we propose a methodology that can be used to solve the inverse problem of material characterization using instrumented indentation of a prestretched surface when the surface stretching is not equal-biaxial. Our analysis is supported by a set of finite element calculations and experiments.