An approach to stress conversion between different deformation states for incompressible first‐invariant hyperelastic models

Abstract

AbstractTo characterize generally valid hyperelastic material parameters, tensile tests at different deformation states are essential. This necessity arises from the hyperelasticity theory for incompressible materials, which is based on the first and second invariants of the right Cauchy–Green tensor. These invariants describe the elongation and surface change during a deformation process. By comparing different deformation states using the incompressibility plane of invariants, an equivalent deformation state can be determined for first‐invariant hyperelastic models. This deformation equivalence results in equal strain energy and is used to derive a method for converting stress‐strain relations of different deformation modes. The presented approach is verified and validated with experimental data.