A simple interpolation-based approach towards the development of an accurate phenomenological constitutive relation for isotropic hyperelastic materials

Abstract Soft materials such as rubber and hydrogels are commonly used in industry for their excellent hyperelastic behaviour. There are various types of constitutive models for soft materials, and phenomenological models are very popular for finite element method (FEM) simulations. However, it is not easy to construct a model that can precisely predict the complex behaviours of soft materials. In this paper, we suggest that the strain energy density functions should be expressed as functions of ordered principal stretches, which have more flexible expressions and are capable of matching various experimental curves. Moreover, the feasible region is small, and simple experiments, such as uniaxial tension/compression and hydrostatic tests, are on its boundaries. Therefore, strain energy density functions can be easily constructed by the interpolation of experimental curves, which does not need initial guessing in the form of the strain energy density function as most existing phenomenological models do. The proposed strain energy density functions are perfectly consistent with the available experimental curves for interpolation. It is interesting to find that for incompressible materials, a 3D constitutive relation can be obtained from single uniaxial stress–strain experimental curve (from compression to tension) via interpolation, which can predict other experimental curves reasonably well. To further improve the accuracy, additional experiments can be used in the interpolation.