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Soft materials such as rubber and hydrogels are commonly used in industry fortheir excellent hyperelastic behaviour. There are various types of constitutivemodels for soft materials, and phenomenological models are very popular forfinite element method (FEM) simulations. However, it is not easy to construct amodel that can precisely predict the complex behaviours of soft materials. Inthis paper, we suggest that the strain energy functions should be expressed asfunctions of ordered principal stretches, which have more flexible expressionsand are capable of matching various experimental curves. Moreover, the feasibleregion is small, and simple experiments, such as uniaxial tension/compressionand hydrostatic tests, are on its boundaries. Therefore, strain energyfunctions can be easily constructed by the interpolation of experimentalcurves, which does not need initial guessing in the form of the strain energyfunction as most existing phenomenological models do. The proposed strainenergy functions are perfectly consistent with the available experimentalcurves for interpolation. It is found that for incompressible materials, thefunction via an interpolation from two experimental curves can already predictother experimental curves reasonably well. To further improve the accuracy,additional experiments can be used in the interpolation.

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