  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 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
functions can be easily constructed by the interpolation of experimental
curves, which does not need initial guessing in the form of the strain energy
function as most existing phenomenological models do. The proposed strain
energy functions are perfectly consistent with the available experimental
curves for interpolation. It is found that for incompressible materials, the
function via an interpolation from two experimental curves can already predict
other experimental curves reasonably well. To further improve the accuracy,
additional experiments can be used in the interpolation.
