Determination of the parameters of the Prony series in hyper-viscoelastic material models using the finite element method

This paper is devoted to the description of a newly developed methodology for the determination of the parameters of the Prony series in rubber compounds. Four hyperelastic constitutive equations were selected and combined with the Prony equation to describe the hyper-viscoelastic behaviour of a rubber compound. An in-house simple uniaxial tension test was designed and performed on the three rubber strips with the same length and different widths of 1, 2 and 3 cm. The corresponding finite element meshes of these samples were developed using an adaptive meshing technique. The numerical result of the first sample was compared with experimental results of the associated experiment in conjunction with a Nelder–Mead Simplex optimization method to determine the parameters of the Prony equation. These parameters were further used for the simulation of the other two samples to show applicability and repeatability of the developed method. The comparison of the associated force–extension curves with the experimentally measured data of the two samples confirmed the accuracy and reliability of the predicted parameters by this technique.