Behavior characterization of viscoelastic materials for the finite element method calculation applying Prony series

In this study, we have been working within the framework of mathematical characterization of materials with complex behavior, and we used this characterization as input data for simulations in finite elements codes. We have researched the behavior of hyperelastic materials with viscoelastic qualities. There are models for the characterization of this type of materials; however, they lean on parameters that have to be previously determined for each material, and only then, their calculation models can estimate an answer for each material under specific loading conditions. We have focused on the viscoelastic characterization applying Prony series for finite elements simulations. We have developed a procedure to obtain the adequate number of terms of the series as well as the coefficients of characterization from a relaxation spectrum generated by a rheological model. We expect that this new procedure can effectively help researchers in the characterization of materials using Prony series and hence be implemented for later use of it in programs of finite elements.