A Case Study on the Use of Fractional Derivatives: The Low-Frequency Viscoelastic Uni-Directional Behavior of Polyurethane Foam

A fractional derivative model of dissipative effects is combined with a nonlinear elastic model to model the response of polyurethane foam in quasi-static compression tests. A system identification method is developed based on a separation of the elastic and viscoelastic parts of the response, which is possible because of symmetries in the imposed deformation time-history. Simulations are used to evaluate the proposed identification method when noise is present in the response. The system identification technique is also applied with some success to experimental data taken from several compression experiments on two types of polyurethane foam blocks.