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The efficiency of fractional derivative and hereditary combined approach in modeling viscoelastic behavior of soft foams was successfully addressed in Elfarhani et al. (2016a). Since predictions obtained on flexible polyurethane foam (FPF) type A (density 28 kg m⁻³) were found very promoting, the purpose of this paper is to apply the approach basing on two other types of foams. Both soft polyurethane foams type B of density 42 kg m⁻³ and type C of density 50 kg m⁻³ were subjected to multi-cycles compressive tests.

The total foam response is assumed to be the sum of a non-linear elastic component and viscoelastic component. The elastic force is modeled by a seven-order polynomial function of displacement. The hereditary approach was applied during the loading half-cycles to simulate the short memory effects while the fractional derivative approach was applied during unloading cycles to simulate the long memory effects. An identification methodology based on the separation of the measurements of each component force was developed to avoid parameter admixture problems.

The proposed model reveals good reliability in predicting the responses of the two considered flexible foams. Predictions as measurements establish that residual responses were negligible compared to elastic and viscoelastic damping responses.

The development of a new combined model reveals good reliability in predicting the responses of the two polyurethane foams type A and B.

The purpose of this paper is to cover an experimental investigation of the impulse response of the foam-mass system (FMS) to unveil some of the foam dynamic behavior features needed to optimize the impact comfort of seat-occupant system. The equation of motion of the studied system is modeled as a sum of a linear elastic, pneumatic damping and viscoelastic residual forces. An identification methodology based on two separated calibration processes of the viscoelastic parameters was developed.

The viscoelastic damping force representing the foam short memory effects was modeled through the hereditary formulation. Its parameters were predicted from the free vibrational response of the FMS using iterative Prony method for autoregressive–moving–average model. However, the viscoelastic residual force resulting in the long memory effects of the material was modeled with fractional derivative term and its derivative order was predicted from previous cyclic compression standards.

The coefficients of the motion law were determined using closed form solution approach. The predictions obtained from the simulations of the impulse and cyclic tests are reasonably accurate. The physical interpretations as well as the mathematical correlations between the system parameters were discussed in details.

The prediction model combines hereditary and fractional derivative formulations resulting in short and long physical memory effects, respectively. Simulation of impulse and cyclic behavior yields good correlation with experimental findings.