An applied model for predicting memory effects of flexible polyurethane foams: Fractional derivative-to-hereditary combined approach

Abstract

Purpose

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.

Design/methodology/approach

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.

Findings

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.

Originality/value

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

Citation

Elfarhani, M., Mkaddem, A., Alzahrani, A.A., Bin Mahfouz, A.S., Jarraya, A. and Haddar, M. (2020), "An applied model for predicting memory effects of flexible polyurethane foams: Fractional derivative-to-hereditary combined approach", Multidiscipline Modeling in Materials and Structures, Vol. 16 No. 3, pp. 519-537. https://doi.org/10.1108/MMMS-05-2019-0094