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A visco-elastic model for polymeric foams under cyclic compression. A block of polyurethane foam subject to cyclic compression exhibits a softening phenomenon as the number of cycles increases. In particular, one observes a stepping down of the loading curves while the unloading curves remain the same. In tests performed by the authors, it has been observed a partial recovery of the initial stiffness after a resting period was observed. This behaviour can be described as a long memory effect. We propose a viscoelastic model, coupling a non convex energy with a dissipation of viscous type. The model is in a good qualitative agreement with the experiments. [ABSTRACT FROM AUTHOR]