The behavior of open-cell polymeric foams under cyclic compression is rather complex. During experiments performed by the author on poly-urethane foams, several phenomena have been observed :- a localisation of deformations in bands orthogonal to the loading direction ;- a difference between the response curves at loading and at unloading, that originates an important hysteresis loop ;- a stress softening effect, that is, a progressive stress reduction in the subsequent cycles of a cyclic test ;- a strain rate dependence, revelead by an increase of stress with increasing loading rate ;- a memory effect, characterized by a dependence of the response curves on the deformation history.The aim of this thesis is to study these phenomena by means of experiments, theoretical models and numerical simulations.First, to describe strain localization and hysteresis, a model based on non linear elasticity is proposed. The foam is described as a chainof non linear elastic springs with non convex strain energy. The non convexity of the strain energy let each spring have several equilibrium configurations (phases) under a given force. This opens the possibility of describing the strain localization as a progressive change of phase of the springs.Then, we propose an extension of the previous model to other non elastic phenomena. Inspired by experimental evidence, we introduce a vis-coelastic model by adding two dissipative elements with a constitutive law of the Boltmann-Volterra type. The linear viscoelastic model captures many of the observed inelastic aspects of the response, but the description of stress softening and of rate dependence requires further developments.Finally, with the purpose of improving the description of the stress softening effect, damage of the foam is introduced. Numerical simulationresults and experiments are compared for different loading conditions. The model provides a description for the phenomena listed above, butalso it satisfactorily reproduces the behavior of foams under complex loading-unloading tests.
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