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Smart flexible materials with piezoresistive property are increasingly used in the field of sensors. When embedded in structures, they would allow for in situ structural health monitoring and damage assessment of impact loading, such as crash, bird strikes and ballistic impacts; however, this could not be achieved without a deep characterization of the relation between piezoresistivity and mechanical behavior. The aim of this paper is to study the potential use of the piezoresistivity effect of a conductive foam made of a flexible polyurethane matrix filled with activated carbon for integrated structural health monitoring (SHM) and low-energy impact detection. To do so, polyurethane foam filled with activated carbon, namely PUF-AC, is tested under quasi-static compressions and under a dynamic mechanical analyzer (DMA) with in situ measurements of its electrical resistance. A new relation is proposed for describing the evolution of the resistivity versus strain rate showing that a link exists between electrical sensitivity and viscoelasticity. In addition, a first demonstrative experiment of feasibility of an SHM application using piezoresistive foam embedded in a composite sandwich structure is realized by a low-energy impact (2 J) test.