Cosmological models with two interacting fluids, each satisfying the strong energy condition, are studied in the framework of classical General Relativity. If the interactions are phenomenologically described by a power law in the scale factor, the two initial interacting fluids can be equivalently substituted by two non interacting effective fluids, where one of them may violate the strong energy condition and/or have negative energy density. Analytical solutions of the Friedmann equations of this general setting are obtained and studied. One may have, depending on the scale where the interaction becomes important, non singular universes with early accelerated phase, or singular models with transition from decelerated to accelerated expansion at large scales. Among the first, there are bouncing models where contraction is stopped by the interaction. In the second case, one obtains dark energy expansion rates without dark energy, like $Lambda$CDM or phantomic accelerated expansions without cosmological constant or phantoms, respectively.
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