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In this paper we propose a simplified two-dimensional model to describe some aspects of the turbulent breakage of bubbles at subcritical Weber numbers. In particular we focus on the breakup of bubbles owing to their interaction with an array of successive eddies, modeled by a train of straining flows. Our simulations show that, under certain conditions, a bubble accumulates energy due to its interaction with a sequence of turbulent structures until it eventually breaks, even if none of the eddies is sufficiently energetic to split the particle by itself. It is also shown that the different strain directions of the eddies acting on the surface of the bubble, and the resonance effect between their characteristic frequency and the natural oscillation frequency of the bubble immersed into the straining flow are the two key factors in the bubble deformation, and subsequent breakup mechanism. Moreover, the breakup patterns obtained from our simulations seem to agree qualitatively well with the experimental observations.