Breaks in DNA, resulting in fragmented parts, can be produced by ionizing radiation which, in turn, is the starting point in the search for novel physical aspects of DNA strands. Double-strand breaks in particular cause disruption of the DNA strand, splitting it into several fragments. In order to study effects produced by radiation in plasmid DNA, a new simple mechanical model for this molecule is proposed. In this model, a Morse-like potential and a high-LET component are used to describe the DNA-radiation interaction. Two power laws, used to fit results of the model, suggest that, firstly, distribution of fragment size is nonextensive and, secondly, that a transition phase is present in the DNA fragment distribution pattern.