We present a classification of area-strict limits of planar BV homeomorphisms. This class of mappings allows for cavitations and fractures but fulfil a suitable generalization of the INV condition. As pointed out by J. Ball, these features are expected in limit configurations of elastic deformations. In a recent work, De Philippis and Pratelli introduced the no-crossing condition which characterizes the Sobolev W^{1,p} closure of planar homeomorphisms. In our work we show that a suitable generalization of this concept is equivalent with a map being the area-strict limit of BV homeomorphisms. This is a joint work with Daniel Campbell and Aapo Kauranen.