Many scientific problems involve dealing with high-dimensional data which can be interpreted as samples drawn from different curves. These so-called functional data might be characterized by the presence of discontinuity points which are shared among different functions. In this work we propose a predictive Bayesian non-parametric model for such data which is capable to cluster similar patterns between different curves. Assuming that each function is composed by the combination of a smooth function and a step function, we use a functional Bayesian latent factor model for the smooth components and a hierarchical normalized generalized Gamma prior for the step functions. This choice allows for flexible but parsimonious estimation and clustering, with a complete sharing of information across curves. To test the performance and the robustness of the proposed model we conduce a simulation study.