Calving of icebergs is a major negative component of polar ice-sheet mass balance. Here we present a new calving model relying on both continuum damage mechanics and linear elastic fracture mechanics. This combination accounts for both the slow sub-critical surface crevassing and the rapid propagation of crevasses when calving occurs. First, damage to the ice occurs over long timescales and enhances the viscous flow of ice. Then brittle fractures propagate downward, at very short timescales, when the ice body is considered as an elastic medium. The model was calibrated on Helheim Glacier, Southeast Greenland, a well-monitored glacier with fast-flowing outlet. This made it possible to identify sets of model parameters to enable a consistent response of the model and to produce a dynamic equilibrium in agreement with the observed stable position of the Helheim ice front between 1930 and today.