On the continuum damage mechanics approach to modeling of polar ice fracture: a reply

Fracture of ice is an important process in ice-sheet dynamics, leading to the detachment of icebergs from glaciers and ice shelves and allowing the propagation of water-filled crevasses from the surface to the bottom of ice shelves and ice sheets (Benn and others, 2007). Historically, fracture propagation in ice has been treated using linear elastic fracture mechanics (LEFM) (Lawn, 1993; Van der Veen, 2007) or the Nye zero-stress model (Nye, 1957; Jezek, 1984; Nick and others, 2010). In our two recent papers (Duddu and Waisman, 2012, 2013) we proposed a nonlocal continuum damage mechanics (CDM) approach as an alternative to the commonly used LEFMand Nye-model-based approaches. In the first paper (Duddu and Waisman, 2012), we presented a viscoelastic constitutive damage model for polycrystalline ice aimed at capturing its time-dependent creep behavior at low stresses leading to failure. An interesting finding of our study is that a power-law-based creep damage model is sufficient to phenomenologically capture the tertiary creep behavior of ice. In a follow-up paper (Duddu and Waisman, 2013), we presented a nonlocal damage mechanics formulation of the constitutive model within a finite-element framework that alleviates the pathological mesh dependence of damage computations. In Duddu and Waisman (2013), tensile creep fracture was studied and crack propagation was simulated under uniaxial and biaxial tension. In their comment, Gagliardini and others (2013) claim that we did not accurately consider the specificities of ice rheology under compression and that, as a consequence, the damage mechanics model is inappropriate for studying crevasse propagation. However, it is important to note that crevasses are tensile cracks, so Galiardini and others’ main criticism regarding the damage description under compression in Duddu and Waisman (2012) is not relevant to crevasse propagation, which is our main interest. The appropriateness of our model for investigating tensilestress-induced surface crevasse propagation in glaciers and ice sheets is demonstrated in our recent publication (Duddu and others, 2013). In the next section, we briefly respond to the two criticisms by Gagliardini and others (2013) and clarify the important aspects of the damage model under compression. We conclude with a discussion on the calibration and validation of damage models for studying crevasse propagation and iceberg calving.