This correspondence relates to two papers by Reference Duddu and WaismanDuddu and Waisman (2012, Reference Duddu and Waisman2013), recently published in Mechanics of Materials and Computational Mechanics, respectively. We thought it pertinent to comment on the ice rheology approach considered in their damage model, and its application to the prediction of crevasse opening and iceberg calving. The Journal of Glaciology appeared to be the appropriate journal for this purpose, in order to interact with as many potential users of this model as possible.

Reference Duddu and WaismanDuddu and Waisman (2012, Reference Duddu and Waisman2013) presented a new damage model, with the aim of applying it to the formation of glacier crevasses and the calving of icebergs. Reference Duddu and WaismanDuddu and Waisman (2012) estimated the parameters entering the damage model using published data from laboratory mechanical tests. Reference Duddu and WaismanDuddu and Waisman (2013) presented the concepts of the model, as well as some numerical aspects. The model itself appears to be very sophisticated, with interesting and innovative aspects such as a nonlocal formulation which avoids mesh-size dependency of the results. However, the ice rheology specificities are not accurately considered due to a misunderstanding of the physical mechanisms in play. We have two main criticisms of the way the model has been formulated and calibrated, which are significant enough to suggest that caution is needed in adopting the model for use in its current form.

First, the model relies on the formalism of Reference MurakamiMurakami (1983), which was initially developed to account for the ductile failure induced by the nucleation and growth of cavities. Adopting this formalism renders the fundamental basis of the proposed damage model incompatible with the negligible contribution of diffusion creep to ice deformation. Indeed, ductile failure requires strong intra- or intergranular diffusion while diffusion in ice is low (Reference Duval, Ashby and AndermanDuval and others, 1983). Damage in ice occurs through the nucleation of brittle microcracks, arising from stress concentrations created by elastic mismatch between grains, dislocation pile-up formation and/or grain-boundary sliding (Reference Weiss, Schulson and FrostWeiss and others, 1996; Reference FrostFrost, 2001). Following the formalism of Reference MurakamiMurakami (1983), the damage is initiated using a strain criterion (equation (23) of Reference Duddu and WaismanDuddu and Waisman, 2012). With such a formulation, as soon as the deformation reaches the strain threshold ε _th, the ice damages continuously whatever the applied stress. Such a strain threshold is unphysical: ice can deform up to very large values without damage if the strain rate is sufficiently low. As a matter of fact, a critical strain rate can instead define, macroscopically, the transition from a purely ductile behaviour to a more brittle behaviour involving damage (e.g. Reference Schulson and DuvalSchulson and Duval, 2009). Hence, adopting ε _th = 0.8% is not appropriate for the many places in ice sheets and glaciers where tensile stress remains too small to initiate any damage, whatever the deformation level (e.g. Reference Budd and JackaBudd and Jacka, 1989).

Second, the model is calibrated using the experimental creep tests of Reference Mellor and ColeMellor and Cole (1982) for compression, of Reference Mahrenholtz, Wu, Murthy, Sackinger and WadhamsMahrenholtz and Wu (1992) for tension and of Reference JackaJacka (1984) for temperature dependency. For these creep tests, damage may only explain a small part of the total deformation (Reference Mellor and ColeMellor and Cole, 1982) or even not have occurred during the tests (Reference JackaJacka, 1984). The underlying hypothesis in Reference Duddu and WaismanDuddu and Waisman (2012) is that all the tertiary creep deformation is due to damage, neglecting other softening processes, such as dynamic recrystallization, associated with the nucleation of new grains and grain boundary migration, which is very active in glaciers and ice sheets (e.g. Reference Schulson and DuvalSchulson and Duval, 2009). In Jacka’s (1984) experiments, the increase in strain rate during tertiary creep is clearly associated with dynamic recrystallization alone, applied compression stresses being much lower than those required to form microcracks (Reference Schulson and DuvalSchulson and Duval, 2009). To discriminate the effects of damage and other processes on tertiary creep, sequential tests must be performed (e.g. Reference Meyssonnier and DuvalMeyssonnier and Duval, 1989; Reference Weiss, Tuhkuri and RiskaWeiss, 1999). Ice is pre-damaged up to a certain level during the first sequence, either under strain-rate control or creep (constant stress). The creep response of the damaged samples is then analysed under low applied stress (low enough to avoid additional damage). These studies have shown that viscous strain is indeed enhanced by damage, whereas delayed elastic strain is not, contrary to the postulate in Reference Duddu and WaismanDuddu and Waisman (2012, Reference Duddu and Waisman2013). Beyond these problems in identifying appropriate damage models for ice, we also stress that the automatic application of such models, inspired by processes occurring at the microscale, to geophysical situations must be treated with caution. Indeed, little is known so far about the role of microscopic damage in crevasse propagation or iceberg calving. While continuous damage models may be promising tools with which to simulate crevassing, the construction and calibration of such models must be based on a comparison with large-scale (field or remote-sensing) measurements (e.g. Reference Pralong and FunkPralong and Funk, 2005).

For the above reasons, we consider that this model is not, at the present stage, adapted to reproduce the rheological behaviour of ice for the conditions prevailing in glaciers and ice sheets, and so cannot be relied on to accurately predict crevasse opening and iceberg calving.