We investigate the appropriateness of calving or crevasse models from the literature using linear elastic fracture mechanics (LEFM). To this end, we compare LEFM model-predicted stress intensity factors (SIFs) against numerically computed SIFs using the displacement correlation method in conjunction with the finite element method. We present several benchmark simulations wherein we calculate the SIF at the tips of water-filled surface and basal crevasses penetrating through rectangular ice slabs under different boundary conditions, including grounded and floating conditions. Our simulation results indicate that the basal boundary condition significantly influences the SIF at the crevasse tips. We find that the existing calving models using LEFM are not generally accurate for evaluating SIFs in grounded glaciers or floating ice shelves. We also illustrate that using the ‘single edge crack’ weight function in the LEFM formulations may be appropriate for predicting calving from floating ice shelves, owing to the low fracture toughness of ice; whereas, using the ‘double edge crack’ or ‘central through crack’ weight functions is more appropriate for predicting calving from grounded glaciers. To conclude, we recommend using the displacement correlation method for SIF evaluation in real glaciers and ice shelves with complex geometries and boundary conditions.
We describe 14 hominin teeth and tooth fragments excavated recently from Swartkrans Cave (South Africa). The fossils derive from Members 1 (Lower Bank) and 3, from the Member 2/3 interface and from two deposits not yet assigned to member (the "Talus Cone Deposit" and "Underground North Excavation" [UNE]) of the Swartkrans Formation, and include the first hominin fossil from the UNE, the two smallest Paranthropus robustus deciduous maxillary second molars in the entire hominin fossil record, and one of the smallest P. robustus permanent maxillary second molars from Swartkrans. The small permanent molar is accompanied by another tooth from a different individual but from the same stratigraphic level of the Swartkrans Formation; this second tooth is among (if not) the largest P. robustus permanent maxillary first molars known from anywhere-lending credence to assertions that degrees of body size sexual dimorphism previously ascribed to this species may be underestimated. It is more equivocal whether this evidence also supports hypotheses proposing that P. robustus assemblages from Swartkrans (as well as those from other South African cave sites) formed through the taphonomically biasing actions of large carnivores.
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