Revisiting Weertman's tombstone bed

Johannes Weertman published his first glaciological paper in 1957 only 5 years after getting his DSc in metallurgy from the Carnegie Institute of Technology. The paper presented the very first sliding law developed quantitatively from first principles, and involved the unconventional idealization of bed roughness using cubic ‘tombstones’ of rock. Since 1957, there has been a great deal of progress in understanding glacier sliding, but few studies, if any, have preserved the original tombstone geometry that was a hallmark of this first theory. The current study presents a partial reanalysis of the sliding process over a bed with tombstone obstacles using modern numerical methods. The result confirms the enduring applicability of Weertman's model as a pedagogical tool and motivates new questions about (1) folding flow near bedrock obstacles that invert normal ice stratigraphy, (2) the presence and role of stress singularities on sharp edges of bedrock, and (3) the validity of a presumption that regelation flow can be plug-like.

Bistable polar-orthotropic shallow shells

We investigate stabilizing and eschewing factors on bistability in polar-orthotropic shells in order to enhance morphing structures. The material law causes stress singularities when the circumferential stiffness is smaller than the radial stiffness ( β < 1), requiring a careful choice of the trial functions in our Ritz approach, which employs a higher-order geometrically nonlinear analytical model. Bistability is found to strongly depend on the orthotropic ratio, β , and the in-plane support conditions. An investigation of their interaction offers a new perspective on the effect of the hoop stiffness on bistability: while usually perceived as promoting, it is shown to be only stabilizing insofar as it prevents radial expansions; however, if in-plane supports are present, it becomes a redundant feature. Closed-form approximations of the bistable threshold are then provided by single-curvature-term approaches. For significantly stiffer values of the radial stiffness, a strong coupling of the orthotropic ratio and the support conditions is revealed: while roller-supported shells are monostable, fixed-pinned ones are most disposed to stable inversions; insight is given by comparing to a simplified beam model. Eventually, we show that cutting a central hole is a suitable method to deal with stress singularities: while fixed-pinned shells are barely affected by a hole, the presence of a hole strongly favours bistable inversions in roller-supported shells.