Three-Dimensional Analysis of Ice Sheet Indentation: Lower- Bound Solutions

• Main Author: D G Karr
• Other Authors: The Pennsylvania State University CiteSeerX Archives
• Format: Text
• Language: English
• Subjects: Ice Sheet; Sea ice
• Online Access: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1053.9584; http://offshoremechanics.asmedigitalcollection.asme.org/data/Journals/JMOEEX/28048/81_1.pdf

The methods of plastic limit analysis are used to determine the indentation pressures of aflat rigid punch on a columnar ice sheet. The ice sheet is idealized as a semiinfinite layer of elastic-perfectly plastic material The effects of varying the aspect ratio (defined as the ratio ofindentor width to ice thickness) are then addressed. A comparison of results for intermediate aspect ratios to results for extremely high (plane stress) and extremely low (plane strain) aspect ratios is presented. It is found that the transition from plane stress to plane strain is governed by the tensile strength of the ice medium. Introduction The methods of plastic limit analysis are used to calculate the pressures required to indent an ice sheet. Lower-bound solutions are obtained by optimizing a three-dimensional stress field in order to determine the indentation pressures which cause yielding of the ice medium. The numerical results thus indicate the minimum loads required to initiate penetration of the indentor into the edge of the ice sheet. The failure mechanism of the ice is assumed to be purely plastic deformation and the conditions of the lower-bound theorem are thus strictly satisfied. The failure envelopes or yield criteria used to describe ice strength are highly dependent upon strain rate. The use of a particular failure envelope thus corresponds to a given ice type, temperature and strain rate. The Von Mises and the Drucker-Prager yield criteria are used to compare the threedimensional lower-bound results to previous limit analysis results obtained using these criteria. Anisotropic criteria, applicable to columnar sea ice are also used to study the effects of indentation aspect ratios. The stress field addressed in this study includes a rigorous three-dimensional elasticity solution for a semi-infinite sheet subjected to a distributed edge load. For certain stress states and higher strain rates, the failure envelope for ice may actually correspond to fracture rather than ductile flow. Thus, a knowledge of the state ...