Alley, RB, Dupont, TK, Parizek, BR and Anandakrishnan, S (2005) Access of surface meltwater to beds of sub-freezing glaciers: Preliminary insights. Annals of Glaciology 40, 8–14. doi: 10.3189/172756405781813483
Alnæs, MS and 9 others (2015) The FEniCS project version 1.5. Archive of Numerical Software 3(100), 9–23. doi: 10.11588/ans.2015.100.20553
Anderson, TL (2005) Fracture Mechanics: Fundamentals and Applications, 3rd Edn.Taylor & Francis.
Banwell, AF and 5 others (2014) Supraglacial lakes on the Larsen B ice shelf, Antarctica, and at Paakitsoq, West Greenland: A comparative study. Annals of Glaciology 55(66), 1–8. doi: 10.3189/2014AoG66A049
Bary, B, Bournazel, JP and Bourdarot, E (2000) Poro-damage approach applied to hydro-fracture analysis of concrete. Journal of Engineering Mechanics 126(9), 937–943. doi: 10.1061/(ASCE)0733-9399(2000)126:9(937)
Bassis, J and Jacobs, S (2013) Diverse calving patterns linked to glacier geometry. Nature Geoscience 6(10), 833–836. doi: 10.1038/ngeo1887
Bassis, J and Ma, Y (2015) Evolution of basal crevasses links ice shelf stability to ocean forcing. Earth and Planetary Science Letters 409, 203–211. doi: 10.1016/j.epsl.2014.11.003
Bassis, JN and Walker, CC (2012) Upper and lower limits on the stability of calving glaciers from the yield strength envelope of ice. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 468(2140), 913–931. doi: 10.1098/rspa.2011.0422
Bazant, ZP (1994) Nonlocal damage theory based on micromechanics of crack interactions. Journal of Engineering Mechanics 120(3), 593–617. doi: 10.1061/(ASCE)0733-9399(1994)120:3(593)
Benn, DI, Hulton, NR and Mottram, RH (2007a) ‘Calving laws’,‘sliding laws’ and the stability of tidewater glaciers. Annals of Glaciology 46(1), 123–130. doi: 10.3189/172756407782871161
Benn, DI, Warren, CR and Mottram, RH (2007b) Calving processes and the dynamics of calving glaciers. Earth-Science Reviews 82(3), 143–179. doi: 10.1016/j.earscirev.2007.02.002
Benn, DI and 7 others (2017) Melt-under-cutting and buoyancy-driven calving from tidewater glaciers: New insights from discrete element and continuum model simulations. Journal of Glaciology 63(240), 691–702. doi: 10.1017/jog.2017.41
Biot, MA (1955) Theory of elasticity and consolidation for a porous anisotropic solid. Journal of Applied Physics 26(2), 182–185. doi: 10.1063/1.1721956
Borstad, CP and McClung, DM (2013) A higher-order method for determining quasi-brittle tensile fracture parameters governing the release of slab avalanches and a new tool for in situ indexing. Journal of Geophysical Research: Earth Surface 118(2), 900–912. doi: 10.1002/jgrf.20065
Borstad, CP and 6 others (2012) A damage mechanics assessment of the Larsen B ice shelf prior to collapse: Toward a physically-based calving law. Geophysical Research Letters 39(18). doi: 10.1029/2012GL053317
Christmann, J, Plate, C, Müller, R and Humbert, A (2016) Viscous and viscoelastic stress states at the calving front of Antarctic ice shelves. Annals of Glaciology 57(73), 10–18. doi: 10.1017/aog.2016.18
Colgan, W and 6 others (2016) Glacier crevasses: Observations, models, and mass balance implications. Reviews of Geophysics 54(1), 119–161. doi: 10.1002/2015RG000504
Cook, S, Zwinger, T, Rutt, I, O'Neel, S and Murray, T (2012) Testing the effect of water in crevasses on a physically based calving model. Annals of Glaciology 53(60), 90–96. doi: 10.3189/2012AoG60A107
Cook, S and 7 others (2014) Modelling environmental influences on calving at Helheim Glacier in eastern Greenland. The Cryosphere 8(3), 827–841. doi: 10.5194/tc-8-827-2014
Coussy, O (1995) Mechanics of Porous Continua. Wiley.
Cuffey, K and Paterson, W (2010) The Physics of Glaciers. Elsevier Science.
DeConto, RM and Pollard, D (2016) Contribution of Antarctica to past and future sea-level rise. Nature 531, 591–597. doi: 10.1038/nature17145
De Robin, GQ (1974) Depth of water-filled crevasses that are closely spaced. Journal of Glaciology 13(69), 543–543. doi: 10.3189/S0022143000023285
Duddu, R and Waisman, H (2012) A temperature dependent creep damage model for polycrystalline ice. Mechanics of Materials 46, 23–41. doi: 10.1016/j.mechmat.2011.11.007
Duddu, R and Waisman, H (2013) A nonlocal continuum damage mechanics approach to simulation of creep fracture in ice sheets. Computational Mechanics 51(6), 961–974. doi: 10.1007/s00466-012-0778-7
Duddu, R, Bassis, J and Waisman, H (2013) A numerical investigation of surface crevasse propagation in glaciers using nonlocal continuum damage mechanics. Geophysical Research Letters 40(12), 3064–3068. doi: 10.1002/grl.50602
Enderlin, EM and Bartholomaus, TC (2019) Poor performance of a common crevasse model at marine-terminating glaciers. The Cryosphere Discussions 2019, 1–19. doi: 10.5194/tc-2019-128
Glen, JW (1955) The creep of polycrystalline ice. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 228(1175), 519–538. doi: 10.1098/rspa.1955.0066
Greve, R and Blatter, H (2009) Dynamics of Ice Sheets and Glaciers. Berlin: Springer.
Hayhurst, D (1972) Creep rupture under multi-axial states of stress. Journal of the Mechanics and Physics of Solids 20(6), 381–382. doi: 10.1016/0022-5096(72)90015-4
Hillerborg, A, Modéer, M and Petersson, P (1976) Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement and Concrete Research 6, 773–782. doi: 10.1016/0008-8846(76)90007-7
Hutchinson, J (1968) Singular behaviour at the end of a tensile crack in a hardening material. Journal of the Mechanics and Physics of Solids 16(1), 13–31. doi: 10.1016/0022-5096(68)90014-8
Jezek, KC (1984) A modified theory of bottom crevasses used as a means for measuring the buttressing effect of ice shelves on inland ice sheets. Journal of Geophysical Research: Solid Earth 89(B3), 1925–1931. doi: 10.1029/JB089iB03p01925
Jiménez, S and Duddu, R (2018b) On the evaluation of the stress intensity factor in calving models using linear elastic fracture mechanics. Journal of Glaciology 64(247), 759–770. doi: 10.1017/jog.2018.64
Jiménez, S, Duddu, R and Bassis, J (2017) An updated-Lagrangian damage mechanics formulation for modeling the creeping flow and fracture of ice sheets. Computer Methods in Applied Mechanics and Engineering 313, 406–432. doi: 10.1016/j.cma.2016.09.034
Kachanov, LM (1958) Time of the rupture process under creep conditions. Izvestia Akademii Nauk SSSR. Otdelenie Tekhnicheskich Nauk 8(8), 26–31.
Karr, DG and Choi, K (1989) A three-dimensional constitutive damage model for polycrystalline ice. Mechanics of Materials 8(1), 55–66. doi: 10.1016/0167-6636(89)90005-7
Keller, A and Hutter, K (2014a) Conceptual thoughts on continuum damage mechanics for shallow ice shelves. Journal of Glaciology 60(222), 685–693. doi: 10.3189/2014JoG14J010
Keller, A and Hutter, K (2014b) A viscoelastic damage model for polycrystalline ice, inspired by Weibull-distributed fiber bundle models. Part II: Thermodynamics of a rank-4 damage model. Continuum Mechanics and Thermodynamics 26(6), 895–906. doi: 10.1007/s00161-014-0335-z
Krug, J, Weiss, J, Gagliardini, O and Durand, G (2014) Combining damage and fracture mechanics to model calving. The Cryosphere 8(6), 2101–2117. doi: 10.5194/tc-8-2101-2014
Lemaitre, J (1971) Evaluation of dissipation and damage in metals. Proceedings of the International Congress on the Mechanical Behavior of Materials (I.C.M.), Kyoto, Japan, 1.
Lo, YS, Borden, MJ, Ravi-Chandar, K and Landis, CM (2019) A phase-field model for fatigue crack growth. Journal of the Mechanics and Physics of Solids 132, 103684. doi: 10.1016/j.jmps.2019.103684
Ma, Y, Tripathy, CS and Bassis, JN (2017) Bounds on the calving cliff height of marine terminating glaciers. Geophysical Research Letters 44(3), 1369–1375. doi: 10.1002/2016GL071560
Meier, MF and 7 others (2007) Glaciers dominate eustatic sea-level rise in the 21st century. Science (New York, N.Y.) 317(5841), 1064–1067. doi: 10.1126/science.1143906
Mobasher, ME, Duddu, R, Bassis, JN and Waisman, H (2016) Modeling hydraulic fracture of glaciers using continuum damage mechanics. Journal of Glaciology 62(234), 794–804. doi: 10.1017/jog.2016.68
Mobasher, ME, Berger-Vergiat, L and Waisman, H (2017) Non-local formulation for transport and damage in porous media. Computer Methods in Applied Mechanics and Engineering 324(Supplement C), 654–688. doi: 10.1016/j.cma.2017.06.016
Moore, JC, Grinsted, A, Zwinger, T and Jevrejeva, S (2013) Semiempirical and process-based global sea level projections. Reviews of Geophysics 51(3), 484–522. doi: 10.1002/rog.20015
Mottram, RH and Benn, DI (2009) Testing crevasse-depth models: A field study at Breid. h. oamerkurjökull, Iceland. Journal of Glaciology 55(192), 746–752. doi: 10.3189/002214309789470905
Murakami, S (1983) Notion of continuum damage mechanics and its application to anisotropic creep damage theory. Journal of Engineering Materials and Technology – Transactions of the ASME 105(2), 99–105. doi: 10.1115/1.3225633
Murakami, S, Kawai, M and Rong, H (1988) Finite element analysis of creep crack growth by a local approach. International Journal of Mechanical Sciences 30(7), 491–502. doi: 10.1016/0020-7403(88)90003-3)
Nick, F, Van der Veen, C, Vieli, A and Benn, D (2010) A physically based calving model applied to marine outlet glaciers and implications for the glacier dynamics. Journal of Glaciology 56(199), 781–794. doi: 10.3189/002214310794457344
Nye, JF (1957) The distribution of stress and velocity in glaciers and ice-sheets. Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences 239, 113–133. doi: 10.1098/rspa.1957.0026
Paterson, W (1994) The Physics of Glaciers, 3rd Edn.Oxford: Pergamon/Elsevier.
Pollard, D, DeConto, RM and Alley, RB (2015) Potential Antarctic Ice Sheet retreat driven by hydrofracturing and ice cliff failure. Earth and Planetary Science Letters 412, 112–121. doi: 10.1016/j.epsl.2014.12.035
Pralong, A and Funk, M (2005) Dynamic damage model of crevasse opening and application to glacier calving. Journal of Geophysical Research: Solid Earth 110(B1), 1–12. doi: 10.1029/2004JB003104
Pralong, A, Hutter, K and Funk, M (2006) Anisotropic damage mechanics for viscoelastic ice. Continuum Mechanics and Thermodynamics 17(5), 387–408. doi: 10.1007/s00161-005-0002-5
Rabotnov, YN (1963) On the equations of state for creep. Progress in Applied Mechanics, the Prager Anniversary, 8.
Rice, JR (1968) A path independent integral and the approximate analysis of strain concentration by Notches and Cracks. Journal of Applied Mechanics 35(2), 379–386. doi: 10.1115/1.3601206
Rice, J and Rosengren, G (1968) Plane strain deformation near a crack tip in a power-law hardening material. Journal of the Mechanics and Physics of Solids 16(1), 1–12. doi: 10.1016/0022-5096(68)90013-6
Rist, MA, Sammonds, PR, Oerter, H and Doake, CSM (2002) Fracture of Antarctic shelf ice. Journal of Geophysical Research: Solid Earth 107(B1), ECV 2–1–ECV 2–13. doi: 10.1029/2000JB000058
Rist, MA and 6 others (1999) Experimental and theoretical fracture mechanics applied to Antarctic ice fracture and surface crevassing. Journal of Geophysical Research: Solid Earth 104(B2), 2973–2987. doi: 10.1029/1998JB900026
Scambos, T and 7 others (2009) Ice shelf disintegration by plate bending and hydro-fracture: Satellite observations and model results of the 2008 Wilkins ice shelf break-ups. Earth and Planetary Science Letters 280(1), 51–60. doi: 10.1016/j.epsl.2008.12.027
Scambos, TA, Hulbe, C, Fahnestock, M and Bohlander, J (2000) The link between climate warming and break-up of ice shelves in the Antarctic Peninsula. Journal of Glaciology 46(154), 516–530. doi: 10.3189/172756500781833043
Schulson, EM and Duval, P (2009) Creep and Fracture of Ice. Cambridge: Cambridge University Press.
Smith, RA (1976) The application of fracture mechanics to the problem of crevasse penetration. Journal of Glaciology 17(76), 223–228. doi: 10.3189/S0022143000013563
Sun, S, Cornford, SL, Moore, JC, Gladstone, R and Zhao, L (2017) Ice shelf fracture parameterization in an ice sheet model. The Cryosphere 11(6), 2543–2554. doi: 10.5194/tc-11-2543-2017
Tada, H, Paris, P and Irwin, G (1973) The Stress Analysis of Cracks Handbook. Number v. 1 in The Stress Analysis of Cracks Handbook. Del Research Corporation.
Tada, H, Paris, P and Irwin, GH (2000) The Stress Analysis of Cracks Handbook, 3rd Edn.New York, NY: The American Society of Mechanical Engineers.
Terzaghi, K (1951) Theoretical Soil Mechanics. London: Chapman And Hall, Limited.
Terzaghi, K (2007) Stress Conditions for Failure in Soils. John Wiley and Sons, Inc., pp. 7–25. doi: 10.1002/9780470172766.ch2)
Todd, J and Christoffersen, P (2014) Are seasonal calving dynamics forced by buttressing from ice mélange or undercutting by melting: Outcomes from full-Stokes simulations of Store Glacier, West Greenland. The Cryosphere 8(6), 2353–2365. doi: 10.5194/tc-8-2353-2014
Todd, J and 10 others (2018) A full-Stokes 3-D calving model applied to a large Greenlandic glacier. Journal of Geophysical Research: Earth Surface 123(3), 410–432. doi: 10.1002/2017JF004349
van der Veen, C (1998a) Fracture mechanics approach to penetration of bottom crevasses on glaciers. Cold Regions Science and Technology 27(3), 213–223. doi: 10.1016/S0165-232X(97)00022-0
van der Veen, C (1998b) Fracture mechanics approach to penetration of surface crevasses on glaciers. Cold Regions Science and Technology 27(1), 31–47. doi: 10.1016/S0165-232X(97)00022-0
van der Veen, CJ (1999) Crevasses on glaciers. Polar Geography 23(3), 213–245. doi: 10.1080/10889379909377677
van der Veen, CJ (2013) Fundamentals of Glacier Dynamics. CRC Press.
Weertman, J (1957) Deformation of floating ice shelves. Journal of Glaciology 3(21), 38–42. doi: 10.3189/S0022143000024710
Weertman, J (1971) Theory of water-filled crevasses in glaciers applied to vertical magma transport beneath oceanic ridges. Journal of Geophysical Research 76(5), 1171–1183. doi: 10.1029/JB076i005p01171
Weertman, J (1973) Can a water-filled crevasse reach the bottom surface of a glacier? IASH Publications 95, 139–145.
Weertman, J (1974) Depth of water-filled crevasses that are closely spaced. Journal of Glaciology 13(69), 544–544. doi: 10.3189/S0022143000023297
Weertman, J (1977) Penetration depth of closely spaced water-free crevasses. Journal of Glaciology 18(78), 37–46. doi: 10.1017/S0022143000021493
Weertman, J (1980) Bottom crevasses. Journal of Glaciology 25(91), 185–188. doi: 10.3189/S0022143000010418
Weiss, J (2003) Scaling of fracture and faulting of ice on Earth. Surveys in Geophysics 24(2), 185–227. doi: 10.1023/A:1023293117309
Weiss, J (2004) Subcritical crack propagation as a mechanism of crevasse formation and iceberg calving. Journal of Glaciology 50(168), 109–115. doi: 10.3189/172756504781830240
Wu, JY and Nguyen, VP (2018) A length scale insensitive phase-field damage model for brittle fracture. Journal of the Mechanics and Physics of Solids 119, 20–42. doi: 10.1016/j.jmps.2018.06.006
Yu, H, Rignot, E, Morlighem, M and Seroussi, H (2017) Iceberg calving of Thwaites Glacier, West Antarctica: Full-Stokes modeling combined with linear elastic fracture mechanics. The Cryosphere 11(3), 1283–1296. doi: 10.5194/tc-11-1283-2017