A material model is presented that includes the following deformation mechanisms: the instantaneous response of ice due to distortion of crystal lattices, creep, the formation of microcrack nuclei due to creep, the formation of microcracks, and deformation due to microcracks. The new material model has a strict foundation on deformation mechanisms. This constitutive equation was applied to sea ice for engineering applications through implementation in the Abaqus explicit code by writing a VUMAT subroutine. The computed results show that the model correctly predicts the uniaxial tensile and the uniaxial compressive strengths of ice. The computed compressive strength versus strain-rate relation takes an almost linear relation when expressed in the log–log coordinates, which fits well with the data obtained from the literature. The material model shows the Hall–Petch type of strength dependency on the grain size.

References

References
1.
Duddu
,
R.
, and
Waisman
,
H.
,
2012
, “
A Temperature Dependent Creep Damage Model for Polycrystalline Ice
,”
Mech. Mater.
,
46
, pp.
23
41
.
2.
Duddu
,
R.
, and
Waisman
,
H.
,
2013
, “
A Nonlocal Continuum Damage Mechanics Approach to Simulation of Creep Fracture in Ice Sheets
,”
Comput. Mech.
,
51
(
6
), pp.
961
974
.
3.
Borstad
,
C. P.
,
Rignot
,
E.
,
Mouginot
,
J.
, and
Schodlok
,
M. P.
,
2013
, “
Creep Deformation and Buttressing Capacity of Damaged Ice Shelves: Theory and Application to Larsen C Ice Shelf
,”
Cryosphere
,
7
(
6
), pp.
1931
1947
.
4.
Londono
,
J. G.
,
Berger-Vergiat
,
L.
, and
Waisman
,
H.
,
2016
, “
A Prony-Series Type Viscoelastic Solid Coupled With a Continuum Damage Law for Polar Ice Modelling
,”
Mech. Mater.
,
98
, pp.
81
97
.
5.
Sinha
,
N. K.
,
1978
, “
Rheology in Columnar-Grained Ice
,”
Exp. Mech.
,
18
(
12
), pp.
464
470
.
6.
Santaoja
,
K.
,
1987
, “
An Effective Approximate Algorithm to Predict the Delayed Elastic Strain
,”
9th International Conference on Port and Ocean Engineering Under Arctic Conditions
, W. M. Sackinger and M. O. Jeffries, eds., Fairbanks, AK, Vol.
III
, pp.
31
43
.
7.
Santaoja
,
K.
,
1988
, “
Three-Dimensional Ductile Constitutive Equation for Ice
,”
ASME J. Offshore Mech. Arct. Eng.
,
112
(3), pp. 270–275.
8.
Santaoja
,
K.
,
1990
, “
Mathematical Modelling of Deformation Mechanisms in Ice
,” Helsinki University of Technology, The Technical Research Centre of Finland, Espoo, Finland,
VTT Research Reports No. 676
.
9.
Evgin
,
E.
,
Zhan
,
C.
, and
Frederking
,
R. M. W.
,
1991
, “
Nonlinear Analysis of Stress Distribution in an Ice Floe
,” 10th International Conference on Offshore Mechanics and Arctic Engineering, Stavanger, Norway, June 23–28.
10.
Zhan
,
C.
,
Evgin
,
E.
, and
Sinha
,
N. K.
,
1994
, “
A Three-Dimensional Anisotropic Constitutive Model for Ductile Behaviour of Columnar Grained Ice
,”
Cold Reg. Sci. Technol.
,
22
(
3
), pp.
269
284
.
11.
Zhan
,
C.
,
Sinha
,
N. K.
, and
Evgin
,
E.
,
1996
, “
A Three-Dimensional Anisotropic Constitutive Model for Ductile Behaviour of Columnar Grained Ice
,”
Acta Mater.
,
44
(
5
), pp.
1839
1847
.
12.
Frost
,
H. J.
,
2001
, “
Mechanisms of Crack Nucleation in Ice
,”
Eng. Fract. Mech.
,
68
(
17–18
), pp.
1823
1837
.
13.
Janson
,
J.
, and
Hult
,
J.
,
1977
, “
Fracture Mechanics and Damage Mechanics: A Combined Approach
,”
J. Méc. Appl.
,
1
, pp.
69
84
.
14.
Karr
,
D. G.
,
1985
, “
A Damage Mechanics Model for Uniaxial Deformation of Ice
,”
ASME J. Energy Resour. Technol.
,
107
(3), pp. 363–368.
15.
Karr
,
D. G.
,
1985
, “
Constitutive Equations for Ice as a Damaging Material
,”
ASCE Speciality Conference
,
ARCTIC’85
, Civil Engineering in the Arctic Offshore, F. L. Bennett and J. L. Machemel, eds., pp.
908
916
.
16.
Bazant
,
Z. P.
, and
Kim
,
J. K.
,
1985
, “
Fracture Theory for Non-Homogeneous Brittle Materials With Application to Ice
,”
ASCE Speciality Conference
,
ARCTIC’85
, Civil Engineering in the Arctic Offshore, F. L. Bennet and J. L. Machemel, eds., pp.
917
929
.
17.
Tomin
,
M. J.
,
Cormeau
,
A.
, and
Jordaan
,
I. J.
,
1985
, “
Development of Analytical Models to Experimental Work on Ice-Structure Interaction
,” Det Norske Veritas (Canada) Ltd., DSS File No. 05SV.EN280-4-2687.
18.
Ting
,
S.-K.
, and
Sunder
,
S. S.
,
1985
, “
Constitutive Modelling of Sea Ice With Applications to Indentation Problems
,” MIT CSEOE, Massachusetts Institute of Technology, Cambridge, MA, Research Report No. 3.
19.
Pralong
,
A.
, and
Funk
,
M.
,
2005
, “
Dynamic Damage Model of Crevasse Opening and Application to Clavier Calving
,”
J. Geophys. Res.
,
110
(B1), p.
B01309
.
20.
Pralong
,
A.
,
Hutter
,
K.
, and
Funk
,
M.
,
2006
, “
Anisotropic Damage Mechanics for Viscoelastic Ice
,”
Continuum Mech. Thermodyn.
,
17
(
5
), pp.
387
408
.
21.
Sain
,
T.
, and
Narasimhan
,
R.
,
2011
, “
Constitutive Modelling of Ice in the High Strain-Rate Regime
,”
Int. J. Solids Struct.
,
48
(
5
), pp.
817
827
.
22.
Santaoja
,
K.
,
1989
, “
Continuum Damage Mechanics Approach to Describe Multidirectional Microcracking of Ice
,” Eight International Conference on Offshore Mechanics and Arctic Engineering. The Hague, The Netherlands, pp. 55–65.
23.
Wu
,
M. S.
, and
Sunder
,
S. S.
,
1992
, “
Elastic Anisotropy and Micro-Damage Processes in Polycrystalline Ice—Part I: Theoretical Formulation
,”
Int. J. Fract.
,
55
(
3
), pp.
223
243
.
24.
Wu
,
M. S.
, and
Sunder
,
S. S.
,
1992
, “
Elastic Anisotropy and Micro-Damage Processes in Polycrystalline Ice—Part II: Numerical Simulation
,”
Int. J. Fract.
,
55
(
3
), pp.
375
396
.
25.
Nanthikesan
,
S.
, and
Sunder
,
S. S.
,
1995
, “
Tensile Cracks in Polycrystalline Ice Under Transient Creep: Part I—Numerical Modelling
,”
Mech. Mater.
,
21
(
4
), pp.
265
379
.
26.
Nanthikesan
,
S.
, and
Sunder
,
S. S.
,
1995
, “
Tensile Cracks in Polycrystalline Ice Under Transient Creep: Part I—Numerical Simulations
,”
Mech. Mater.
,
21
(
4
), pp.
281
301
.
27.
Kuutti
,
J.
,
Kolari
,
K.
, and
Marjavaara
,
O.
,
2013
, “
Simulation of Ice Crushing Experiments With Cohesive Surface Methodology
,”
Cold Reg. Sci. Technol.
,
92
, pp.
17
28
.
28.
Renshaw
,
C. E.
,
Golding
,
N.
, and
Schulson
,
E. M.
,
2014
, “
Maps for Brittle and Brittle-Like Failure in Ice
,”
Cold Reg. Sci. Technol.
,
97
, pp.
1
6
.
29.
Sakharov
,
A.
,
Karulin
,
E.
,
Marchenko
,
A.
,
Karulina
,
M.
,
Sodhi
,
D.
, and
Chistyakov
,
P.
,
2015
, “
Failure Envelope of the Brittle Strength of Ice in the Fixed-End Beam Test (Two Scenarios)
,”
23rd International Conference on Port and Ocean Engineering Under Arctic Conditions
, Trondheim, Norway.
30.
Marchenko
,
A.
, and
Lishman
,
B.
,
2015
, “
Properties of Thermo-Elastic Waves in Saline Ice
,”
23rd International Conference on Port and Ocean Engineering Under Arctic Conditions
, Trondheim, Norway, June 14–18.
31.
Snyder
,
S. A.
,
Schulson
,
E. M.
, and
Renshaw
,
C. E.
,
2016
, “
Effects of Prestrain on the Ductile-to-Brittle Transition of Ice
,”
Acta Mater.
,
108
, pp.
110
127
.
32.
Schulson
,
E. M.
,
Fortt
,
A. L.
,
Iliescu
,
D.
, and
Renshaw
,
C. E.
,
2006
, “
Failure Envelope of First-Year Arctic Sea Ice: The Role of Friction in Compressive Fracture
,”
J. Geophys. Res.
,
111
(C11), pp. 3923–3932.
33.
Kolari
,
K.
,
2007
, “
Damage Mechanics Model for Brittle Failure of Transversely Isotropic Solids: Finite Element Implementation
,” VTT Publications, The Technical Research Centre of Finland, Espoo, Finland,
Report No. 628
.
34.
Wachter
,
L. M.
,
Renshaw
,
C. E.
, and
Schulson
,
E. M.
,
2009
, “
Transition to Brittle Failure Mode in Ice Under Low Confinement
,”
Acta Mater.
,
57
(
2
), pp.
345
355
.
35.
Kolari
,
K.
,
2015
, “
Simulation of the Temperature and Grain Size Dependent Uniaxial Compressive Strength Using 3D Wing Crack Model
,”
23rd International Conference on Port and Ocean Engineering Under Arctic Conditions
, POAC’15, K. Høyland, E. Kim, R. Lubbad, and W. Lu, eds., Trondheim, Norway.
36.
Lubbad
,
R.
, and
Løset
,
S.
,
2011
, “
A Numerical Model for Real-Time Simulation of Ship-Ice Interaction
,”
Cold Reg. Sci. Technol.
,
65
(
2
), pp.
111
127
.
37.
Su
,
B.
,
Riska
,
K.
, and
Moan
,
T.
,
2011
, “
Numerical Simulation of Local Ice Loads in Uniform and Randomly Varying Ice Conditions
,”
Cold Reg. Sci. Technol.
,
65
(
2
), pp.
145
159
.
38.
Gagnon
,
R. E.
,
2011
, “
A Numerical Model of Ice Crushing Using a Foam Analogue
,”
Cold Reg. Sci. Technol.
,
65
(
3
), pp.
335
350
.
39.
Serré
,
N.
,
2011
, “
Numerical Modelling of Ice Ridge Keel Action on Subsea Structures
,”
Cold Reg. Sci. Technol.
,
67
(
3
), pp.
107
119
.
40.
Paavilainen
,
J.
, and
Tuhkuri
,
J.
,
2013
, “
Pressure Distributions and Force Chains During Simulated Ice Rubbling Against Sloped Structures
,”
Cold Reg. Sci. Technol.
,
85
, pp.
157
174
.
41.
Basista
,
M.
,
2002
, “
Micromechanics of Damage in Brittle Solids
,”
Anisotropic Behaviour of Damaged Materials
,
J. J.
Skrzypek
and
A. W.
Ganczarski
, eds.,
Springer-Verlag
,
Berlin, Germany
, pp.
221
258
.
42.
Santaoja
,
K.
,
2014
, “
Thermodynamic Formulation of a Material Model for Microcracking Applied to Creep Damage
,”
Procedia Mater. Sci.
,
3
, pp.
1179
1184
.
43.
Santaoja
,
K.
,
2015
, “
Thermodynamics of a Material Model Showing Creep and Damage
,”
3rd Polish Congress of Mechanics & 21st Computer Methods in Mechanics
, Gdańsk, Poland.
44.
Chaboche
,
J.-L.
,
1978
, “
Description Thermodynamique et phénoménologique de la viscoplasticité cyclique avec endommagement Publication
,” Office National d'Etudes et Recherches Aérospatiales,
Chatillon, France
.
45.
Schulson
,
E. M.
, and
Duval
,
P.
,
2009
,
Creep and Fracture of Ice
,
Cambridge University Press
,
Cambridge, UK
.
46.
Cole
,
D. M.
,
1986
, “
Effect of Grain Size on the Internal Fracturing of Polycrystalline Ice
,” Cold Regions Research & Engineering Laboratory, Hanover, NH,
Report No. 86-5
.
47.
Le Gac
,
H.
, and
Duval
,
P.
,
1980
, “
Constitutive Relations for the Non-Elastic Deformation of Polycrystalline Ice
,”
Physics and Mechanics of Ice
,
P.
Tryde
, ed.,
Springer-Verlag
,
Berlin
, pp.
51
59
.
48.
Timco
,
G. W.
, and
Frederking
,
R. M. W.
,
1983
, “
Confined Compressive Strength of Sea Ice
,” 7th Port and Ocean Engineering Under Arctic Conditions,
P.
Jumppanen
, ed.,
Helsinki
,
Finland
, Vol.
I
, pp.
243
253
.
49.
Timco
,
G. W.
, and
Frederking
,
R. M. W.
,
1986
, “
Confined Compression Tests: Outlining the Failure Envelope of Columnar Grained Sea Ice
,”
Cold Reg. Sci. Technol.
,
12
(
1
), pp.
13
28
.
50.
Timco
,
G. W.
, and
Weeks
,
W. F.
,
2010
, “
A Review of the Engineering Properties of Sea Ice
,”
Cold Reg. Sci. Technol.
,
60
(
2
), pp.
107
129
.
51.
Wakahama
,
G.
,
1965
, “
Internal Fracture of Ice
,”
Low Temp. Sci. A
,
23
, pp.
39
50
(in Japanese With English Summary).
52.
Currier
,
J. H.
,
Schulson
,
E. M.
, and
St. Lawrence
,
W. F.
,
1983
, “
A Study on the Tensile Strength of Ice as a Function of Grain Size
,” Cold Regions Research & Engineering Laboratory, Hanover, NH, Report No. 83-14.
53.
Jones
,
S. J.
,
1997
, “
High Strain-Rate Compression Tests on Ice
,”
J. Phys. Chem. B
,
101
(
32
), pp.
6099
6101
.
54.
Frederking
,
R. M. W.
, and
Timco
,
G. W.
,
1984
, “
Compressive Behaviour of Beaufort Sea Ice Under Vertical and Horizontal Loading
,”
3rd International Offshore Mechanics and Arctic Engineering Symposium
, Vol.
3
, pp.
145
149
.
55.
Schwarz
,
J.
,
1970
, “
The Pressure of Floating Ice-Fields on Piles
,”
IAHR 70 1st International Symposium on Ice
, Reykjavik, Iceland, Paper No. 6.3.
56.
Kuehn
,
G. A.
, and
Schulson
,
E. M.
,
1994
, “
The Mechanical Properties of Saline Ice Under Uniaxial Compression
,”
Symposium on Applied Ice and Snow Research
, Rovaniemi, Finland.
57.
Michel
,
B.
,
1978
,
Ice Mechanics
,
Les Presses de l'Université Laval
,
QC, Canada
.
58.
Lee
,
R. W.
, and
Schulson
,
E. M.
,
1988
, “
The Strength and Ductility of Ice Under Tension
,”
ASME J. Offshore Mech. Arct. Eng.
,
110
(
2
), pp.
187
191
.
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