Abstract

This paper presents a finite element model for the simulation of ice–structure interaction problems, which are dominated by crushing. The failure mode of ice depends significantly on the strain rate. At low strain rates, the ice behaves ductile, whereas at high strain rates it reacts in brittle mode. This paper focuses on the brittle mode, which is the dominating mode for ship–ice interactions. A multitude of numerical approaches for the simulation of ice can be found in the literature. Nevertheless, the literature approaches do not seem suitable for the simulation of continuous ice–structure interaction processes at low and high confinement ratios in brittle mode. Therefore, this paper seeks to simulate the ice–structure interaction with the finite element method (FEM). The objective of the here introduced Mohr-Coulomb Nodal Split (MCNS) model is to represent the essential material behavior of ice in an efficient formulation. To preserve mass and energy as much as possible, the node splitting technique is applied, instead of the frequently used element erosion technique. The intention of the presented model is not to reproduce individual cracks with high accuracy, because this is not possible with a reasonable element size, due to the large number of crack fronts forming during the ice–structure interaction process. To validate the findings of the model, the simulated maximum ice forces and contact pressures are compared with ice extrusion and double pendulum tests. During validation, the MCNS model shows a very good agreement with these experimental values.

References

1.
Transport Safety Agency
,
2010
,
Finnish-Swedish Ice Class Rules 2010
,
Helsinki
.
2.
International Maritime Organization
,
2014
, “
International Code for Ships Operating in Polar Waters (POLAR CODE)
”.
3.
International Organization for Standardization
,
2010
, “
Petroleum and Natural Gas Industries—Arctic Offshore Structures (ISO 19906:2010)
,” DIN EN ISO 19906:2011-04.
4.
Sanderson
,
T. J.
,
1988
,
Ice Mechanics: Risks to Offshore Structures
,
Graham & Trotman
,
London
.
5.
Timco
,
G. W.
, and
Sudom
,
D.
,
2013
, “
Revisiting the Sanderson Pressure–Area Curve: Defining Parameters That Influence Ice Pressure
,”
Cold Reg. Sci. Technol.
,
95
, pp.
53
66
.
6.
Herrnring
,
H.
,
Kubiczek
,
J. M.
, and
Ehlers
,
S.
,
2020
, “
The Ice Extrusion Test: A Novel Test Setup for the Investigation of Ice-Structure Interaction—Results and Validation
,”
Ships Offshore Struct.
,
15
(
sup1
), pp.
1
9
.
7.
Nowacki
,
H.
,
2010
, “
Five Decades of Computer-Aided Ship Design
,”
Comput.-Aided Des.
,
42
(
11
), pp.
956
969
.
8.
Okumoto
,
Y.
,
Takeda
,
Y.
,
Mano
,
M.
, and
Okada
,
T.
,
2009
,
Design of Ship Hull Structures
,
Springer
,
Berlin/Heidelberg
.
9.
von Bock und Polach
,
F. R. U.
,
Klein
,
M.
,
Kubiczek
,
J.
,
Kellner
,
L.
,
Braun
,
M.
, and
Herrnring
,
H.
,
2019
, “
State of the Art and Knowledge Gaps on Modelling Structures in Cold Regions
,”
International Conference on Offshore Mechanics and Arctic Engineering
, Paper No. OMAE2019-95085.
10.
Schulson
,
E. M.
,
1999
, “
The Structure and Mechanical Behavior of Ice
,”
JOM
,
51
(
2
), pp.
21
27
.
11.
Schulson
,
E. M.
, and
Duval
,
P.
,
2009
,
Creep and Fracture of Ice
,
Cambridge University Press
,
Cambridge
.
12.
Jordaan
,
I. J.
,
2001
, “
Mechanics of Ice–Structure Interaction
,”
Eng. Fract. Mech.
,
68
(
17–18
), pp.
1923
1960
.
13.
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
.
14.
Croasdale
,
K. R.
,
Morgenstern
,
N. R.
, and
Nuttall
,
J. B.
,
1977
, “
Indentation Tests to Investigate Ice Pressures on Vertical Piers
,”
J. Glaciol.
,
19
(
81
), pp.
301
312
.
15.
Frederking
,
R.
,
Jordaan
,
I.
, and
McCallum
,
J.
,
1990
, “
Field Tests of Ice Indentation at Medium Scale Hobson's Choice Ice Island, 1989
,”
Proceedings of the 10th International Symposium on Ice
,
Espoo, Finland
, pp.
931
944
.
16.
Gagnon
,
R.
,
Andrade
,
S. L.
,
Quinton
,
B.
,
Daley
,
C.
, and
Colbourne
,
B.
,
2020
, “
Pressure Distribution Data From Large Double-Pendulum Ice Impact Tests
,”
Cold Reg. Sci. Technol.
,
175
, p.
103033
.
17.
Browne
,
T.
,
Taylor
,
R.
,
Jordaan
,
I.
, and
Gürtner
,
A.
,
2013
, “
Small-Scale Ice Indentation Tests With Variable Structural Compliance
,”
Cold Reg. Sci. Technol.
,
88
, pp.
2
9
.
18.
Gürtner
,
A.
,
2009
, “
Experimental and Numerical Investigations of Ice-Structure Interaction
,”
Doctoral thesis
,
NTNU
,
Trondheim
.
19.
Ralston
,
T.
,
1977
, “
Yield and Plastic Deformation in Ice Crushing Failure
,”
Proceeding of the Arctic Ice Dynamics Joint Experiment International Commission on Snow and Ice Symposium
,
Seattle, WA
,
September
, pp.
234
245
.
20.
Derradji-Aouat
,
A.
,
2003
, “
Multi-surface Failure Criterion for Saline Ice in the Brittle Regime
,”
Cold Reg. Sci. Technol.
,
36
(
1–3
), pp.
47
70
.
21.
Liu
,
Z.
,
Amdahl
,
J.
, and
Løset
,
S.
,
2011
, “
Plasticity Based Material Modelling of Ice and Its Application to Ship–Iceberg Impacts
,”
Cold Reg. Sci. Technol.
,
65
(
3
), pp.
326
334
.
22.
Ince
,
S. T.
,
Kumar
,
A.
,
Park
,
D. K.
, and
Paik
,
J. K.
,
2017
, “
An Advanced Technology for Structural Crashworthiness Analysis of a Ship Colliding With an Ice-Ridge: Numerical Modelling and Experiments
,”
Int. J. Impact Eng.
,
110
, pp.
112
122
.
23.
Gagnon
,
R. E.
,
2011
, “
A Numerical Model of Ice Crushing Using a Foam Analogue
,”
Cold Reg. Sci. Technol.
,
65
(
3
), pp.
335
350
.
24.
Kim
,
H.
,
Daley
,
C.
, and
Colbourne
,
B.
,
2015
, “
A Numerical Model for Ice Crushing on Concave Surfaces
,”
Ocean Eng.
,
106
, pp.
289
297
.
25.
von Bock und Polach
,
R.
, and
Ehlers
,
S.
,
2013
, “
Model Scale Ice—Part B: Numerical Model
,”
Cold Reg. Sci. Technol.
,
94
, pp.
53
60
.
26.
Kolari
,
K.
,
2007
, “Damage Mechanics Model for Brittle Failure of Transversely Isotropic Solids: Finite Element Implementation,”
Doctoral thesis
, Vol.
628
,
VTT Publications
,
Espoo, Finland
.
27.
Elvin
,
A. A.
,
1996
, “
Number of Grains Required to Homogenize Elastic Properties of Polycrystalline ice
,”
Mech. Mater.
,
22
(
1
), pp.
51
64
.
28.
Schneider
,
D.
,
Schoof
,
E.
,
Huang
,
Y.
,
Selzer
,
M.
, and
Nestler
,
B.
,
2016
, “
Phase-Field Modeling of Crack Propagation in Multiphase Systems
,”
Comput. Methods Appl. Mech. Eng.
,
312
, pp.
186
195
.
29.
Grennerat
,
F.
,
Montagnat
,
M.
,
Castelnau
,
O.
,
Vacher
,
P.
,
Moulinec
,
H.
,
Suquet
,
P.
, and
Duval
,
P.
,
2012
, “
Experimental Characterization of the Intragranular Strain Field in Columnar Ice During Transient Creep
,”
Acta Mater.
,
60
(
8
), pp.
3655
3666
.
30.
Suquet
,
P.
,
Moulinec
,
H.
,
Castelnau
,
O.
,
Montagnat
,
M.
,
Lahellec
,
N.
,
Grennerat
,
F.
,
Duval
,
P.
, and
Brenner
,
R.
,
2012
, “
Multi-Scale Modeling of the Mechanical Behavior of Polycrystalline Ice Under Transient Creep
,”
Procedia IUTAM
,
3
, pp.
76
90
.
31.
Kellner
,
L.
,
Lu
,
W.
,
Sören
,
E.
, and
Høyland
,
K. V.
,
2021
, “
Study on the Cohesive Edge Crack in a Square Plate With the Cohesive Element Method
,”
Int. J. Fract.
,
231
(
1
), pp.
21
41
.
32.
LSTC
,
2019
, “
LS-DYNA Keyword User's Manual: Volume I
,” Livermore Software Technology Corporation (LSTC).
33.
Amiri
,
A.
,
2018
, “
Similar Overestimation of Sandstone Bending Strength by Coupled FEM-SPH Based Linear Drucker Prager and Discrete Element Based Bonded Particles: Calibration & Diagnosis
,”
Proceedings of the 15th Annual International Conference on Modelling and Simulation (ICMS)
,
Ottawa, Ontario, Canada
,
June
.
34.
Lu
,
W.
,
Li
,
M.
,
Vazic
,
B.
,
Oterkus
,
S.
,
Oterkus
,
E.
, and
Wang
,
Q.
,
2020
, “
Peridynamic Modelling of Fracture in Polycrystalline Ice
,”
J. Mech.
,
2
, pp.
1
12
.
35.
Wu
,
Y.
,
Wu
,
C. T.
, and
Hu
,
W.
,
2018
, “
Parametric and Convergence Studies of the Smoothed Particle Galerkin (SPG) Method in Semi-Brittle and Ductile Material Failure Analyses
,”
Proceedings of the 15th International LS-Dyna User Conference
,
Dearborn, MI
,
June
.
36.
Zhang
,
N.
,
Zheng
,
X.
,
Ma
,
Q.
, and
Hu
,
Z.
,
2019
, “
A Numerical Study on Ice Failure Process and Ice-Ship Interactions by Smoothed Particle Hydrodynamics
,”
Int. J. Nav. Archit. Ocean Eng.
,
11
(
2
), pp.
796
808
.
37.
Tabiei
,
A.
, and
Zhang
,
W.
,
2016
, “
Evaluation of Various Numerical Methods in LS-Dyna for 3D Crack Propagation
,”
Proceedings of the 14th International LS-Dyna Users Conference
,
Detroit, MI
,
June
.
38.
Kellner
,
L.
,
Stender
,
M.
,
von Bock und Polach
,
R. U. F.
,
Herrnring
,
H.
,
Ehlers
,
S.
,
Hoffmann
,
N.
, and
Høyland
,
K. V.
,
2019
, “
Establishing a Common Database of Ice Experiments and Using Machine Learning to Understand and Predict Ice Behavior
,”
Cold Reg. Sci. Technol.
,
162
, pp.
56
73
.
39.
Hudson
,
J.
, and
Harrison
,
J.
,
1997
,
Engineering Rock Mechanics: An Introduction to the Principles
,
Elsevier
,
New York
.
40.
Gross
,
D.
, and
Seelig
,
T.
,
2016
,
Bruchmechanik: Mit Einer Einführung in die Mikromechanik
,
Springer
,
Berlin, Heidelberg
.
41.
Renshaw
,
C.
, and
Schulson
,
E.
,
2001
, “
Universal Behaviour in Compressive Failure of Brittle Materials
,”
Nature
,
412
(
6850
), pp.
897
900
.
42.
Fish
,
A. M.
, and
Zaretsky
,
Y. K.
,
1998
, “
Strength and Creep of Ice in Terms of Mohr-Coulomb Fracture Theory
,”
Proceedings of the Eighth (1998) International Offshore and Polar Engineering Conference
,
Montreal, Quebec, Canada
,
May 24–29
, pp.
416
424
.
43.
Michaloudis
,
G.
,
Blankenhorn
,
G.
,
Mattern
,
S.
, and
Schweizerhof
,
K.
,
2010
, “Modelling Structural Failure With Finite Element Analysis of Controlled Demolition of Buildings by Explosives Using LS-DYNA,”
High Performance Computing in Science and Engineering ‘09
,
W. E.
Nagel
,
D. B.
Kröner
, and
M. M.
Resch
, eds.,
Springer
,
Berlin/Heidelberg
, pp.
539
551
.
44.
Timco
,
G. W.
, and
O'Brien
,
S.
,
1994
, “
Flexural Strength Equation for Sea Ice
,”
Cold Reg. Sci. Technol.
,
22
(
3
), pp.
285
298
.
45.
Feistel
,
R.
, and
Wagner
,
W.
,
2006
, “
A New Equation of State for H2O Ice Ih
,”
J. Phys. Chem. Ref. Data
,
35
(
2
), pp.
1021
1047
.
46.
Wells
,
J.
,
Jordaan
,
I.
,
Derradji-Aouat
,
A.
, and
Taylor
,
R.
,
2011
, “
Small-Scale Laboratory Experiments on the Indentation Failure of Polycrystalline Ice in Compression: Main Results and Pressure Distribution
,”
Cold Reg. Sci. Technol.
,
65
(
3
), pp.
314
325
.
47.
Jordaan
,
I.
, and
Timco
,
G.
,
1988
, “
Dynamics of the Ice-Crushing Process
,”
J. Glaciol.
,
34
(
118
), pp.
318
326
.
48.
LS-DYNA® Aerospace Working Group
,
2017
, “
Modeling Guidelines Document
,” 17-1.
49.
Kessler
,
D.
,
2014
, “
Best Practise in Crash Analysis and LS-Dyna Tools
,”
German LS-DYNA Forum 2014
,
Bamberg, Germany
,
October
.
50.
LSTC
,
2019
, “
LS-DYNA Theory Manual
” Livermore Software Technology Corporation (LSTC).
51.
Moore
,
P. F.
,
Jordaan
,
I. J.
, and
Taylor
,
R. S.
,
2013
, “
Explicit Finite Element Analysis of Compressive Ice Failure Using Damage Mechanics
,”
Proceedings of the 22th International Conference on Port and Ocean Engineering Under Arctic Conditions.
,
Espoo, Finland
,
June
.
52.
Xiao
,
J.
,
1997
, “
Damage and Fracture of Brittle Viscoelastic Solids With Application to Ice Load Models
,”
Doctoral thesis
,
Memorial University of Newfoundland
,
St. John’s, Canada
.
53.
Singh
,
S. K.
, and
Jordaan
,
I. J.
,
1999
, “
Constitutive Behaviour of Crushed Ice
,”
Int. J. Fract.
,
97
(
1/4
), pp.
171
187
.
54.
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
.
55.
Schwalbe
,
K.-H.
,
Scheider
,
I.
, and
Cornec
,
A.
,
2013
,
Guidelines for Applying Cohesive Models to the Damage Behaviour of Engineering Materials and Structures
,
Springer
,
Heidelberg, New York
.
56.
Herrnring
,
H.
,
Kellner
,
L.
,
Kubiczek
,
J. M.
, and
Ehlers
,
S.
,
2019
, “
A Cohesive Model for Ice and Its Verification With Tensile Splitting Tests
,”
Proceedings of the 12th European LS-DYNA Conference 2019
,
Koblenz, Germany
,
May
.
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