The increasing marine activities in Arctic area have brought growing interest in shipiceberg collision study. The purpose of this paper is to study the iceberg geometry shape effect on the collision process. In order to estimate the sensitivity parameter, five different geometry iceberg models and two iceberg material models are adopted in the analysis. The FEM numerical simulation is used to predict the scenario and the related responses. The simulation results including energy dissipation and impact force are investigated and compared. It is shown that the collision process and energy dissipation are more sensitive to iceberg local shape than other factors when the elasticplastic iceberg material model is applied. The blunt iceberg models act rigidly while the sharp ones crush easily during the simulation process. With respect to the crushable foam iceberg material model, the iceberg geometry has relatively small influence on the collision process. The spherical iceberg model shows the most rigidity for both iceberg material models and should be paid the most attention for iceresist design for ships.
Because of the promising natural resources in Arctic region and the upcoming northern sea route, marine activities in Arctic region have increased significantly in the past decade. Consequently, the possibility of ship collisions with icebergs increases with the rising number of vessels. According to a damage survey made by Finnish and Swedish maritime administration [
One approach to predict ice load during shipiceberg interaction is carrying out the related experiments. Nevertheless, the experiment data are scarce and only limited sets of the data are available to researchers. Besides, ice rules are conventionally adopted by researchers, which are issued by the maritime authorities and classification societies. But these rules are far from enough to provide ice load assessment since they are limited to certain ship types and regions. For example, the ice load provided by the frequently employed ice class rules “Finnish and Swedish Ice class Rules” [
The numerical simulation is able to provide detailed insight of the dynamics of ice during shipice interaction. A valid ice material model is the premise of reliable simulation results. The discrete element method (DEM) is occasionally employed to model the iceberg, but it may lead to a lack of generally accepted mathematical foundation and therefore often results in purposely built algorithms for a certain application [
A good understanding of the iceberg mechanics properties is of crucial importance to model a valid ice material model. Due to the fact that the high homologous temperature of ice occurs in nature,
Spalling, extruding, and cracking accompanied by recrystallization all occur when ice fails, so modeling a material which can completely capture the ice behavior during the shipiceberg collision is a challenging task. For engineering purposes, a representative load model is applied rather than a physical correct material model [
Since ice is a very complicated material, a generally accepted ice material model for shipiceberg collision has not been well established. Jebaraj et al. [
Different iceberg geometry shapes contribute to quite different shipiceberg interaction processes. Some icebergs penetrate the hull structure, leaving ships at risk. While some icebergs crush easily in the collision. One primary purpose of the present analysis is to estimate the iceberg geometry effect on the collision scenario. Another purpose is to define the most dangerous iceberg shape to design against, giving support for iceresist design for ships. Five different geometry icebergs are modeled in the present collision simulation. Two iceberg material models are utilized for comparing the geometry effects. The impact force and energy dissipation are analyzed and compared to illustrate the different collision processes.
In this section, comprehensive shipiceberg collision analyses are carried out using five different shape iceberg models. An elasticplastic material model and a crushable foam model proposed by Gagnon [
The main stages that the ice undergoes during shipiceberg interaction are illustrated in Figure
Ice development process of the elasticplastic material.
The crushable foam material is also utilized to estimate the geometry sensitivity, compared with the aforementioned elasticplastic material model. The stressstrain relationship of the crushable foam model shown in Figure
Ice mechanics parameters.
Iceberg details  Elasticplastic material  Crushable foam material 

Density kg/m^{3}  900  900 
Young’s modulus MPa  9500  9500 
Poisson’s ratio  0.3  0 
Material  *MAT_USER_DEFINED  *MAT_CRUSHABLE FOAM 
Volume strainyield stress relationship of the crushable foam material.
The collision scenario is defined as follows: the iceberg model strikes the FPSO side structure with a constant speed of 2 m/s. The computation time is 1 second due to the balancing of the computation time and accuracy. A rigid surface is attached aft to each iceberg to supply an even force distribution into the local part of the iceberg. In addition, the constant velocity is given to one node in the rigid surface to push the iceberg model forward. Since the iceberg model and the rigid surface share nodes, no contact area is defined between them. The boundary of the FPSO side structure is fixed in all freedom degrees to compensate for the nonemodeled structure. The different geometry iceberg models and FPSO side structure model are illustrated in Figure
FPSO segment geometry details.
FPSO segment details  

Length overall m  288  Density kg/m^{3}  7890 
Moulded breadth m  65  Young’s modulus GPa  2.1 
Moulded depth m  29.4  Poisson’s ratio  0.3 
Draft m  22  Yield stress MPa  289 
Side shell spacing m  3.4  Failure strain  0.35 
Outer shell thickness mm  20  Typical element dimension mm  225 
Side stringer thickness mm  14  Element type  *SECTION_SHELL 
Inner shell thickness mm  15  Segment length m  35 
Segment height m  26  Element number  105664 
Length between perpendiculars m  281  Material type  *MAT_PIECEWISE_LINEAR_PLASTICITY 
Iceberg models geometry details.
Geometry  Sphere  Cube  Prism  Cone  Ellipsoid 

Size m 





Shipiceberg collision models.
Shipiceberg collision scenario schematic.
The results of numerical simulations are obtained, including the data of contact force, energy dissipation, and structural deformation. The contact pressure in the spherical iceberg model collision case using the elasticplastic material is displayed in Figure
Contact pressure at
The pressurearea relationship is commonly employed to denote the ice mechanics during shipiceberg interaction. The pressure is defined as the collision force divided by the nominal contact area. Taking the shipspherical iceberg collision scenario as an example, the pressurearea curves obtained by the elasticplastic material model and the crushable foam material model are compared in Figure
Pressurearea relationships.
As mentioned above, ice mechanics properties of both the material models are similar in the spherical iceberg model case. Thus, the outer shell deformation and the largest stress place do not differ obviously in both material models. The outer shell deformation with elasticplastic material at the moment of
Outershell deformation.
The largest stress place.
As mentioned before, five different iceberg models are utilized to investigate the geometry shape sensitivity in view of the two comparative material models. The deformation situations of the spherical and conic iceberg cases for the foam material model are demonstrated in Figure
Deformation plot of the crushable foam material.
On the contrary, the collision processes vary considerably between different iceberg geometry models when the elasticplastic material is employed. The blunt iceberg model acts nearly rigidly and shows similar property as one of the crushable foam material models. Compared with the blunt iceberg model, the sharp model crushes easily. The deformation situations for the spherical and conic iceberg model cases are shown in Figure
Deformation plot of the elasticplastic material.
In order to conduct a more quantitative geometry sensitivity study, the ice dissipated energy in these four cases is compared and illustrated in Figure
(a) Energy dissipated by ice with the material models. (b) Prism and spherical iceberg model crushing processes.
On the purpose of analyzing the iceberg shape sensitivity more detailedly, the results of resistance force, total energy dissipation, and the ratio of dissipated energy by iceberg to total dissipated energy are investigated from the numerical simulation results, as is shown in Figures
Total resistance forces for both material models.
Elasticplastic material
Crushable foam material
Total energy dissipation for both material models.
Elasticplastic material
Crushable foam material
Ratios of ice energy dissipation to total energy dissipation for both material models.
ElasticPlastic material
Crushable foam material
Considering the crushable foam material models, the resistance force and energy dissipation do not vary obviously for different iceberg geometry shapes. All of the energy ratios are nearly zero in the later collision stage. Considering the collision process, the iceberg models undergo initial deformation and then quickly harden and indent the hull. On the contrary, the collision process is different for different iceberg shapes when the elasticplastic material model is employed. The energy ratios are about 0.4 when the icebergs are in sharp shapes, indicating a “softer” contact in these situations. And due to the crushing of the iceberg, the hull deformations are less than 1 m, which are far smaller than the iceberg geometry sizes. As to the blunt iceberg model, the energy ratios are in the same range of the ones of the foam model. In summary, the iceberg geometry shapes do have a significant effect on collision results when the elasticplastic material is used. Although the iceberg shape effect has been studied by some researchers, the mechanics explanation has not been fully developed. The possible explanation is elaborated as follows. Compared with the ice elements of the sharp iceberg models, the ice elements of the blunt iceberg models in the contact area are highly confined by the surrounding elements; thus, the hydrostatic pressure is at a relatively high level; hence, the deviator stress is lower and then the effective strain is lower. Therefore, the ice elements of the blunt iceberg models are less likely to fail, leading to the rigid properties of the blunt iceberg models. On the contrary, the sharp iceberg models crush easily during the shipice interaction.
Besides the geometry sensitivity analysis, other collision parameters’ effects on the simulation results are also investigated for comparison. The sensitivity analyses of shipiceberg collision with respect to impact velocity and water effect are conducted in this section and the velocity sensitivity analysis is introduced firstly. The field measurement data of Orden experiment [
Velocity sensitivity analyses.
Field measurement data of Orden experiment
Contact force
Energy dissipated by ice
The effect of water is not considered in the above comprehensive simulations; thus, a sensitivity analysis of water effect is carried out by simply using added mass method. The added mass coefficient is assumed to be constant and equal to 0.5 for the ice mass [
Water effect on shipspherical iceberg collision.
Total dissipated energy
Energy dissipated by ice
The numerical simulation problems, such as the negative volume and the hourglass control, are paid a lot of attention in the simulation. The control of negative volume is important because of the explicit finite difference method in LSDYNA. When the crushable foam material model is applied, this problem is especially crucial. A convergent study is conducted by utilizing different ice element sizes. Then, the element length is decided to be 50 mm to gain the most convergent simulation results. In addition, in the case of the prism iceberg model of the crushable foam material model, element distortion occurs at the later stage of simulation. A few ice elements on the contact sharp edge fail due to the negative volume. So, the ratio of the dissipated energy by iceberg to the total dissipated energy is a little higher than the ratios of other geometry models. In order to define the most suitable hourglass control method for the crushable foam material, a sensitivity analysis is also carried out by adopting different hourglass control methods. Finally, the rigid hourglass control method is selected in the simulation, as is mentioned before.
The shipiceberg collision scenario is simulated with finite element method in this paper. The focus of the simulation is the iceberg geometry shape effect on collision process. The elasticplastic material is applied to simulate the ice material model, and the crushable foam material is also used for comparison. In summary, the local shape of the iceberg does affect the responses of shipiceberg collision for some cases. The most important results are shown as follows.
The iceberg local shape does have a significant effect on shipiceberg interaction process when the ice is simulated by the elasticplastic material model.
The blunt iceberg model can penetrate the hull while the sharp iceberg model tends to be crushed easily for the elasticplastic model.
If the iceberg is simulated by the crushable foam material, the simulation results are not sensitive to the iceberg local shape.
The spherical shape is the most dangerous shape to design against in terms of the hardest ice strength. The hull structure undergoes large deformation in the contact area, and it should be icestrengthened when shipping in Arctic region.
Homologous temperature
Shipiceberg interface pressure
Nominal contact area
Second invariant of deviatoric stress tensor
Hydrostatic pressure
Elasticplastic material constants
Effective plastic strain
Failure strain
Initial failure strain
Larger root of the yield function
Cutoff pressure.
The authors declare that there is no conflict of interests regarding the publication of this paper.