## 1 Introduction
### Ice Interaction  
Ice-ship interaction refers to the dynamic interaction between a ship and ice when operating in icy waters (Figure 1(a)). It involves the forces and phenomena that occur as a vessel moves through or interacts with different types of ice, such as pack ice, brash ice, or ice floes [24; 25]. When a ship encounters ice, various factors come into play that influence the interaction, such as:  
1. Ice properties: The type and characteristics of the ice significantly impact the interaction. Factors such as ice thickness, ice concentration, ice strength, and ice temperature affect how the ice interacts with the ship;
2. Ship design: The design of the ship's hull and ice-breaking capabilities play a crucial role in determining how the vessel interacts with the ice;
3. Ship speed and operation: The speed at which the ship moves through the ice affects the magnitude of ice loads and the resulting interaction;
4. Environmental conditions: The environmental conditions, including air temperature, water temperature, wind speed, and ice drift, can influence the ice-ship interaction.  
During ice-ship interactions, various phenomena occur, including ice breaking, ice bending, ice crushing, ice loads on the hull, and vibrations induced by ice impacts. These interactions can exert significant forces on the ship, potentially leading to structural damage or changes in the ship's behavior.  
To categorize the impact conditions, in line with the literature [24; 25; 26], the schemes in Figure 2 can be considered. In Figure 1(a), a crushing scenario is depicted where a vessel impacts a relatively thin ice sheet, while Figure 1(b) details possible contact patterns between the vessel's keel and the ice surface. The ice surface was presented in three different geometry conditions, as it can be found in the real conditions, while the vessel keeps the same configuration. The three cases also demonstrate the evolution of the rules used when considering vessel-ice impact phenomena, progressing towards the consideration of increasingly focused areas.  
Figure 2: Impact on ice: (**a**) one potential scenario, (**b**) scheme of ice interaction with hull.  
Referring to the ice thickness, different authors proposed guidelines for dealing with ice conditions, categorized as _young ice 1_ and _young ice 2_[27; 28; 29], as a practical method to relate to the most frequent conditions. These categories are based on the Bureau Veritas guidelines [28], which pertain to the design and structural requirements for vessels or structures operating in such ice conditions. In the _young ice 1_ environment, the maximum thickness of the ice is limited to 300 mm. This suggests that structures or vessels designed to operate in this environment should be able to withstand or navigate through ice thicknesses up to 30 cm. In the _young ice 2_ environment, the ice is defined in terms of its concentration and refers to the proportion of an area covered by ice compared to open water. In this case, _young ice 2_ would indicate an ice concentration lower than 3/10, meaning that less than 30% of the area is covered by ice.  
The present investigation considers the case of _young ice 1_ and an impact area, as represented in the second scheme of Figure 2b.