## 1 Introduction
### Using Numerical Methods  
When ice undergoes an impact or encounters significant external forces, it can experience large deformations, fractures, and fragmentation. Modelling this complex behaviour with the finite element method (FEM) can be challenging and inefficient due to several factors:  
* Large deformations: Ice can undergo substantial deformations under load, which can result in nonlinear behaviour. FEM typically relies on linear or moderately nonlinear assumptions, making it less suitable for accurately capturing the highly nonlinear response of ice under large deformations;
* Fracture and failure: Ice is prone to fracturing and failure when subjected to high stress concentrations or sudden impacts. Modelling these fracture mechanisms within the FEM framework can be challenging, as it requires accurately representing the crack initiation, propagation, and interaction;
* Fragmentation: Ice can fragment into smaller pieces during impact events, creating a complex system of multiple interacting bodies. Modelling this fragmentation process with FEM would require intricate meshing and tracking of individual ice fragments, which can be computationally demanding and impractical. To address these challenges, researchers often explore alternative numerical methods specifically designed to handle large deformation, fracture, and fragmentation of materials. These methods may include:  
* Discrete element method (DEM): This simulates the behaviour of individual discrete particles, making it suitable for modelling fragmentation and the interaction between ice fragments. It allows for tracking fractures and the realistic representation of ice behaviour during impact [30; 31];
* Peridynamics: This is a non-local continuum method that explicitly accounts for crack initiation, propagation, and interaction. It can efficiently handle large deformations and fractures computationally, making it suitable for modelling ice behaviour during impact [32; 33];
* Smoothed particle hydrodynamics (SPH): This is a meshless method, representing materials as particles. Initially developed as a probabilistic meshfree particle method for simulating astrophysical problems [34], SPH is well suited for simulating fluid behaviour and can accurately capture large deformations, fractures, and fragmentation without the need for complex meshing, as some research demonstrates [35; 36; 37; 38; 39; 40]. These alternative numerical methods offer several advantages over traditional FEM when dealing with the complexities of large deformation, fracture, and fragmentation of ice. However, none have yet emerged as a definitive, leading approach, and researchers continue to explore and develop specialized techniques to improve the accuracy and efficiency of ice modelling under such conditions. The SPH method is primarily used for hydrodynamic problems. When applied to solid materials, it shows advantages over grid-based numerical methods for large deformations. The spalling of ice, for instance, is an event that can be reproduced by an SPH simulation [41; 42]. The spalling effect is particularly distinct for high velocity impacts. A typical application can be the hailstone impact on a structure. There are different approaches for the numerical investigation of ice, yet there is no method that can be recognized as superior, universally applicable, and reliable. A full- scale simulation can be realized by the DEM which predefines the fracture points of the ice. The local effects and the exact physical material behavior can be described by the FEM, as it can rely on the most experience. Even though the impact of a hailstone has little in common with the natural crushing of sea ice, it demonstrates that the SPH method is preferably used for events connected to large distortions [41; 42]. The current study positions itself within this vein of research, introducing a novel and relatively unexplored, yet promising approach. It introduces a hybrid model based on coupling FEM (finite element method) and SPH (smoothed particle hydrodynamics).