Coupling of FEM and Peridynamics for a 3D Brain Model
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This study presents a computational technique for coupling the Finite Element Method (FEM) with Peridynamics (PD) to describe a 3D static problem in a human brain model. While existing PD literature primarily focuses on materials with high Young’s modulus, undergoing small deformations, such as metals, concrete, or rock, there is an increasing interest in simulating soft tissue mechanics, particularly for surgical applications. Computer-Integrated Surgery aims to enhance the precision and outcomes of surgical procedures involving soft organs like the brain, liver, and kidneys. PD-based computational methods are particularly suitable for modeling discontinuities, such as tissue cutting, and provide advantages in simulating large strain conditions. The starting point of the proposed approach is an existing FEM model of a human brain. Following the approach previously proposed [1], the computational domain is divided into three regions; a PDdiscretized region, a FEM-discretized region, and a transition zone where both methods coexist. This hybrid domain allows a seamless transfer of forces between the two modeling approaches. Fictitious FEM and PD nodes are introduced to define the transfer of forces between the two main portions of the model, FEM and PD [2]. In the PD region the FEM nodal configuration is retained while removing the original mesh. Bonds are then established among nodes, forming PD families. The method is applied to a portion of a 3D brain model, subjected to a distributed load. Displacement components and deformed nodal coordinates are evaluated across the domain. The numerical results demonstrate consistency with the FEM method, with no spurious effects observed at the PD-FEM interface, indicating the robustness and accuracy of the coupling strategy.