A Phase-Field Variational Approach to 3D Frictional Sliding Contact in Multiphase Fluid-Structure Interaction Systems
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Collision and contact dynamics in submerged environments pose a significant challenge in computational mechanics due to the strong coupling between multiphase flows, structural deformation, and frictional interaction. Such interactions are central to ship-ice dynamics in Arctic waters, where reliable predictive tools are required to support safe and efficient marine operations. This work presents a fully Eulerian, phase-field-based continuum framework for simulating three-dimensional frictional sliding contact in multiphase fluid-structure interaction (FSI) problems. Building upon our previous work on multiphase FSI [1], we introduce a phase-field based diffuse interface formulation for dynamic frictional contact in 3D. The governing equations consist of a unified momentum balance for fluid and solid phases, coupled with an Allen-Cahn phase-field evolution equation and phase-wise strain evolution laws. Contact detection and traction transfer are achieved through the controlled overlap of diffuse solid interfaces, quantified using phase-fraction fields. This enables robust evaluation of normal and tangential contact forces, including frictional sliding, within a consistent variational framework [2]. The formulation is verified against classical Hertzian contact, demonstrating excellent agreement with analytical solutions, with traction errors below 3%. Additional benchmark problems, including sliding block and ironing configurations, illustrate the method’s ability to capture dynamic frictional response under large deformation and relative motion. Finally, the robustness and scalability of the framework are demonstrated through a representative ship-ice interaction scenario incorporating free-surface effects, multiphase flow, and frictional sliding contact. The proposed methodology provides a unified and scalable computational mechanics tool for simulating complex contact-dominated multiphase FSI systems in three dimensions. REFERENCES [1] Mao, X., Rath, B., & Jaiman, R. (2024). A 3D phase-field based Eulerian variational framework for multiphase fluid-structure interaction with contact dynamics. Computer Methods in Applied Mechanics and Engineering, 429, 117172. [2] Rath, B., & Jaiman, R. K. (2026). A phase-field formulation of frictional sliding contact for 3D fully Eulerian fluid-structure interactions. Computer Methods in Applied Mechanics and Engineering, 451, 118685.
