An Efficient Phase-field Framework for Contact Dynamics between Deformable Solids in Fluid Flow

Abstract: Elastic contact in hydrodynamic environments is a complex multiphysics phenomenon and can be found in applications ranging from engineering to biological systems. Understanding the intricacies of this coupled problem requires the development of a generalized framework capable of handling topological changes and transitioning implicitly from FSI conditions to solid-solid contact conditions. We propose a mono-field interface advancing method for handling multibody contact simulations in submerged environments. Given the physical demands of the problem, we adopt a phase-field based fully Eulerian approach to resolve the multiphase and multibody interactions in the system. We employ a stabilized finite element formulation and a partitioned iterative procedure to solve the unified momentum equation comprising solid and fluid dynamics coupled with the Allen-Cahn phase-field equation. We introduce a contact force approach to handle smooth elastic-elastic and elastic-rigid contact based on the overlap of the diffused interfaces of two colliding bodies. We propose a novel approach to extend the model for multibody contact simulations while using a single phase-field function for all the solids. The method is based on updating the solid boundaries at every time step and checking for collisions among them. The developed approach eliminates the need to solve multiple phase field equations and multiple strain equations at every time step. This reduces the overall computational time by nearly $16\%$ compared to a multi phase-field approach. The implemented model is verified for smooth dry contact and FSI contact scenarios. Using the proposed framework, we demonstrate the collision dynamics between multiple bodies submerged in an open liquid tank.