Numerical Modeling of Large Deformations in Deposition Processes: an Eulerian Approach
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We consider a numerical framework for simulating deposition phenomena on deformable solids, focusing on the management of evolutionary interfaces. The adopted methodology is based on a purely Eulerian formulation for the surface growth phenomena. From a modeling point of view, the Eulerian formulation is adopted to take advantage of solving the governing equations on a fixed computational domain with a fixed spatial discretization. This approach requires the definition of a computational domain that encloses the initial body and fully contains the evolving deformable solid throughout the entire time interval of interest. Our approach centers on the stable integration of time-dependent variables across the Eulerian grid, a task critical for maintaining the consistency of the material’s deformation. We implement stabilization techniques to suppress non-physical artifacts common in fixed-mesh solid mechanics. Furthermore, the framework addresses the challenge of an evolving numerical solution by enforcing a consistent flux-based treatment for newly deposited material, guaranteeing that governing equations are satisfied as the domains expand.
