In this work, a unified updated Lagrangian formulation for solving fluid-structure interaction (FSI) problems is derived. The mixed velocity-pressure formulation for hypoelastic solids and quasi and fully incompressible Newtonian fluids is obtained as an extension of the velocity formulation derived for a general continuum. The space discretization for the fluid domain is performed via the Particle Finite Element Method (PFEM), where for the solid domain a standard FEM is used. Linear interpolation is used for both the velocity and the pressure fields. The global FSI problem is solved using a Gauss-Seidel iterative scheme. The required stabilization for dealing with incompressible situations is given by an enhanced formulation of the Finite Calculus (FIC) technique . The efficiency of the proposed strategy is tested by solving benchmark FSI problems.
Unified updated lagrangian formulation for the analysis of quasi and fully incompressible fluids and solids and their interaction via a partitioned scheme and the PFEM