A position-based PFEM formulation for free-surface non-Newtonian flows with application to fresh concrete

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This work presents a methodology for free surface non-Newtonian incompressible flows using a particle position-based formulation of the Particle Finite Element Method (PFEM) [1], motivated by the simulation of fresh concrete flow. This method is based on the Lagrangian description of the flow and represents the fluid domain by cloud of particles, with a finite element mesh being built, taking the particles as nodes, to solve the motion equations and update the particle positions. To deal with large distortions of fluid flows, such mesh is constantly rebuilt, leading to a method very robust to deal with topological changes within the fluid domain. This approach requires updating the reference configuration, enabling the use of partially or fully updated Lagrangian descriptions. The weak solution is based on the stationary energy principle considering current nodal positions and pressures as variational parameters, deviating from the common practice of employing velocity and pressure as unknowns. Furthermore, smoothed versions of the Bingham and Herschel-Bulkley viscoplastic models are chosen to represent the fresh concrete behavior, keeping stresses independent of strain history and making updating the reference for the fluid simple, without the need for considering the stress distribution in the past reference. The implicit α-generalized strategy is chosen for time integration, enabling second order convergence and ensuring good stability due to the control over numerical dissipation at high frequencies. Finally, selected 2D and 3D examples are simulated to test and verify the proposed methodology.[1] IDELSOHN, S. R.; ONATE, E.; Del Pin, F. The particle finite element method: a powerful tool to solve incompressible flows with free-surfaces and breaking waves. International Journal for Numerical Methods in Engineering, John Wiley and Sons, Ltd, v. 61, n. 7, p. 964–989, oct 2004. ISSN 1097-0207.