Coupling total Lagrangian SPH–EISPH for fluid–structure interaction with large deformed hyperelastic solid bodies

Abstract

In this work, we propose a two-way coupling technique between a total Lagrangian smoothed particle hydrodynamics (SPH) method for Solid Mechanics and the explicit incompressible SPH (EISPH) to simulate fluid–structure interaction problems. In the solid part, the total Lagrangian framework guarantees that the particle distribution keep stable to correctly calculate the deformation gradient and thus the elastic forces. The constitutive model follows hyperelastic formulations, and the stability of the method is enforced by a Jameson–Schmidt–Turkel (JST) stabilization procedure. For the fluid part, we applied an EISPH formulation, which is a fully explicit incompressible scheme based on a projection method capable of providing accurate pressure distributions for free-surface flows, while avoiding costly linear equations. The coupling scheme follows the same manner as the fixed wall ghost particle (FWGP) approach, which was here adapted to include moving walls. In addition, the non-penetration condition is rigorously reinforced through a numerical algorithm to avoid penetration of every fluid particle, including free-surface particles. Our method for solid is then verified through a large deformed tension plate numerical test, and our coupling forces through a series floating tests and hydrostatic water column over a thin infinite plate. Then, the method is validated comparing it with experimental data of a dam break test in which the water column attacks a thin rubber plate.