Alain Combescure

Summary: We propose a method to couple smoothed particle hydrodynamics and finite elements methods for nonlinear transient fluid–structure interaction simulations by adopting different time‐steps depending on the fluid or solid sub‐domains. These developments were motivated by the need to simulate highly non‐linear and sudden phenomena requiring the use of explicit time integrators on both sub‐domains (explicit Newmark for the solid and Runge–Kutta 2 for the fluid). However, due to critical time‐step required for the stability of the explicit time integrators in, it becomes important to be able to integrate each sub‐domain with a different time‐step while respecting the features that a previously developed mono time‐step coupling algorithm offered. For this matter, a dual‐Schur decomposition method originally proposed for structural dynamics was considered, allowing to couple time integrators of the Newmark family with different time‐steps with the use of Lagrange multipliers. Copyright © 2016 John Wiley & Sons, Ltd.

Summary: This paper describes a selective mass scaling method which is designed for the analysis of wave propagation problems in nearly incompressible materials. The incompressibility of materials leads to a high value of the compressional wave speed, which makes the time step extremely small in explicit time integration method. The proposed selective mass scaling method selects the eigenfrequencies related to volumetric deformation modes to decrease them, while it keeps the shear eigenmodes unchanged. This makes the time step no longer limited by the compressional wave speed but by the shear wave speed. A significant reduction of CPU time is obtained with a good accuracy for transient problems in small strains on free or largely prestressed media. Copyright © 2016 John Wiley & Sons, Ltd.