Modeling and simulation of Ultrasonic Guided Waves propagation in the fluid-structure domain by a monolithic approach

Abstract

The present study introduces the coupled multiphysics model as part of the structural health monitoring (SHM) system. In particular, the Ultrasonic Guided Waves (UGWs) propagation is tracked in order to identify the damage to the structure. For this purpose, a multiphysics mathematical model is proposed. The model constitutes a monolithically coupled system of acoustic and elastic wave equations (WpFSI problem) where the wave signal displacement measurements are analyzed as the UGWs propagates in the solid, fluid and their interface. The ultimate goal of this paper is to explore and develop the efficient numerical solution of the WpFSI problem using the finite element method. A detailed description of the modeling framework and conditions that facilitate the coupling is provided. To couple the displacement-based acoustic wave equations for the isothermal fluid with elastic wave equations for the Saint Venant-Kirchhoff material model, the present study uses a monolithic solution algorithm. In particular, at each time step, wave equations are transformed to a fixed reference configuration via the arbitrary Lagrangian-Eulerian (ALE) mapping and automatically adopt the boundary conditions from the previous time step. The implementation is accomplished via the finite element library deal.II (Goll et al., 2017) based software toolbox DOpElib (Bangerth et al., 2007) which provides modularized higher level algorithms. Beyond SHM systems, the model is relevant for problems from biomechanics and biomedicine, vibromechanics, poroelasticity as well as subsurface and porous media flow. The model developed here serves as a first step towards the on-line SHM system modeling, where structural dynamics are accounted for.