A Generic Numerical Solver for Modeling the Influence of Stress Conditions on Guided Wave Propagation for SHM Applications

In leading-edge industrial applications, assessing structure integrity is an important aspect of safety requirements. Structural Health Monitoring (SHM) proposes to use sensors and signal processing units in situ. One of the most attractive SHM techniques relies on ultrasonic guided waves. Modeling and simulation can be helpful tools for the design or the reliability assessment of SHM solutions. Currently available models developed for that purpose do not take into account effects of operational conditions such as internal stresses. These conditions can change wave propagation and therefore affect the interpretation of recorded signals. The objective of this work is to propose a model that fills this gap, and to derive corresponding numerical methods for elastic wave propagation in an arbitrarily deformed medium. Any hyperelastic constitutive law can be considered. As the structures considered are usually thin, we avoid shear-locking by using a shell formulation to solve the quasi-static problem representing the effects of structure loading. The computed displacement is then fed into a spectral elements method (SFEM) kernel to solve the time-domain linearized 3D elastodynamics problem representing the wave propagation. We validate our model against experimental data in the literature for an isotropic aluminium plate under tensile forces. Additionally, we apply these numerical procedures to a realistic bending experiment of a steel pipe. These validations steps show that our generic approach is able to capture the effects of stresses on ultrasonic guided wave propagation such as changes in wave velocity and induced anisotropy.