Conference Agenda

Simulation plays an increasing role in industrial applications as it allows to reduce times and costs associated to several tasks, among which design and certification. It is the case in particular for guided wave SHM, for which many parameters may affect the system performances and may be costly to explore. Typical examples are: uncertainties on material parameters and sensors, varying defect positions and geometries, environmental and operational conditions like temperature, static load or sensor aging. Simulation solutions hence need to be fast enough to enable large simulation campaigns, representative of all expected conditions, while showing a good accuracy with respect to the modeled effects. The SHM module of CIVA has been designed for this purpose. It uses a transient high-order spectral element method coupled with a parametric description of the geometry and its features, such as sensors, stiffeners and defects. Relying on the so-called mass lumping method while performing unassembled stiffness operations in parallel, fast computations with low memory consumptions are obtained.

Two new features have been added to increase the accuracy of simulation and its computational performances, namely damping models and absorbing boundary layers. Damping models play an important role in accurately predicting the propagated field, in particular for composite materials in guided wave SHM applications. However, they come at an increasing cost. We will show in this presentation three available models, namely Maxwell, Zener and Kelvin-Voigt [1], which may be used based on a trade-off between needed accuracy, knowledge of the damping laws, and computational cost. Validation results will also be presented. In parallel, absorbing boundary layers enable to restrict the size of the simulated domain, thus limiting the computational cost. Indeed, these layers damp waves going outward with a small reflection at the interface between the physical domain and the absorbing one. They hence enable to perform the computations in a limited physical domain without introducing boundary reflections. The length of these layers is chosen automatically based on the wavelengths of the propagating modes. These layers, their associated cost as well as comparisons between simulations with and without them, will be presented.

[1] Imperiale, A., Leymarie, N., & Demaldent, E. (2020). Numerical modeling of wave propagation in anisotropic viscoelastic laminated materials in transient regime: Application to modeling ultrasonic testing of composite structures. International Journal for Numerical Methods in Engineering, 121(15), 3300-3338.

Optical fiber sensors can be considered as cutting-edge sensors in many SHM applications since they can be seamlessly embedded within complex structures to provide tens (quasi-distributed) to thousands (distributed) measurements over a single optical fiber, while being able to withstand harsh environments (from a few K up to 1800 K). In particular, Fiber Bragg Gratings (FBG) are promising transducers for ultrasound measurements, but the efficient simulation of their behaviour for such purpose requires to address specific challenges since optical fiber diameters and FBG pitches are small compared to ultrasonic wavelengths, leading in general to small size mesh elements, therefore to heavy computational burdens without any dedicated optimized model.

In this work, we propose a one-way coupling scheme leading to a negligible computational burden overhead linked to the simulation of the FBG spectral response. It assumes a perfect transduction between the host structure and the optical fiber, and a negligible impact of the fiber on the ultrasonic wave propagation within the monitored structure. Ultrasound propagation within the host structure is simulated using transient high-order spectral finite elements, available in the SHM module of CIVA [1], enabling low memory and efficient computations. From this computation, strain at the sensor location is extracted. This strain field is then used to compute the FBG spectral response using a transfer matrix approach [2]. Furthermore, to mimic edge filtering, this response is computed only for one optical wavelength, corresponding to the interrogation laser wavelength. By doing so, no explicit meshing of the FBG is introduced, and the computations corresponding to the transfer matrix approach have only a limited impact on the total computational cost.

Computational performances of the scheme are investigated, and validations regarding specificities of the FBG response, such as its varying sensitivity with respect to the angle between incident wave polarization and fiber orientation, as well as the FBG length compared to the ultrasonic wavelength, will be presented. This model will be added in future versions of the SHM module of CIVA with automatic parametrization to enable reliable parametric studies including FBGs.

[1] MESNIL, Olivier, RECOQUILLAY, Arnaud, DRUET, Tom, et al. Experimental validation of transient spectral finite element simulation tools dedicated to guided wave-based structural health monitoring. Journal of Nondestructive Evaluation, Diagnostics and Prognostics of Engineering Systems, 2021, vol. 4, no 4, p. 041003.

[2] YAMADA, Makoto et SAKUDA, Kyohei. Analysis of almost-periodic distributed feedback slab waveguides via a fundamental matrix approach. Applied optics, 1987, vol. 26, no 16, p. 3474-3478.

Multi-wire cables are high performance structural elements popular in civil engineering applications like bridge systems, offshore structures and the power grid to name a few. Among the non-destructive structural health monitoring techniques available, ultrasonic guided waves afford several advantages in defect detection, as they span large distances and allow inspection in inaccessible areas. On the negative side, the complex helical morphology gives rise to non-trivial tension- and contact-dependent effects, which, combined with the multi-modal and dispersive nature of propagating waves, complicate measurement readings. This necessitates accurate modeling techniques to improve understanding of the underlying physics and facilitate result acquisition.
Finite Element (FE) methods dominate elastic wave propagation modeling in multi-layer strands. The Semi Analytical FE (SAFE) method, which merges cross-section discretization with analytical axial propagation description, has successfully reproduced experimentally observed aspects in the 7-wire strand (1 straight core + 6 twisting peripheral wires). More recently, the Wave FE method was applied on a bi-layer cable, utilizing a bi-helical coordinate system and periodic boundary conditions on a 3D unit cell. In both cases, increased numerical cost, necessary for addressing contact effects, makes a simplified method desirable. Along these lines, a simplified closed-form alternative has been proposed for the 7-wire strand, initially 2D, comprised of masses interconnected via Hertzian springs.
Expanding on that work, the current objective is a simplified method able to accurately describe elastic wave propagation in a) the 7-wire strand and b) a bi-layer strand, analytically accounting for contact effects, at reduced computational cost. First, longitudinal propagation in the 7-wire strand is accounted for by introducing Timoshenko kinematics enriched by Poisson effects. Dispersion relations are successfully acquired (Fig.1), very close to a FE reference solution within a satisfying low-frequency range, with an additional 3 orders of magnitude reduction in computational cost. Additional force and energy analysis enables organizing modes into zones characterized by their dependence on contact effects, improving intuition on the underlying physics.
The addition of a second wire layer (12 wires, twisting in the opposite direction around the 7-wire strand) follows. However, the single-layer method is not readily generalizable to multi-layer cables due to intrinsic modeling restrictions, thus combination with traditional FE is sought. Floquet-Bloch periodic conditions are used on a unit cell, comprised of straight and twisting 1D beam elements, while contact effects are accounted for via appropriate element coupling. Concluding, the method shows potential as a low-cost, elastic wave propagation modeling methodology for multi-wire cables, consistent with complex real-life application requirements.

Cables composed of seven-wire strands, widely used in infrastructures such as cable-stayed bridges and prestressed concrete bridges, undergo degradation over time due to mechanical stresses, corrosion, and environmental conditions. This degradation may compromise the performance and safety of the structures. To help with the monitoring of cables, the GeoEND laboratory develops numerical methods for the simulation of guided wave propagation.
In this framework, a simplified numerical model of tensioned seven-wire strands is proposed, in order to facilitate the development of a hybrid method for scattering by defects. This is done by preserving the width of interwire contact areas under tension while neglecting parameters with less influence on wave propagation.
The proposed hybrid method is based on applying modal expansions at the cross-section boundaries of the finite element model in order to impose transparent boundary conditions that ensure non-reflecting wave propagation.This method is validated through a numerical test conducted on a seven-wire strand without defects, by checking the absence of reflections.
After validating the method, we studied the interaction of three incident modes: the longitudinal modes L(0,1) and L’(0,1), as well as the torsional mode T(0,1), with defects. In a strand under tension, the particular L’(0,1) longitudinal mode is confined into the core wire of the strand due to the contact forces exerted on it by the adjacent wires. These modes are analyzed with three types of defects: a free-end extremity, a broken central wire, and a broken peripheral wire. The results show that when these modes interact with defects, they not only reflect on themselves but can also significantly convert into other modes due to coupling between wires. We observed, for instance, a strong reflection of the longitudinal mode L(0,1) during its interaction with a broken central wire of the seven-wire strand. This reflection is accompanied by a significant conversion of the longitudinal mode L(0,1) into the longitudinal mode L’(0,1) above its cutoff frequency.
The power balance, serving as a validation criterion for the model, is verified with satisfactory accuracy.

This paper presents a comprehensive investigation of zero-group-velocity (ZGV) Lamb mode excitation in thin aluminum plates driven by piezoelectric wafers, employing the normal mode expansion (NME) framework. By expressing an arbitrary surface loading as the superposition of symmetric and anti-symmetric components, the model simultaneously captures the generation of S- and A-type modes under general actuation conditions. A shear-lag representation of the adhesive layer is introduced to quantify strain transfer within the loading zone and determine modal amplitudes beyond the loading region. The study focuses on the first symmetric and anti-symmetric ZGV modes, using analytical derivations supported by numerical simulations to elucidate their resonance behavior and propagation characteristics. Particular emphasis is placed on the geometric influence of the piezoelectric patch, demonstrating that its length governs the energy coupling efficiency and the prominence of each ZGV response. Spatial and spectral analyses based on two-dimensional fast Fourier transform (2D-FFT) further verify the resonant frequencies predicted by theory and highlight the localized vibration features typical of ZGV phenomena. The proposed analytical formulation and results advance the understanding of ZGV Lamb mode excitation mechanisms and provide a rigorous foundation for optimizing piezoelectric actuation in high-resolution ultrasonic inspection and structural health monitoring systems.