The inverse finite element method (iFEM) is a model-based technique to compute the displacement (and then the strain) field of a structure from strain measurements and a geometrical discretization of the same. Different literature works exploit the error between the numerically reconstructed strains and the experimental measurements to perform damage identification in a structural health monitoring framework. However, only damage detection and localization are performed, without attempting a proper damage size estimation. The latter could be based on machine learning techniques; however, an a priori definition of the damage conditions would be required. To overcome these limitations, the present work proposes a new approach in which the damage is systematically introduced in the iFEM model to minimize its discrepancy with respect to the physical structure. This is performed with a maximum likelihood estimation framework, where the most accurate damage scenario is selected among a series of different models. The proposed approach was experimentally verified on an aluminum plate subjected to fatigue crack propagation, which enables the creation of a digital twin of the structure itself. The strain field fed to the iFEM routine was experimentally measured with an optical backscatter reflectometry fiber and the methodology was validated with independent observations of lasers and the digital image correlation.

The inverse Finite Element Method (iFEM) has recently gained much popularity within the Structural Health Monitoring (SHM) field since, given sparse strain measurements, it reconstructs the displacement field of any beam or shell structure independently of the external loading conditions and of the material properties. However, in principle, the iFEM requires a triaxial strain measurement for each inverse finite element, which is seldom feasible in practical applications due to both costs and cabling-related limitations. To alleviate this problem several techniques to pre-extrapolate the measured strains have been developed, so that interpolated or extrapolated strain values are inputted to elements without physical sensors: the benefit is that the required number of sensors can be reduced. Nevertheless, whenever the monitored components comprise regions of different thicknesses, each region of constant thickness must be extrapolated separately, due to thickness-induced discontinuities in the strain field. This is the case in many practical applications, especially those concerning fiber-reinforced composite laminates. This paper proposes to extrapolate the measured strain field in a thickness-normalized space, where the thickness-induced trends are removed; this novel method can significantly decrease the number of required sensors, effectively reducing the costs of iFEM-based SHM systems. The method is validated in a simple but informative numerical case study, highlighting the potentialities and benefits of the proposed approach for more complex application scenarios.

In the past two decades, the aerospace industry has massively shifted from aluminum-made components to composite materials such as carbon fiber reinforced polymers (CFRP), striving for more fuel efficient and lighter aircrafts. Consequently, traditional joints have been replaced by adhesive bonded interfaces, which are also the most common choice to repair damaged components. Although adhesive bonding is the most efficient choice for permanent connections, it is not free of disadvantages: one of the most common failure modes, the debonding of the two laps, is very problematic to detect and predict in practice. Therefore, frequent inspections must be performed to ensure structural safety, increasing maintenance costs, and lessening the availability of the platforms. The development of innovative sensing technologies has allowed for a close monitoring of structural interfaces, and several structural health monitoring techniques have been proposed to monitor adhesive bonded connections. Sensitivity and correlation between measurements and debonding entity has been demonstrated in the literature: nevertheless, hardly any technique has been proposed and quantitively evaluated to estimate the debonding entity independently of the applied loads, such as misalignment-induced torsion, which is a major confounding influence in the traditional backface strain gauge technique. This paper proposes the inverse finite element method (iFEM) as a load and material independent approach to infer the debonding entity from strain measurements in adhesive-bonded joints. Two approaches to estimate the debonding entity with the iFEM are compared on cracked leap shear specimens representative of CFRP repair patches: one is based on anomaly indexes, the other on performing a model selection with multiple iFEM models including different damages. The latter demonstrates satisfactory performances; thus, it is considered a significant scientific advancement in this field.