Fiber-reinforced Composite Layer Research Articles

Low-Velocity Impact of Clamped Rectangular Sandwich Tubes with Fiber Metal Laminated Tubes.

Fiber metal laminated sandwich tubes are made up of alternating fiber-reinforced composite and metal layers. Fiber metal laminated tubes have the advantages of the high strength and high stiffness of fiber and the toughness of metal, so they have become an excellent load-bearing and energy-absorbing, lightweight structure. Due to the complexity of the fiber layup, it is difficult to establish an analytical model of the relevant structural properties. In this work, introducing the number and volume fraction of fiber layup, based on the modified rigid-plastic model, an analytical model is established for low-velocity impacts on sandwich tubes with fiber metal laminated tubes, which provided a theoretical basis for the design of fiber-metal composite tubes. In addition, a numerical simulation was conducted for low-velocity impacts on clamped rectangular sandwich tubes with fiber metal laminated (FML) tubes and a foam core. By comparing the results obtained from the theoretical analysis and numerical calculations, it is shown that the analytical results can reasonably agree with the numerical results. The influences of the metal volume fraction (MVF), the strength ratio factor of the FML metal layer to the FML composite layer, and the relative strength of the foam on the dynamic response of the rectangular sandwich tubes with FML tubes and a metal foam core (MFC) are discussed. It is shown that by increasing the fiber content and fiber strength of the FML tubes and the foam strength, the load-carrying and energy-absorbing capacity of the rectangular sandwich tubes can be effectively improved, especially by changing the fiber properties. In addition, present analytical solutions can be applied to make predictions about the dynamic response of the rectangular sandwich tubes with FML tubes and MFC during impacts with low-velocity and reasonably heavy-mass.

The Effect of Load Steps and Initial Crack Length on Stress Distribution of Fiber Metal Laminates

Fiber Metal Laminates (FMLs) are advanced composite materials composed of alternating layers of fiber-reinforced composites and metal sheets, offering a unique blend of high strength, stiffness, and fatigue resistance. Understanding the behavior of FMLs under different loading conditions, particularly in the presence of initial cracks, is crucial for predicting their structural integrity and performance. This study investigates the effect of initial crack length and load steps on the stress distribution within FML structures through numerical simulation. A glass fiber-reinforced epoxy (GFRE) composite is constituted by glass fibers in off-axis directions of 0o/90o. The crack length of 3 mm, 6 mm, 9 mm, and 12 mm is initially defined on the side of fiber metal laminates. The tensile load was gradually applied to the laminates for five different ratios. The ratios are defined by dividing the tensile load with the area of the laminates which is then called stress ratio. The results show that the greater the initial crack length and load step ratio, the greater the stress around the crack tip. The stress distribution in each layer of the laminates shows different characteristics between tensile and compressive. This will affect the crack propagation behavior of the laminates. Moreover, the findings also provide valuable insights for optimizing FML design, improving damage tolerance, and extending service life in diverse engineering applications.

Impact of surface/interface elasticity on the propagation of torsional vibration in piezoelectric fiber-reinforced composite and anisotropic medium

This work has explored surface/interface theory-based torsional wave propagation in a piezoelectric fiber-reinforced composite (PFRC) layer on top of a functionally graded elastic substrate. PFRC is assumed to be composed of piezoelectric fiber and epoxy matrix. Micro-mechanical investigations have been performed to determine the coefficients of PFRC using strength of materials (SM) and rule of mixtures (RM) techniques. The dispersion relation for the torsional wave under nonclassical boundary conditions is determined using surface/interface theory. The effects of surface/interface, fiber volume fractions, and heterogeneities on the phase velocity and the mode shapes of the wave have been demonstrated graphically.

An investigation of torsional surface wave in a piezoelectric fiber-reinforced composite layer imperfectly bonded to a functionally graded half-space

This article presents a comprehensive study of torsional surface wave propagation in a piezoelectric fiber-reinforced composite (PFRC) layer bonded to functionally graded (FG) half-space considering electrically short and open boundary conditions. The Strength of Materials (SM) and Rule of Mixtures (ROM) approaches have been adopted to determine the effective properties of the PFRC. The non-ideal mechanical and electrical interfacial boundary has been considered for the problem which appears in various realistic scenarios. For the torsional surface wave propagation through PFRC bonded to FG half-space, the dispersion equation has been derived analytically using Whittaker function. The obtained results are validated and matched with existing results by considering special cases. The variation of phase velocity due to the influence of fiber volume fraction, interfacial imperfection parameters and functionally grading parameters have been analyzed and illustrated by means of graphs. Furthermore, the distribution of the field variables, stress and electric displacements across the composite are presented through surface plots. The model holds potential applications in designing and manufacturing transducers, actuators and sensors. The use of PFRC can be found in a wide range of cutting-edge technology, including vibration-canceling gadgets, energy harvesters, and pressure sensors.

Behavioral response of reinforced concrete beams with ultra-ductile fiber-reinforced cementitious composite layers – Experiments, models and reinforcement limits

Ultra-ductile fiber-reinforced cementitious composite-reinforced concrete beams (RC-UDFRC) lack well-established bar-reinforcement limits and accurate behavioral modeling. Based on the experimental results obtained in this study, analytical formulae have been presented for calculating bar reinforcement limits for RC-UDFRC beams. A comprehensive numerical method has also been proposed that combines the use of equilibrium conditions, constitutive material models, and finite layers for predicting the entire flexural behavior of RC-UDFRC beams. Results of the study showed that introducing UDFRC into RC beam construction significantly impacted the minimum bar reinforcement requirements. Further, the simplified analytical approach for the ultimate moment capacity of RC-UDFRC beams exhibited reasonable predictability. The proposed model produced relatively accurate curvatures at cracking and ultimate loading with mean error values of 15 and 7%, respectively. Additionally, the proposed numerical method had rational cracking, yielding, and ultimate loading calculations with the mean of the tested-predicted values of 1.08, 1.11, and 0.98, respectively.

Vibration isolation of a self-powered piezoelectric pipe conveying fluid composed of laminated fiber-reinforced composites

Based upon the wave manipulating characteristics of phononic crystals (PCs), this paper aims to isolate flexural vibration of laminated composite pipes conveying fluid by introducing a self-powered periodic piezoelectric design. The pipe is composed of three layers of fiber-reinforced composites along the thickness, and is periodically attached with a number of shunted piezoelectric sensor/actuator pairs along the axis. A negative proportional feedback strategy is adopted to amplify the sensing voltage to the actuators, which can generate periodic active stiffness to the pipe and thus enable tunable wave propagation and frequency band gap (BG). The dynamical equation of motion for a single piezoelectric laminated pipe conveying fluid is deduced from classical laminated beam theory as well as one-dimensional piezoelectric constitution. The BG distribution and amplitude transmission of topological structure are obtained by the spectral element method (SEM). Numerical results demonstrate that the present self-powered piezoelectric PC design can achieve excellent vibration isolation effect for the laminated composite pipe conveying fluid. Major parameter regulations including cross-ply angle, lamina sequence, feedback control gain, geometry of piezoelectric layers and fluid effect are examined. Free vibration and stability of the system are also discussed to perfect the vibration isolation design.

Behavioral Evaluation of Strengthened Reinforced Concrete Beams with Ultra-Ductile Fiber-Reinforced Cementitious Composite Layers

In the literature, there is little information available regarding the behavior of composite beams made up of reinforced concrete (RC) and ultra-ductile fiber-reinforced concrete (UDFRC). In this study, UDFRC was examined for its effectiveness in enhancing the strength of RC beams. With a tensile strength of 4.35 MPa and a strain capacity of 2.5%, PVA-based UDFRC was prepared. The performance of 12 medium-sized reinforced concrete (RC) beams was measured under four-point flexural loading. The beams measured 1800 mm long, 150 mm wide, and 200–260 mm deep. The experimental program on beam specimens was divided into two phases. In the first, four 150 × 200 × 1800 mm RC beams with UDFRC layer thicknesses of 0, 30, 60, and 90 mm were tested. Additionally, four concrete and four concrete–UDFRC beams were investigated, measuring 150 × 230 × 1800 mm and 150 × 260 × 1800 mm, respectively. The study focused on medium-sized, slender RC beams under quasi-static loads and room temperature with additional or substituted UDFRC layers. As a result of replacing concrete with UDFRC, the load-carrying capacity at first crack and steel yield significantly increased between 18.4 and 43.1%, but the ultimate load-carrying capacity increased only in the range of 6.3–10.8%. Furthermore, beams with additional UDFRC layers could carry 30–50% more load than their concrete counterparts. An RC-UDFRC beam had a load-carrying capacity 10–15% greater than that of a comparable RC beam. Generally, there is a lower deflection response in UDFRC–concrete composite RC beams than in control concrete beams. The UDFRC layering can potentially improve the load-carrying capacity of RC beams, at least when ductility provisions are considered.

Reliability analysis of smart laminated composite plates under static loads using artificial neural networks

The applications of smart structures with integrated piezoelectric elements have been expanding in the last few decades due to the abilities of such structures to withstand mechanical loads and operate as sensors or actuators using their electromechanical coupling. The available manufacturing techniques can result in uncertainties in the structure's geometric parameters, which, coupled with uncertainties in material properties, can lead to unexpected failures or unreliable performance. This paper presents a reliability analysis of a smart laminated composite plate made of a graphite/epoxy cross-ply substrate with a piezoelectric fiber-reinforced composite (PFRC) actuator layer under static electrical and mechanical loads. A coupled finite element (FE) model was developed in COMSOL Multiphysics, from which nondimensional stresses and displacements were calculated. To investigate the effects of randomness in the material and geometric properties, an artificial neural network (ANN) model was developed and trained using generated FE data. Monte Carlo Simulation (MCS) and First- and Second-Order Reliability Methods (FORM/SORM) were then used to shed light on the significance of considering randomness in the various material and geometric parameters and the effect of such uncertainty on the resulting nondimensional stresses and displacements. A coefficient of variation (CV) study identified the piezoelectric stress coefficient as the most significant contributing factor to the variation of all nondimensional parameters. Variation in the nondimensional parameters also increases under the application of an electric load. ANN-based FORM, SORM, and MCS all indicate a pattern of low probability of failure until a threshold value of about 3% of input parameter variation is reached, beyond which there is a rapid nonlinear increase in failure probability with increasing input parameter variation.

Transference of SH waves in a piezoelectric fiber-reinforced composite layered structure employing perfectly matched layer and infinite element techniques coupled with finite elements

Most commercially used piezoelectric materials suffer from certain drawbacks like low piezoelectric output, brittle nature, etc. Thus, they cannot be utilized to their fullest extent in dynamic applications involving actuators, transducers, Surface Acoustic Wave (SAW) devices, and Love wave sensors, among others. The present work focuses on the transference attributes of anti-plane SH wave in a layered structure composed of a piezoelectric fiber-reinforced composite (PFRC) layer lying over a piezoelectric half-space. The PFRC composed of PZT-5A-epoxy is micro-mechanically modeled using Strength of Materials and Rule of Mixtures, and some of its electro-mechanical advantages over monolithic PZT-5A are discussed. The dispersion relation is obtained by analytical means, as well as two numerical techniques, viz., Semi-Analytical Finite Element - Perfectly Matched Layer (SAFE-PML) technique and Semi Analytical Infinite Element (SAIFE) technique with (1/r) type decay. The Rayleigh–Ritz method and Gauss 3-point quadrature formula are employed to derive the dispersion relation numerically. The effects of the existing parameters, viz. fiber volume fraction, PML length, PML function, etc., on the dispersion curves are graphically demonstrated and discussed. The present work is validated by matching the obtained results with the ones found in the extant literature.

Flexural behavior of sandwich panels combining curauá fiber-reinforced composite layers and autoclaved aerated concrete core

The mechanical response of sandwich panels with two layers of curauá fiber cement composites and a core layer of autoclaved aerated concrete (AAC) was investigated. Each layer consisted of long unidirectional curauá fibers and a cementitious matrix. For durability purposes, 50% of the Portland cement was replaced with pozzolanic materials to reduce the content of calcium hydroxide in the matrix. The performance of sandwich panels with 350 mm × 60 mm × 90 mm (length × width × thickness) was evaluated through monotonic and cyclic four-point bending tests to obtain the load–deflection response, flexural strength, and toughness. Monotonic bending tests were performed on each component of the panels – i.e., composites and AAC blocks. Pull-off tests were performed to evaluate the adhesion between the skin layers and the core, while optical and scanning electron microscopes were used to observe the interface's topography. The results revealed the externally bonded layers' efficiency, which provided a higher deflection capacity to the material and increased its flexural strength. The AAC blocks revealed a more ductile response when assisted by the composite layers in the sandwich structure. Under cyclic bending test conditions, the sandwich panels exhibited a satisfactory post-peak ductility so that the energy was not abruptly lost but gradually released throughout its deflection-softening behavior.

Effect of porosity on the bending of functionally graded plates integrated with PFRC layer

This paper will present the analysis of static bending of functionally graded porous plates attached to a piezoelectric fiber-reinforced composite layer. The plate is exposed to sinusoidal electrical and mechanical loads. The displacement field is presented by using a sinusoidal shear deformation theory. The virtual work principle will be used for the derivation of the equilibrium equations and Navier’s method for the solution. Displacements and stresses are confirmed by comparing them with corresponding literature. Lastly, numerical results confirm that the porosity factor, applied voltage, volume fraction exponent, Young’s modulus ratio, aspect ratio, and side-to-thickness ratio have a huge influence on the electromechanical bending of functionally graded porous plates.

Failure mechanism of geopolymer composite lightweight sandwich panel under flexural and edgewise compressive loads

This paper proposes a new lightweight sandwich panel manufactured with Fiber-Reinforced Geopolymer Composite (FRGC) skin layers and PUR foam core for prefabricated buildings. The failure mechanisms of the developed sandwich panel are investigated under flexural bending and edgewise compressive loading to validate the performance of the developed panel. Digital Image Correlation (DIC) technique is used to obtain the deformation and strain during the tests. Two typical failure mechanisms, i.e. shear failure of the core and tensile failure of the skin layers of the one-way sandwich panel under flexural loading are studied by conducting quasi-static three-point bending tests. The influence of the core thickness-to-span ratio of the sandwich panel on shear failure of the core is studied. The test results show that the failure mode transforms from the shear failure of the PUR foam core to delamination between the FRGC skin and PUR foam core, when the thickness-to-span ratio increases from 0.1 to 0.3. The influence of skin thickness-to-span ratio on the skin tensile failure is also studied. Analytical models for the shear failure of the core and the tensile failure of the skin layer are proposed. Furthermore, the failure mechanism of the developed sandwich panel with different thickness-to-length ratios under edgewise compressive loading is studied. It is found that the failure mode changes from the material failure of the FRGC skin to the global buckling when the thickness-to-length ratio reduces from 0.90 to 0.30. Analytical models for predicting the critical failure load under edgewise compressive loading are also proposed.

Recent trend in developing advanced fiber metal laminates reinforced with nanoparticles: A review study

Recently, fiber metal laminates (FMLs) have attracted considerable application in many industries due to their outstanding properties. FMLs are hybrid materials that are fabricated by adhesion of thin layers of metals and fiber-reinforced composites. It should be noted that the reinforcing mechanisms of nanoparticles on the polymeric composites have been well-established, but there is limited literature regarding the influence of nanoparticles on the mechanical behavior of FMLs and adhesively bonded joints (ABJs) between metal sheets and polymeric composites. To date, various nanofillers including carbon nanotubes, graphene nanoplatelets, clay nanoparticles and oxide nanoparticles have been used for improving the mechanical properties of FMLs, and ABJs. The performed studies revealed that the efficiency of nanoparticles in improving the properties of FMLs and ABJs mainly dependent on various factors such as surface treatment of metal sheets, type of nanoparticles, the morphology of nanoparticles, the size of samples, fabrication parameters, etc. However, the effects of parameters on the properties of FMLs and ABJs reinforced with nanoparticles have not considerably discussed in the literature. This review paper aims to review the existing related papers regarding the effects of nanoparticles on the mechanical properties of FMLs and ABJs in the term of adhesion between metal sheets and polymers.

Springback Behavior of Fiber Metal Laminates with Carbon Fiber-Reinforced Core in V-Bending Process

Fiber metal laminates (FMLs) are a kind of hybrid composite material that consist of metal sheets and fiber-reinforced composite layers. The use of FMLs has been particularly increasing in the production of aircraft bodies. However, the springback behavior that occurs during the formation of FML parts has a negative impact on the form of the final product. In the present study, FMLs were manufactured by combining aluminum 5754-H22 sheets and carbon fiber-reinforced plastic sheets by using adhesive. A set of experiments were performed to determine the effect of bending angle, face sheet thickness and core thickness on the springback behavior of FMLs. The results showed that the amount of springback in the FML specimen increased as the bending angle increased. It was found that when the thickness of the face sheet increased, the amount of springback in FML specimens was higher in all bending angles. In addition, the amount of springback in FML specimens decreased as core thickness increased.

Uni-axial tensile response and failure of glass fiber reinforced titanium laminates

Abstract Layers of thin metallic sheets and fiber-reinforced composite layers bonded together is known as fiber metal laminates (FMLs). In the current study, titanium Ti–6Al–4V sheets are used with thicknesses 0.2 mm, 0.4 mm and, 0.6 mm along with layers of unidirectional glass-fiber reinforced composite to produce FMLs and the tensile response of these laminates are examined. Four different stacking sequences of FMLs have been considered exhibiting the same thickness for the total metal layer and the hand layup process is used to prepare these laminates. An orthotropic plasticity theory of macro mechanical type and classical laminated plate theory are considered to model the elastic-plastic type of behavior of titanium-based FMLs. A plastic potential function based on three parameters is used to the model the orthotropic plasticity. Behavior with linearly elastic and orthotropic elastic-plastic types is assumed for the layers of glass composite and titanium, respectively in the laminated plate theory. The results show that the initial modulus of FMLs has not been influenced by the sequence of the layup, while this sequence of layup does considerably affect the response of FMLs following ultimate strength. The properties of FMLs such as failure strain and toughness which are important parameters from a design point of view of FMLs can be altered to absorb energy at dissimilar rates, i.e., by insulating the composite layers from each other by metallic layers in case of FMLs 3/2–0.4, 4/3–0.2(O) and 4/3–0.4(O). The model with orthotropic plasticity is found to be precise up to the total strain level of 2.1%, i.e., close to the failure of composite layers within FMLs, when compared with results measured from experiments. The behavior with stress-strain predicted by laminated plate theory also finds realistic up to the total strain of 2.1% to describe the corresponding behavior obtained from experiments.

Modeling large amplitude vibration of pretwisted hybrid composite blades containing CNTRC layers and matrix cracked FRC layers

A modeling of the large amplitude free vibration of pretwisted hybrid composite blades is studied by considering the laminated structure which is composed of carbon nanotube reinforced composite (CNTRC) layers and matrix cracked fiber reinforced composite (FRC) layers. Two assumptions are made to facilitate this vibration study of hybrid nanocomposite: (1) CNTs are distributed across the layer thickness uniformly or functionally graded, and (2) the parallel slit matrix cracks disperse in the matrix homogeneously. Based on the theory of differential geometry, a novel shell model for pretwisted hybrid nanocomposites blade is developed. The von Kármán strains are adopted to capture the geometrically nonlinear behaviors of blades. The established governing equations are solved accurately and efficiently via the IMLS-Ritz method. The proposed numerical model is verified by making comparison studies and then the influence of crack density, pretwisted angle, CNT distribution and volume fraction, aspect ratio, width-to-thickness ratio, and ply-angle on the large amplitude vibration characteristics of matrix cracked pretwisted hybrid composite blade are scrutinized systematically. The present study serves as a useful benchmark to researchers who intend do further research in this topic.

An Experimental Study on Impact Resistance of Different Layup Configuration of Fiber Metal Laminates

Fiber metal laminates (FMLs) are composed of thin metal sheets and fiber-reinforced composite layers. Compared to monolithic aluminum alloys, FMLs combine lower density, higher fatigue resistance, and improved damage tolerance. The present study aimed to investigate the low-velocity impact induced by drop-weight instrument and the tensile strength on various lay-up configurations of FMLs fabricated. FML samples were composed of two layers of aluminum 2024-T3 and two layers of epoxy resin, which were reinforced with carbon fabric, glass fabric, and Kevlar fabric made in pairs. In addition, another type of FMLs was developed with carbon/Kevlar fabric under the same circumstances. Force-time histories of impact forces were recorded, and the damaged specimens were inspected using optical microscopy in terms of the impact side, nonimpact side, and cross-sectional side. Experimental results indicated that the maximum impact force corresponded to the FMLs that were composed of Kevlar fabric on the impact side and glass fabric on the non-impact side. In addition, the highest tensile strength and Young’s modulus among FMLs belonged to FML with Kevlar fabric and glass fabric.

Static and fatigue performance of reinforced concrete beam strengthened with strain-hardening fiber-reinforced cementitious composite

The static and fatigue performance of reinforced concrete beams strengthened by strain-hardening fiber-reinforced cementitious composite is investigated. Two series of strengthened beam specimens are prepared with different thicknesses of the enhancement layer (40 mm and 50 mm), and three fatigue stress levels (0.9, 0.8, and 0.7) are tested. The fatigue life, mid-span deflection, and crack mode of the tested specimens are analyzed. Emphasis is placed on the fatigue response of the strain-hardening fiber-reinforced cementitious composite layer and longitudinal reinforcements. A simplified method is proposed to model the fatigue performance of the composite beam. The mechanism of the fatigue enhancement of the strengthened beam compared to a conventional reinforced concrete beam is as follows: (1) the enhancement layer physically contributes by taking part of the stress in the tension zone, and (2) the enhancement layer can lower the strain localization and stress concentration of the longitudinal reinforcements. Several methods for further improvement in the fatigue performance of reinforced concrete beams are suggested.

Active control of thermal buckling and vibration for a sandwich composite laminated plate with piezoelectric fiber-reinforced composite actuator facesheets

The present paper is concerned with the active control of thermal buckling and vibration of a sandwich composite laminated plate with piezoelectric fiber-reinforced composite actuator facesheets in a thermal environment. An active temperature feedback control strategy is proposed for the thermal buckling of the composite sandwich plate. The results of numerical simulations show that the piezoelectric actuator can significantly improve the thermal buckling characteristics of the composite plates. The influence of the active thermal buckling control gain on the damping ratio and natural frequency of the structure is also investigated. From the numerical results it is observed that the active thermal buckling control with temperature feedback gain can not only enlarge the critical buckling temperature but can also reduce the resonant amplitude of the structure. Furthermore, the optimization problem is studied and it is found that the critical buckling temperature can be optimized by varying the fiber orientation in the piezoelectric fiber-reinforced composite layer. The active thermal buckling control method presented in this paper working in combination with the vibration control strategy can significantly improve the stability of the laminated composite plates. The present study will be useful for designing laminated composite structures used in the thermal environment.

Optimized dynamic design of laminated piezocomposite multi-entry actuators considering fiber orientation

Laminated piezocomposite actuators (LAPA) are structures composed of piezoelectric and non-piezoelectric materials layers. Due to several parameters and the multiphysics domain involved in the design of LAPA, simple forms are commonly found in industrial applications. However, its design can be systematized by using the topology optimization method (TOM) that permits the solution of complex problems. The design of LAPA with TOM has traditionally considered the optimization of piezoelectric materials over an isotropic substrate, yet some previous researches suggest that LAPA including fiber-reinforced composite layers can increase the performance of these transducers. In addition, works dealing with fiber-based composite focus on static or harmonic analysis with sinusoidal excitations, although other signal inputs are used in practice. In fact, the design of fiber-based LAPA in transient regime has not been assessed before. Thus, a methodology is proposed here to design LAPA with TOM. The actuator is electrically excited with a combined waveform: a sine wave treated as a harmonic problem and a step excitation addressed as a transient problem. Both waves have the same frequency, however they are not applied at the same time. This approach allows the development of a multi-entry actuator since it generates the same level of output displacement independently of the type of excitation input. Consequently, the optimization problem is formulated with the purpose of distributing the material in all layers, the polarization sign in piezoelectric layers and the fiber orientation angle in composite layers, in which the objective function simultaneously seeks for the maximization of the vibration amplitude at certain points of the actuator and its response speed. Eight-node shell elements taking into account the piezoelectric effects are used in the finite element method (FEM) and the “layer wise theory is adopted to model the laminated structure. The Generalized-α method is used to solve the transient problem. In order to optimize the material distribution and the polarization sign, the classical SIMP and PEMAP-P models are used respectively, while to optimize the fiber orientation angles in the composite material, a novel self-penalizable interpolation model is proposed. This optimization problem is solved by using the sequential linear programming (SLP) technique with the CVX solver and the sensitivity analysis is performed with the adjoint method. Discrete signal processing concepts are applied to solve the adjoint problem involving specific points of curves obtained by time integration methods in transient analysis. Numerical techniques are implemented to avoid TOM instabilities. Finally, the potential of this approach is demonstrated with two numerical examples.