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1. Monitoring damage growth and topographical changes in plate structures using sideband peak count-index and topological acoustic sensing techniques

   https://doi.org/10.1016/j.ultras.2024.107354  

   Zhang, Guangdong; Deymier, Pierre A; Runge, Keith; Kundu, Tribikram (May 2024, Ultrasonics)

   Some topographies in plate structures can hide cracks and make it difficult to monitor damage growth. This is because topographical features convert homogeneous structures to heterogeneous one and complicate the wave propagation through such structures. At certain points destructive interference between incident, reflected and transmitted elastic waves can make those points insensitive to the damage growth when adopting acoustics based structural health monitoring (SHM) techniques. A newly developed nonlinear ultrasonic (NLU) technique called sideband peak count – index (or SPC-I) has shown its effectiveness and superiority compared to other techniques for nondestructive testing (NDT) and SHM applications and is adopted in this work for monitoring damage growth in plate structures with topographical features. The performance of SPC-I technique in heterogeneous specimens having different topographies is investigated using nonlocal peridynamics based peri-ultrasound modeling. Three types of topographies – “X” topography, “Y” topography and “XY” topography are investigated. It is observed that “X” and “XY” topographies can help to hide the crack growth, thus making cracks undetectable when the SPC-I based monitoring technique is adopted. In addition to the SPC-I technique, we also investigate the effectiveness of an emerging sensing technique based on topological acoustic sensing. This method monitors the changes in the geometric phase; a measure of the changes in the acoustic wave’s spatial behavior. The computed results show that changes in the geometric phase can be exploited to monitor the damage growth in plate structures for all three topographies considered here. The significant changes in geometric phase can be related to the crack growth even when these cracks remain hidden for some topographies during the SPC-I based single point inspection. Sensitivities of both the SPC-I and the topological acoustic sensing techniques are also investigated for sensing the topographical changes in the plate structures. 

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2. A Comparative Study of Geometric Phase Change- and Sideband Peak Count-Based Techniques for Monitoring Damage Growth and Material Nonlinearity

   https://doi.org/10.3390/s24206552  

   Zhang, Guangdong; Kundu, Tribikram; Deymier, Pierre A; Runge, Keith (October 2024, Sensors)

   This work presents numerical modeling-based investigations for detecting and monitoring damage growth and material nonlinearity in plate structures using topological acoustic (TA) and sideband peak count (SPC)-based sensing techniques. The nonlinear ultrasonic SPC-based technique (SPC-index or SPC-I) has shown its effectiveness in monitoring damage growth affecting various engineering materials. However, the new acoustic parameter, “geometric phase change (GPC)” and GPC-index (or GPC-I), derived from the TA sensing technique adopted for monitoring damage growth or material nonlinearity has not been reported yet. The damage growth modeling is carried out by the peri-ultrasound technique to simulate nonlinear interactions between elastic waves and damages (cracks). For damage growth with a purely linear response and for the nonlinearity arising from only the nonlinear stress–strain relationship of the material, the numerical analysis is conducted by the finite element method (FEM) in the Abaqus/CAE 2021 software. In both numerical modeling scenarios, the SPC- and GPC-based techniques are adopted to capture and compare those responses. The computed results show that, from a purely linear scattering response in FEM modeling, the GPC-I can effectively detect the existence of damage but cannot monitor damage growth since the linear scattering differences are small when crack thickness increases. The SPC-I does not show any change when a nonlinear response is not generated. However, the nonlinear response from the damage growth can be efficiently modeled by the nonlocal peri-ultrasound technique. Both the GPC-I and SPC-I techniques can clearly show the damage evolution process if the frequencies are properly chosen. This investigation also shows that the GPC-I indicator has the capability to distinguish nonlinear materials from linear materials while the SPC-I is found to be more effective in distinguishing between different types of nonlinear materials. This work can reveal the mechanism of GPC-I for capturing linear and nonlinear responses, and thus can provide guidance in structural health monitoring (SHM). 

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3. Peridynamics Based Modeling for Investigating the Effect of Topography and Topological Acoustic Sensing Performance in Monitoring Damage Growth

   https://doi.org/10.1115/QNDE2024-137228  

   Zhang, Guangdong; Deymier, Pierre A; Runge, Keith; Kundu, Tribikram (July 2024, American Society of Mechanical Engineers)

   Abstract A newly developed nonlinear ultrasonic (NLU) technique called sideband band peak count-index (or SPC-I) measures the degree of nonlinearity associated with the inspected specimen – larger SPC-I values indicate higher nonlinearity. In various published papers, the SPC-I technique has shown its effectiveness and superiority in comparison to other techniques for nondestructive testing (NDT) and structural health monitoring (SHM) applications. In this work, the performance of SPC-I in non-homogeneous specimens having different topographies is investigated using peridynamics based periultrasound modeling. Three types of topographies – “X” topography, “Y” topography and “XY” topography are introduced by adding thin strips made up of a second material and thus converting the homogeneous plate into a heterogeneous structure. It is observed that “X” and “XY” topographies can help to hide the crack growth, thus making cracks undetectable to the nonlinear SPC-I based monitoring technique. In addition to the SPC-I technique, we investigate the applicability of the emerging method of topological acoustic sensing. This method monitors the changes in the geometric phase; a measure of the changes in linear or nonlinear wave’s spatial behavior during its propagation in plate structures having various topographies. The computed results show that the magnitudes of jumps in geometric phase change plots can be good indicators to distinguish cracks with different thicknesses although these cracks can remain hidden in some topographies during the single point inspection based on the nonlinear SPC-I based monitoring technique. 

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4. Monitoring defects in plates using topological acoustic sensing and sideband peak counting

   https://doi.org/10.1016/j.ultras.2025.107568  

   Ho, I-Ting; Muralidharan, Krishna; Runge, Keith; Hernandez_Granados, Araceli; Kundu, Tribikram; Deymier, Pierre A (May 2025, Ultrasonics)

   We demonstrate an integrated non-destructive inspection methodology that employs the nonlinear ultrasonics-based sideband peak counting (SPC) technique in conjunction with topological acoustics (TA) sensing to comprehensively characterize the acoustic response of steel plates that contain differing levels of damage. By combining the SPC technique and TA, increased sensitivity to defect/damage detection as well as the ability to spatially resolve the presence of defects was successfully established. Towards this end, using a Rockwell hardness indenter, steel plates were subject to one, three and five centrally located indentations respectively. The acoustic response of the plate as a function of number of indentations was examined at a frequency range between 50 kHz and 800 kHz, from which the change in a global geometric phase was valuated. Here, geometric phase is a measure of the topological acoustic field response to the spatial locations of the indentations within the steel plates. The global geometric phase unambiguously showed an increase with increasing number of indentations. In addition, spatial variations in a ‘local’ geometric phase as well as spatial variations in the PC index (SPC-I) were also determined. Spatial variations in both the local geometric phase as well as the SPC-I were particularly significant across the indentations for frequencies below 300 kHz, and by combining the respective spatial variations in the SPC-I and geometric phase, the locations of the indentations were accurately identified. The developed SPC-TA nondestructive method represents a promising technique for detecting and evaluating defects in structural materials. 

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5. Sideband Peak Count – a new nonlinear ultrasonic technique for monitoring damage progression in engineering materials

   https://doi.org/10.58286/29889  

   Kundu, Tribikram; Zhang, Guangdong (June 2024, e-Journal of Nondestructive Testing)

   Linear ultrasonic (LU) techniques used by majority of the researchers working in material damage monitoring, are reliable for detecting relatively large defects. If the defect dimensions are in the range of the ultrasonic wavelength or larger, then those defects can be detected by analyzing the scattered ultrasonic fields. Material damage affects LU parameters such as ultrasonic wave speed and attenuation and their changes are detectable for relatively large defects. However, for small defects (when defect dimensions are significantly smaller than the wavelength of the propagating signal) the changes in the LU parameters are too small to detect or measure reliably. For detecting small defects engineers often use high frequency ultrasonic signals to make the defect dimensions greater than the wavelength. However, high frequency signals attenuate quickly and therefore, only very small regions near the ultrasonic probe can be inspected in this manner. Inspecting large structures by high frequency ultrasonic signals requires moving the probe mechanically from one point to the next and therefore, can be very time consuming. Nonlinear ultrasonic (NLU) technique on the other hand does not need to satisfy this restricting condition that the wavelength of the signal must be smaller than the defect size. NLU works well when the signal wavelength is much larger than the defect size. Therefore, relatively low frequency signals that can propagate a long distance and monitor a large area of a structure can be used for NLU measurements. Different NLU techniques can be used for detection and monitoring of small damages in a specimen. A relatively new NLU technique called the Sideband Peak Count-Index or SPC-I technique has been developed by the author and his collaborators. SPC-I technique for monitoring different types of materials – composites, metals, concrete, and other cement-based materials has been found to be effective. Along with those success stories of SPC-I the effect of topography and the advantage of topological sensing is also discussed in this presentation. 

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