Analytical extension of Finite Element solution for computing the nonlinear far field of ultrasonic waves scattered by a closed crack

Nonlinear Coda Wave Interferometry: Sensitivity to wave-induced material property changes analyzed via numerical simulations in 2D

“…The cracking performed in the experimental study [21] is in fact not a controlled process, and the resulting cracks do display a high degree of randomness (shape, size, orientation, etc.). Moreover, it can be expected that for a crack with wavy surfaces [30], the clapping and stickslip processes generated by pump waves are involved in the nonlinear mixing of coda waves [31,32]. Depending on the pump wave amplitude, some parts of the cracks can stay open, and the presence of cracks generates both linear scattering and nonlinear mixing of coda waves.…”

Characterization of Microcrack Orientation Using the Directivity of Secondary Sound Source Induced by an Incident Ultrasonic Transverse Wave

“…Wang et al explored the interaction between the probing guided ultrasonic waves and a nonlinear scatterer (e.g., ‘breathing’ fatigue crack) from analytical, simulation, and experimental perspectives, and ascertained the principal orientation of a fatigue crack [ 28 ]. Blanloeuil et al provided the near-field solution for the interaction between an in-plane elastic wave and a closed crack with different orientations using a finite element (FE) approach, yielding the directivity patterns for all linear and nonlinear components of the scattered waves [ 32 ]. Zhang et al developed a FE model to compute the scattering coefficient matrix for arbitrarily shaped defects, where the orientation of a defect was deduced from the location of the maximum scattering coefficient if it lay within the range of probing angles [ 33 ].…”

“…Obviously, knowledge of the microcrack orientation-related wave scattering phenomena can be beneficial to quantitative evaluation of microcrack severity, which is a crucial but unsolved problem in practical engineering applications. As an effective candidate, second-harmonic generation based approach can be used to realize the identification of the microcrack in an early stage, and to further assess the microcrack orientation in a quantitative manner, which has been one of the most common objectives of the NDE communities [ 28 , 32 , 34 ]. Recently, a primary attempt has been made by studying the nonlinear interaction between an incident ultrasonic longitudinal wave (ULW) and a microcrack based on the model of CAN [ 35 ].…”

Simulation of crack induced nonlinear elasticity using the combined finite-discrete element method

“…In particular, Kawashima et al [24] used a FEM model to study CAN in which Rayleigh waves were employed to detect surface cracks; Blanloeuil et al [12,25] studied the nonlinear scattering of ultrasonic waves by closed cracks subjected to CAN; to investigate the clapping and friction induced nonlinearity in solids containing cracks, Van Den Abeele and colleagues [2,3,11,26] implemented a series of comprehensive normal and tangential constitutive models into FEM to control the nonlinear behavior of crack surfaces. Among the many numerical simulations, some of them use hypothetical defects in which artificial nonlinear stress-strain relations are introduced into special elements to represent defects [24]; others employ physical defects by splitting the computational nodes along defects, and then the normal and tangential contact stresses, which are calculated based on the relative distances between the corresponding Gauss points located on the defects surfaces, are applied to the same Gauss point pairs as boundary conditions for the bulk material simulation [2][3][4][5]11,12,22,23,[25][26][27][28][29]. The former only captures the defect behavior in an approximate manner; the latter may be difficult to explicitly realize complicated scenarios such as defects with irregular shapes and especially, the interactions between many defects of different types.…”