Numerical study of nonlinear interaction between a crack and elastic waves under an oblique incidence

2D finite element modeling of the non-collinear mixing method for detection and characterization of closed cracks

“…The y axis velocity recorded on the upper face is shown in Fig. 8, for a pre-stress This result is similar to that obtained for the amplitude of second harmonic generated by clapping in the case of a contacting interface between two solids for example [43,44]. In this case where two shear waves interact with an oblique incidence on a contacting interface, clapping is activated, as shown in Fig.…”

“…11 respectively to sticking contact, slipping contact and separation. Both sliding and clapping are activated and it has been shown that clapping is the strongest nonlinear effect [44]. The evolution of the longitudinal wave amplitude is driven by the clapping effect.…”

“…As showed in [44], the clapping effect generated by a plane shear wave is optimal for angle of incidence of 45…”

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

“…Therefore, it is assumed that a static normal stress σ 0 ≤ 0 closes the crack. This pre-stress σ 0 is directly considered in the contact laws, as introduced in [22], and reviewed here briefly.…”

“…The contact parameters are σ 0 = −0.25 MPa and µ = 0.3. In this case, the incident normal stress is too low to activate the clapping and only sliding is activated at the interface whatever the angle of incidence [22]. The directions of propagation corresponding to the transmission through a perfect interface and the reflection at a free surface are marked by the arrows.…”