Two-dimensional modeling of wave propagation in materials with hysteretic nonlinearity

Abstract

A multiscale model for the two-dimensional nonlinear wave propagation in a locally microdamaged medium is presented, and numerical simulations are analyzed in view of nondestructive testing applications. The multiscale model uses a statistical distribution of hysterons and upscales their microscopic stress-strain relations to a mesoscopic level. Macroscopic observations are then predicted by finite integration techniques. The influence of a small region with hysteretic nonlinearity on the generation of harmonics is investigated, and numerical results for different amplitudes of the input signal and different analysis techniques of the response signal are presented. Second, a study is conducted on the interaction of a Rayleigh wave with a microdamaged zone with hysteretic nonlinearity at the surface of an otherwise linear body, and the influence of the microdamaged zone on the surface wave velocity and on the generation of harmonics is examined. It is found that the effect of hysteresis on the Rayleigh wave propagation can be barely seen in the surface wave velocity measurement, but shows up nicely in the wave spectrum. The potential of a nonlinearity based depth profiling technique is explored by evaluating the nonlinear responses at different frequencies for a vertically stratified medium with spatially varying hysteresis properties.

Nonlinear wave propagation in damaged hysteretic materials using a frequency domain-based PM space formulation

“…11). These findings are in perfect agreement with the ones reported in Vanaverbeke and Van Den Abeele, 2007 and with the experimental evidences.…”

“…Finite difference schemes like elastodynamic finite integration technique (EFIT) have been used in Van Den Abeele et al (2004) for a resonant bar with localized damage. Recently, Vanaverbeke and Van Den Abeele (2007) proposed a 2D model of wave propagation, generalizing the previous work (Van Den Abeele et al, 2004) by implementing PM space in a step by step procedure where the stress strain relationship is updated each time. To avoid cumbersome reassembling of the matrices, Zumpano and Meo (2007) proposed the evaluation of a ''nonlinear forces" contribution given by the updated stress-strain relationship matrix.…”

Dual energy time reversed elastic wave propagation and nonlinear signal processing for localisation and depth-profiling of near-surface defects: A simulation study

“…A finite difference scheme based on the staggered grid Elastodynamic Finite Integration Technique EFIT [23], finally translates the mesoscopic relations to the macro scale level. We refer the reader to Vanaverbeke and Van Den Abeele [22] for details and basic examples of the multiscale wave propagation model.…”

“…The simulations have been performed using a multiscale wave propagation model [22] that takes into account heterogeneity in the nonlinear equation of state as a representation of intact materials with damage zones. The results that will be shown here all apply to the 2D case, however an extension to 3D is straightforward.…”

“…However, this is beside the goal of this paper. The nonlinearity is introduced by the above mentioned multiscale hysteretic wave propagation model based on the PM formalism [22][23][24][25][26]. The density of the statistical distribution of hysteretic units within a mesoscopic cell is taken to be uniform, and limited to the volumetric stress-strain behavior (i.e.…”