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Time Reversal Nonlinear Elastic Wave Spectroscopy

  LISA-Spring Mass Numerical Simulations


 

Time Reversal Acoustics (TRA) imaging techniques for the localization and characterization of defects (behaving like nonlinear scatterers) in solid media can be enhanced by using nonlinear elasticity methods. By combining Nonlinear Elastic Wave Spectroscopy (NEWS) methods with TRA, it is possible to implement an imaging method for the selective localization of those scatterers embedded within solid samples that add frequency-spectrum content to the probing elastic waves propagating throughout the sample itself by which they are excited. Those types of scatterers correspond to localized macro-fractures or distributed micro-cracks or dislocations in crystalline materials, as opposed to inclusions and interfaces behaving like linear scatterers.

The following movies show the results of 2-D numerical simulations of a TRA experiment in a solid specimen containing both a linear scatterer (an inclusion) and a nonlinear one. It is shown that it is necessary to apply specific signal processing methods in order to selectively retro-focus the elastic energy of the forward propagation signals only on the nonlinear scatterer location. These are the first-ever peer-reviewed published numerical simulation results about the implementation of this technique, TR NEWS.

(See A.S. Gliozzi, M. Griffa, M. Scalerandi, Efficiency of time-reversed acoustics in nonlinear damage detection in solids, J. Acous. Soc. Amer. 120 (5), 2506-2517, 2006 for complete data.)

The simulations have been realized with the Local Interaction Simulation Approach (LISA)-Spring Mass model for elastic wave propagation in composite and heterogeneous solids with nonclassical nonlinear elastic behavior. The work has been performed at the Department of Physics, Polytechnic Institute of Torino.

The first experimental results of the success of TR NEWS in detecting only nonlinear scatterers embedded in a solid highly-heterogeneous specimen were published by Ulrich, et al. (PDF File - 468 KB)

Above - Schematic representation of the 2D aluminum specimen used for the 2D LISA TR NEWS simulations with three extended and thin forward propagation sources on the left, a very-thin and long nonclassical nonlinear scatterer in the center, and a square linear scatterer on the top right.


 

Forward Propagation Simulation

Simulation of the forward propagation, during which the probing waves travel throughout the specimen, excite the linear and nonlinear scatterers and are collected by the TRM.

The specimen is a 12 x 6 cm aluminum sample containing a very thin and long (0.1 mm x 10 mm) nonlinear scatterer and a square-shaped (5 mm x 5 mm) linear inclusion. With N varying from 124 to 22 in different simulations, TR transducers are arranged along a square path close to the specimen boundaries and completely surrounding the two scatterers. They constitute the Time Reversal Mirror (TRM). Three extended sources are embedded within the specimen outside the TRM. The movie shows the temporal evolution of the norm of the displacement vector wave field (expressed in nm) during the forward propagation. Very little interaction occurs among the probing waves and the two scatterers.

Schematic representation of the simulated Al specimen with a long and very thin nonlinear scatterer and a square-shaped linear one. The three lines along the x = 2 cm vertical line indicate the three sources of the forward propagation. The two scatterers are surrounded by a rectangular Time Reversal Mirror (each dot indicates a single point-like Time Reversal transducer). The numbers indicate specific elements of the TRM where the signals are collected and showed in the previously cited paper by Gliozzi et al.

Click image above to view movie.

 

Pure Simulated TR Backpropagation

Simulation of the TR backpropagation within a sample identical to the one of the forward propagation except for the presence of the scatterers. The forward propagation signals are time reversed within a certain temporal window, amplified and rebroadcasted back within the specimen. They retro-focus on the locations of the three original sources. The movie shows the temporal evolution of the norm of the displacement vector wave field (expressed in nm) due to the rebroadcasting by the TRM.

Click image above to view movie.

 

Subtraction of the Boundary Reflections + TR Backpropagation

Same type of simulation and movie of the previous case but with an additional signal processing on the TR input signal: a forward propagation simulation in the same specimen without every scatterer has been done, the recorded signals have been subtracted from the ones of the forward propagation with scatterers, in order to remove from them the effects of the reflections from the boundaries. The movie shows that the backpropagated waves do focus on both scatterers locations, with higher constructive interference amplitudes at the linear scatterer position. This is an evidence of the fact that rebroadcasting the full frequency-domain content of the forward propagation signals cannot lead to the selective localization of only the nonlinear scatterers.

Click image above to view movie.

 

TR NEWS Processing

Same type of simulation and movie of the previous case, but applying a frequency-domain band pass filter to the forward propagation signals before their time reversal , in order to select only the contributions of the nonlinear scatterers to the forward propagation waves. The movie shows that this time the backpropagated waves focus only on the nonlinear scatterer (the defect) location.

Click image above to view movie.

 

For more information, please contact Michele Griffa, Marco Scalerandi, or Antonio Gliozzi

 

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