Article Article
Qualitative Analysis of a 3D Multiphysics Model for Nonlinear Ultrasonics and Vibration Induced Heating at Closed Defects

Upon exciting a material using elastic waves, the locally induced deformation at the interfaces of internally closed defects may cause nonlinear wave mechanics and dynamics in the form of clapping and friction. As a result, both phenomena instigate spectral broadening of the excitation spectrum as well as the production of heat, directly originating from the defect. To better understand and account for the physics behind the dissipation of energy by internally closed defects as a result of the wave–interface interaction, dedicated models can be developed. In this work, we propose a 3D finite element multiphysics model that is capable of simultaneously describing the generation of nonlinearities and heating at a defect’s interface experiencing clapping and friction induced by elastic wave propagation. The model consists of three different modules. The first module describes the elastic wave propagation in a virgin/bulk material, whereas the second module captures the contact physics at the defect level. The third module is implemented to calculate the diffusion of thermal energy in the specimen. The contact physics module accounts for anharmonic and hysteretic effects, describing the nonlinear behavior of the defect’s interfaces, which is echoed in both the ultrasound spectrum and in the vibration-induced heating. A qualitative analysis of the computational model, integrating the three modules, is performed to validate the approach. Examples show that nonlinear spectral components are indeed observed as a result of the friction and the clapping experienced by the faces of the defect. At the same time, a localized temperature increase due to the induced friction is noted, and its response at the outer surface of the sample is examined. The qualitative validation approves that the model is ready to be tested further quantitively, and to compare its predictions to experiments.



1. S. Delrue and K. Van Den Abeele, Ultrasonics 52, 315–324 (2012). DOI: 10.1016/j.ultras.2011.09.001.

2. P. Blanloeuil, A. Meziane, and C. Bacon, Wave Motion. 51, 425–437 (2014). DOI: 10.1016/j.wavemoti.2013.10.002.

3. R. Plum and T. Ummenhofer, Quant. Infrared Thermogr. J. 8, 201–220 (2011). DOI: 10.3166/qirt.8.201-220.

4. V. V. Aleshin et al., Ultrasonics 82, 11–18 (2018). DOI: 10.1016/j.ultras.2017.07.002.

5. S. Delrue et al., Ultrasonics 82, 19–30 (2018). DOI: 10.1016/j.ultras.2017.07.003.

6. D. Wang et al., Tribol. Int. 159, 106947 (2021). DOI: 10.1016/j.triboint.2021.106947.

7. J. Bonari, M. Paggi, and J. Reinoso, Finite Elem. Anal. Des. 196, 103605 (2021). DOI: 10.1016/j.finel.2021.103605.

8. K. Truyaert et al., Proceedings of the 1st International Conference on Numerical Modelling in Engineering Volume 2: Numerical Modelling in Mechanical and Materials Engineering. Springer, Singapore, 2019, pp. 77–89.

9. K. Truyaert et al., Int. J. Solids Struct. 158, 268–276 (2019). DOI: 10.1016/j.ijsolstr.2018.09.014.

10. J. Barber, M. Davies, and D. Hills, Int. J. Solids Struct. 48 (13), 2041–2047 (2011). DOI: 10.1016/j.ijsolstr.2011.03.008.

11. C. Putignano, M. Ciavarella, and J. Barber, J. Mech. Phys. Solids 59 (12), 2442–2454 (2011). DOI: 10.1016/j.jmps.2011.09.005.

12. R. Mindlin and H. Deresiewicz, J. Appl.Mech. 20 (3), 327–344 (1953). DOI: 10.1115/1.4010702.

13. S. Biwa, S. Nakajima, and N. Ohno, J. Appl. Mech. 71 (4), 508–515 (2004). DOI: 10.1115/1.1767169.

14. M. Yuan et al., Nondestr.Test. Eval. 30 (4), 356–372 (2015). DOI: 10.1080/10589759.2015.1041523.

15. T. J. Ulrich et al., Int. J. Non-Linear Mech. 43, 209–216 (2008). DOI: 10.1016/j.ijnonlinmec.2007.12.017.

16. K. A. Van Den Abeele, P. A. Johnson, and A. Sutin, J. Res. Nondestr. Eval. 12 (1), 17–30 (2000). DOI: 10.1080/09349840009409646.

17. M. Yuan et al., Wave Motion. 57, 143–153 (2015). DOI: 10.1016/j.wavemoti.2015.03.009.

18. S. Delrue et al., Ultrasonics 68, 71–79 (2016). DOI: 10.1016/j.ultras.2016.02.012.

19. I. Solodov et al., Quant. Infrared Thermogr. J. 12 (1), 98–111 (2015). DOI: 10.1080/17686733.2015.1026018.

20. I. Solodov et al., Appl. Phys. Lett. 99 (21), 211911 (2011). DOI: 10.1063/1.3663872.

21. G. P. M. Fierro et al., J. Sound Vib. 404, 102–115 (2017). DOI: 10.1016/j.jsv.2017.05.041.

22. J. Renshaw et al., NDT& E Int. 44 (8), 736–739 (2011). DOI: 10.1016/j.ndteint.2011.07.012.

23. A. S. Rizi et al., Infrared Phys. Technol. 61, 101–110 (2013). DOI: 10.1016/j.infrared.2013.07.011.


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