{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,3]],"date-time":"2026-08-03T12:46:34Z","timestamp":1785761194422,"version":"3.56.0"},"reference-count":23,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Region Provence-Alpes-C\u00f4te d\u2019Azur"},{"id":[{"id":"https:\/\/ror.org\/056efzf78","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Nonlinear acoustics has emerged as a sensitive and promising non-destructive approach to damage detection in concrete structures. This study proposes a method based on nonlinear acoustics that uses collinear mixing ultrasonic waves to detect and locate defects (microcracks, macrocracks, spalling) in concrete. The method consists of analyzing the interaction between a low-frequency pump wave and a high-frequency probe wave, both travelling along the width of the block in opposite directions. This interaction produces a measurable time-of-flight shift in the probe wave, which accumulates along the sampling path. A nonlinear parameter (NL), defined as the spatial gradient of the normalized time shift, is introduced to suppress cumulative propagation effects and improve damage localization. The proposed technique is tested to detect and locate a thermally damaged concrete prism (0.25 \u00d7 0.08 \u00d7 0.15 m3) cast inside a sound concrete block (0.40 \u00d7 0.40 \u00d7 0.70 m3). The results enabled the detection, localization, and characterization of the damaged concrete prism with a sensitivity beyond that of conventional linear ultrasound. The effectiveness of the method is therefore validated, and it demonstrates its potential for damage monitoring of structures in civil and nuclear engineering applications.<\/jats:p>","DOI":"10.3390\/s26154856","type":"journal-article","created":{"date-parts":[[2026,8,3]],"date-time":"2026-08-03T11:50:21Z","timestamp":1785757821000},"page":"4856","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Nonlinear Wave Mixing Approach for Internal Damage Localization in Concrete"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5076-5920","authenticated-orcid":false,"given":"Klayne","family":"Dos Santos Silva","sequence":"first","affiliation":[{"name":"French Authority for Nuclear Safety and Radiation Protection (ASNR), 92120 Montrouge, France"},{"name":"Laboratory of Mechanics and Acoustics (LMA), UMR 7031, CNRS, Centrale M\u00e9diterran\u00e9e, Aix-Marseille University, 13013 Marseille, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vincent","family":"Garnier","sequence":"additional","affiliation":[{"name":"Laboratory of Mechanics and Acoustics (LMA), UMR 7031, CNRS, Centrale M\u00e9diterran\u00e9e, Aix-Marseille University, 13013 Marseille, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6549-4975","authenticated-orcid":false,"given":"Benoit","family":"Durville","sequence":"additional","affiliation":[{"name":"French Authority for Nuclear Safety and Radiation Protection (ASNR), 92120 Montrouge, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Menes","family":"Badika","sequence":"additional","affiliation":[{"name":"French Authority for Nuclear Safety and Radiation Protection (ASNR), 92120 Montrouge, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sandrine","family":"Morin","sequence":"additional","affiliation":[{"name":"French Authority for Nuclear Safety and Radiation Protection (ASNR), 92120 Montrouge, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David","family":"Marlot","sequence":"additional","affiliation":[{"name":"MISTRAS Group SAS, 94730 Sucy-en-Brie, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pierre","family":"Delvart","sequence":"additional","affiliation":[{"name":"MISTRAS Group SAS, 94730 Sucy-en-Brie, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ruben","family":"Edery","sequence":"additional","affiliation":[{"name":"MISTRAS Group SAS, 94730 Sucy-en-Brie, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5736-0766","authenticated-orcid":false,"given":"C\u00e9dric","family":"Payan","sequence":"additional","affiliation":[{"name":"Laboratory of Mechanics and Acoustics (LMA), UMR 7031, CNRS, Centrale M\u00e9diterran\u00e9e, Aix-Marseille University, 13013 Marseille, France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Hamilton, M.F., and Blackstock, D.T. 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