{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T18:07:37Z","timestamp":1768586857608,"version":"3.49.0"},"reference-count":42,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2021,8,16]],"date-time":"2021-08-16T00:00:00Z","timestamp":1629072000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science Foundation of China","award":["61773283"],"award-info":[{"award-number":["61773283"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, the possibility of using nonlinear ultrasonic guided waves for early-life material degradation in metal plates is investigated through both computational modeling and study. The analysis of the second harmonics of Lamb waves in a free boundary aluminum plate, and the internal resonance conditions between the Lamb wave primary modes and the second harmonics are investigated. Subsequently, Murnaghan\u2019s hyperelastic model is implemented in a finite element (FE) analysis to study the response of aluminum plates subjected to a 60 kHz Hanning-windowed tone burst. Different stages of material degradation are reflected as the changes in the third order elastic constants (TOECs) of the Murnaghan\u2019s model. The reconstructed degradations match the actual ones well across various degrees of degradation. The effects of several relevant factors on the accuracy of reconstructions are also discussed.<\/jats:p>","DOI":"10.3390\/s21165498","type":"journal-article","created":{"date-parts":[[2021,8,16]],"date-time":"2021-08-16T02:32:10Z","timestamp":1629081130000},"page":"5498","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Nonlinear Guided Wave Tomography for Detection and Evaluation of Early-Life Material Degradation in Plates"],"prefix":"10.3390","volume":"21","author":[{"given":"Chengwei","family":"Zhao","sequence":"first","affiliation":[{"name":"State Key Laboratory of Precision Measuring Technology and Instruments, Tianjin University, 92 Weijin Road, Tianjin 300072, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7232-0973","authenticated-orcid":false,"given":"Sunia","family":"Tanweer","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, School of Mechanical and Manufacturing Engineering, National University of Sciences and Technology, Islamabad 44000, Pakistan"},{"name":"Department of Mechanical Engineering, University of Wyoming, 1000 E. University Ave, Laramie, WY 82071, USA"}]},{"given":"Jian","family":"Li","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Precision Measuring Technology and Instruments, Tianjin University, 92 Weijin Road, Tianjin 300072, China"}]},{"given":"Min","family":"Lin","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, University of Wyoming, 1000 E. University Ave, Laramie, WY 82071, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7984-6003","authenticated-orcid":false,"given":"Xiang","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, University of Wyoming, 1000 E. University Ave, Laramie, WY 82071, USA"}]},{"given":"Yang","family":"Liu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Precision Measuring Technology and Instruments, Tianjin University, 92 Weijin Road, Tianjin 300072, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4517","DOI":"10.1016\/j.jsv.2013.03.021","article-title":"On selection of primary modes for generation of strong internally resonant second harmonics in plate","volume":"332","author":"Liu","year":"2013","journal-title":"J. Sound Vib."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"021101","DOI":"10.1063\/5.0038340","article-title":"Nonlinear ultrasonic guided waves-Principles for nondestructive evaluation","volume":"129","author":"Lissenden","year":"2021","journal-title":"J. Appl. 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