{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,25]],"date-time":"2025-11-25T15:56:43Z","timestamp":1764086203384,"version":"3.45.0"},"reference-count":19,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2025,11,25]],"date-time":"2025-11-25T00:00:00Z","timestamp":1764028800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004193","name":"Nanjing University of Aeronautics and Astronautics","doi-asserted-by":"publisher","award":["NS2025003"],"award-info":[{"award-number":["NS2025003"]}],"id":[{"id":"10.13039\/501100004193","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Micromachines"],"abstract":"<jats:p>Based on the Hilbert\u2013Riemann theory, this paper develops a simplified model to address interfacial fracture in bi-layer laminated solar cells with significantly dissimilar thermal properties. The model is used to analyze interfacial normal stress distributions and identify critical stress points, taking into account the substantial mismatch in the coefficients of thermal expansion between the semiconductor and encapsulation layers. The predicted temperature and stress fields are validated through finite element simulations. Furthermore, by investigating commonly used encapsulation films and solar cell modules, the coupled effects of the thermal expansion coefficient and elastic modulus are elucidated. The results demonstrate that, under a constant layer thickness, the position of the stress critical point is governed by two dimensionless parameters: the ratio of thermal expansion coefficients and the ratio of elastic moduli. This work offers an efficient and practical approach for predicting thermal stress concentration trends in laminated solar cell structures, thereby providing useful insights for the design and fabrication of solar modules.<\/jats:p>","DOI":"10.3390\/mi16121320","type":"journal-article","created":{"date-parts":[[2025,11,25]],"date-time":"2025-11-25T15:29:47Z","timestamp":1764084587000},"page":"1320","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Theoretical Solution for Analyzing Bi-Layer Structures with Differing Thermal Properties"],"prefix":"10.3390","volume":"16","author":[{"given":"Qianhua","family":"Peng","sequence":"first","affiliation":[{"name":"State Key Laboratory of Mechanics and Control for Aerospace Structures, Nanjing University of Aeronautics & Astronautics, Nanjing 210016, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Siyuan","family":"Zhou","sequence":"additional","affiliation":[{"name":"H3C Technology Co., Ltd., No.8 Guangshunnan St., Beijing 100102, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7421-3306","authenticated-orcid":false,"given":"Yan","family":"Shi","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Mechanics and Control for Aerospace Structures, Nanjing University of Aeronautics & Astronautics, Nanjing 210016, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaohui","family":"Qian","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Mechanics and Control for Aerospace Structures, Nanjing University of Aeronautics & Astronautics, Nanjing 210016, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1016\/j.polymertesting.2015.04.009","article-title":"Thermal expansion behavior of solar cell encapsulation materials","volume":"44","author":"Knausz","year":"2015","journal-title":"Polym. Test."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/0927-0248(95)00150-6","article-title":"Encapsulation of PV modules using ethylene vinyl acetate copolymer as a pottant: A critical review","volume":"43","author":"Czanderna","year":"1996","journal-title":"Sol. Energy Mater. Sol. Cells"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Eitner, U., Kajari-Schr\u00f6der, S., K\u00f6ntges, M., and Altenbach, H. (2011). Thermal Stress and Strain of Solar Cells in Photovoltaic Modules. Shell-Like Structures: Non-Classical Theories and Applications, Springer.","DOI":"10.1007\/978-3-642-21855-2_29"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"21117","DOI":"10.1007\/s10853-022-07900-7","article-title":"Mechanical properties of the encapsulant material for photovoltaics","volume":"57","author":"Kislyuk","year":"2022","journal-title":"J. Mater. 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