{"title":"Spherical Indentation on a Piezoelectric Semiconductor Film/Elastic Substrate System","authors":"Shijing Gao, Guoquan Nie, Jinxi Liu, Weiqiu Chen","doi":"10.1007/s10338-025-00588-7","DOIUrl":null,"url":null,"abstract":"<div><p>We study the axisymmetric frictionless indentation problem of a piezoelectric semiconductor (PSC) thin film perfectly bonded to a semi-infinite isotropic elastic substrate by a rigid and insulating spherical indenter. The Hankel integral transformation is first employed to derive the general solutions for the governing differential equations of the PSC film and elastic substrate. Then, using the boundary and interface conditions, the complicated indentation problem is reduced to numerically solve a Fredholm integral equation of the second kind. Numerical results are given to demonstrate the effects of semiconducting property, film thickness as well as Young’s modulus and Poisson’s ratio of the substrate on the indentation responses. The obtained findings will contribute to the establishment of indentation experiments for PSC film/substrate systems.</p></div>","PeriodicalId":50892,"journal":{"name":"Acta Mechanica Solida Sinica","volume":"38 5","pages":"872 - 883"},"PeriodicalIF":2.7000,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mechanica Solida Sinica","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s10338-025-00588-7","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATERIALS SCIENCE, MULTIDISCIPLINARY","Score":null,"Total":0}
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Abstract
We study the axisymmetric frictionless indentation problem of a piezoelectric semiconductor (PSC) thin film perfectly bonded to a semi-infinite isotropic elastic substrate by a rigid and insulating spherical indenter. The Hankel integral transformation is first employed to derive the general solutions for the governing differential equations of the PSC film and elastic substrate. Then, using the boundary and interface conditions, the complicated indentation problem is reduced to numerically solve a Fredholm integral equation of the second kind. Numerical results are given to demonstrate the effects of semiconducting property, film thickness as well as Young’s modulus and Poisson’s ratio of the substrate on the indentation responses. The obtained findings will contribute to the establishment of indentation experiments for PSC film/substrate systems.
期刊介绍：
Acta Mechanica Solida Sinica aims to become the best journal of solid mechanics in China and a worldwide well-known one in the field of mechanics, by providing original, perspective and even breakthrough theories and methods for the research on solid mechanics.
The Journal is devoted to the publication of research papers in English in all fields of solid-state mechanics and its related disciplines in science, technology and engineering, with a balanced coverage on analytical, experimental, numerical and applied investigations. Articles, Short Communications, Discussions on previously published papers, and invitation-based Reviews are published bimonthly. The maximum length of an article is 30 pages, including equations, figures and tables
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