{"title":"Second gradient theory of thermopiezoelectricity","authors":"D. Ieşan","doi":"10.1007/s00707-024-03999-8","DOIUrl":null,"url":null,"abstract":"<div><p>This paper is concerned with a linear theory of thermopiezoelectricity in which the second gradient of the displacement, the second gradient of the electric potential and the second temperature gradient are included in the classic set of independent constitutive variables. The present paper is based on Green–Naghdi thermomechanics. The introduction of the entropy flux tensor leads to constitutive equations that depend on the second temperature gradient. The fundamental boundary-initial-value problems are formulated and the uniqueness of the solution is studied. Two applications of the theory are presented. We study the problem of a concentrated charge density acting in an unbounded region, as well as the effects of a concentrated heat source.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"235 8","pages":"5379 - 5391"},"PeriodicalIF":2.3000,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mechanica","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s00707-024-03999-8","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper is concerned with a linear theory of thermopiezoelectricity in which the second gradient of the displacement, the second gradient of the electric potential and the second temperature gradient are included in the classic set of independent constitutive variables. The present paper is based on Green–Naghdi thermomechanics. The introduction of the entropy flux tensor leads to constitutive equations that depend on the second temperature gradient. The fundamental boundary-initial-value problems are formulated and the uniqueness of the solution is studied. Two applications of the theory are presented. We study the problem of a concentrated charge density acting in an unbounded region, as well as the effects of a concentrated heat source.
期刊介绍：
Since 1965, the international journal Acta Mechanica has been among the leading journals in the field of theoretical and applied mechanics. In addition to the classical fields such as elasticity, plasticity, vibrations, rigid body dynamics, hydrodynamics, and gasdynamics, it also gives special attention to recently developed areas such as non-Newtonian fluid dynamics, micro/nano mechanics, smart materials and structures, and issues at the interface of mechanics and materials. The journal further publishes papers in such related fields as rheology, thermodynamics, and electromagnetic interactions with fluids and solids. In addition, articles in applied mathematics dealing with significant mechanics problems are also welcome.
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