{"title":"具有圆柱形空腔的柔性电固体的分析","authors":"Jinchen Xie, C. Linder","doi":"10.1115/1.4063145","DOIUrl":null,"url":null,"abstract":"\n Flexoelectricity, a remarkable size-dependent effect, means that strain gradients can give rise to electric polarization. This effect is particularly pronounced near defects within flexoelectric solids, where large strain gradients exist. A thorough understanding of the internal defects of flexoelectric devices and their surrounding multiphysics fields is crucial to comprehend their damage and failure mechanisms. Motivated by this, strain gradient elasticity theory is utilized to investigate the mechanical and electrical behaviors of flexoelectric solids with cylindrical cavities under biaxial tension. Closed-form solutions are obtained under the assumptions of plane strain and electrically impermeable defects. In particular, this study extends the Kirsch problem of classical elasticity theory to the theoretical framework of higher-order electroelasticity for the first time. Our research reveals that different length scale parameters of the strain gradient and bidirectional loading ratios significantly affect the hoop stress field, radial electric polarization field, and electric potential field near the inner cylindrical cavity of the flexoelectric solid. Furthermore, we validate our analytical solution by numerical verification using mixed finite elements. The congruence between the two methods confirms our analytical solution's accuracy. The findings presented in this paper provide deeper insights into the internal defects of flexoelectric materials and can serve as a foundation for studying more complex defects in flexoelectric solids.","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":" ","pages":""},"PeriodicalIF":2.6000,"publicationDate":"2023-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Analysis of Flexoelectric Solids with a Cylindrical Cavity\",\"authors\":\"Jinchen Xie, C. Linder\",\"doi\":\"10.1115/1.4063145\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n Flexoelectricity, a remarkable size-dependent effect, means that strain gradients can give rise to electric polarization. This effect is particularly pronounced near defects within flexoelectric solids, where large strain gradients exist. A thorough understanding of the internal defects of flexoelectric devices and their surrounding multiphysics fields is crucial to comprehend their damage and failure mechanisms. Motivated by this, strain gradient elasticity theory is utilized to investigate the mechanical and electrical behaviors of flexoelectric solids with cylindrical cavities under biaxial tension. Closed-form solutions are obtained under the assumptions of plane strain and electrically impermeable defects. In particular, this study extends the Kirsch problem of classical elasticity theory to the theoretical framework of higher-order electroelasticity for the first time. Our research reveals that different length scale parameters of the strain gradient and bidirectional loading ratios significantly affect the hoop stress field, radial electric polarization field, and electric potential field near the inner cylindrical cavity of the flexoelectric solid. Furthermore, we validate our analytical solution by numerical verification using mixed finite elements. The congruence between the two methods confirms our analytical solution's accuracy. The findings presented in this paper provide deeper insights into the internal defects of flexoelectric materials and can serve as a foundation for studying more complex defects in flexoelectric solids.\",\"PeriodicalId\":54880,\"journal\":{\"name\":\"Journal of Applied Mechanics-Transactions of the Asme\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2023-08-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied Mechanics-Transactions of the Asme\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1115/1.4063145\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Mechanics-Transactions of the Asme","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1115/1.4063145","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
Analysis of Flexoelectric Solids with a Cylindrical Cavity
Flexoelectricity, a remarkable size-dependent effect, means that strain gradients can give rise to electric polarization. This effect is particularly pronounced near defects within flexoelectric solids, where large strain gradients exist. A thorough understanding of the internal defects of flexoelectric devices and their surrounding multiphysics fields is crucial to comprehend their damage and failure mechanisms. Motivated by this, strain gradient elasticity theory is utilized to investigate the mechanical and electrical behaviors of flexoelectric solids with cylindrical cavities under biaxial tension. Closed-form solutions are obtained under the assumptions of plane strain and electrically impermeable defects. In particular, this study extends the Kirsch problem of classical elasticity theory to the theoretical framework of higher-order electroelasticity for the first time. Our research reveals that different length scale parameters of the strain gradient and bidirectional loading ratios significantly affect the hoop stress field, radial electric polarization field, and electric potential field near the inner cylindrical cavity of the flexoelectric solid. Furthermore, we validate our analytical solution by numerical verification using mixed finite elements. The congruence between the two methods confirms our analytical solution's accuracy. The findings presented in this paper provide deeper insights into the internal defects of flexoelectric materials and can serve as a foundation for studying more complex defects in flexoelectric solids.
期刊介绍:
All areas of theoretical and applied mechanics including, but not limited to: Aerodynamics; Aeroelasticity; Biomechanics; Boundary layers; Composite materials; Computational mechanics; Constitutive modeling of materials; Dynamics; Elasticity; Experimental mechanics; Flow and fracture; Heat transport in fluid flows; Hydraulics; Impact; Internal flow; Mechanical properties of materials; Mechanics of shocks; Micromechanics; Nanomechanics; Plasticity; Stress analysis; Structures; Thermodynamics of materials and in flowing fluids; Thermo-mechanics; Turbulence; Vibration; Wave propagation