Integral-Type Stress Boundary Condition in the Complete Gurtin-Murdoch Surface Model with Accompanying Complex Variable Representation
In the large majority of papers utilizing the Gurtin-Murdoch (G-M) model of a material surface, the complete model is avoided in favor of various modified versions often because they lead to simpler representations of the corresponding stress boundary condition. We propose in this paper an integral-...
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| Veröffentlicht in: | Journal of elasticity Jg. 134; H. 2; S. 235 - 241 |
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| Abstract | In the large majority of papers utilizing the Gurtin-Murdoch (G-M) model of a material surface, the complete model is avoided in favor of various modified versions often because they lead to simpler representations of the corresponding stress boundary condition. We propose in this paper an integral-type stress boundary condition for the plane deformations of a bulk-interface composite system which allows for an equally simple implementation of the
complete
G-M model. Since the mechanical behavior of such composite systems is often analyzed using complex variable methods, we formulate our ideas accordingly, in this context. Remarkably, in contrast to what is often believed to be the case, we find that boundary value problems based on our formulation of the stress boundary condition offer no added difficulty when utilizing the complete G-M model versus its various simplified counterparts. This new representation of the stress boundary condition is concise in form and will prove to be extremely useful in, for example, the calculation of the elastic field in the vicinity of nano-inhomogeneities of irregular shape. |
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| AbstractList | In the large majority of papers utilizing the Gurtin-Murdoch (G-M) model of a material surface, the complete model is avoided in favor of various modified versions often because they lead to simpler representations of the corresponding stress boundary condition. We propose in this paper an integral-type stress boundary condition for the plane deformations of a bulk-interface composite system which allows for an equally simple implementation of the
complete
G-M model. Since the mechanical behavior of such composite systems is often analyzed using complex variable methods, we formulate our ideas accordingly, in this context. Remarkably, in contrast to what is often believed to be the case, we find that boundary value problems based on our formulation of the stress boundary condition offer no added difficulty when utilizing the complete G-M model versus its various simplified counterparts. This new representation of the stress boundary condition is concise in form and will prove to be extremely useful in, for example, the calculation of the elastic field in the vicinity of nano-inhomogeneities of irregular shape. |
| Author | Schiavone, Peter Wang, Yong-Jian Dai, Ming |
| Author_xml | – sequence: 1 givenname: Ming orcidid: 0000-0001-5608-0247 surname: Dai fullname: Dai, Ming organization: State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, School of Mechanical Engineering, Changzhou University – sequence: 2 givenname: Yong-Jian surname: Wang fullname: Wang, Yong-Jian organization: College of Engineering, Nanjing Agricultural University – sequence: 3 givenname: Peter orcidid: 0000-0003-4741-0165 surname: Schiavone fullname: Schiavone, Peter email: p.schiavone@ualberta.ca organization: Department of Mechanical Engineering, University of Alberta |
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| Cites_doi | 10.1016/j.ijsolstr.2007.05.019 10.1016/j.ijsolstr.2011.11.013 10.1007/s00033-016-0706-3 10.1016/j.jmps.2005.02.009 10.1016/j.jmps.2008.01.001 10.1007/s11433-010-0144-8 10.1080/01418619808239977 10.1115/1.4034118 10.1063/1.1539929 10.1007/s00707-006-0371-2 10.1115/1.2424242 10.1007/BF00261375 10.1007/s00419-016-1215-8 |
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| Keywords | 74G05 34B05 74B05 Surface/interface stress Gurtin-Murdoch model Complex variable methods Nano-inhomogeneity |
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| Title | Integral-Type Stress Boundary Condition in the Complete Gurtin-Murdoch Surface Model with Accompanying Complex Variable Representation |
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