A new derivative on the shift property of effective elastic compliances for planar and three–dimensional composites

Abstract

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Hu G. K. and Weng G. J. 2001A new derivative on the shift property of effective elastic compliances for planar and three–dimensional compositesProc. R. Soc. Lond. A.4571675–1684http://doi.org/10.1098/rspa.2001.0783SectionRestricted accessResearch articleA new derivative on the shift property of effective elastic compliances for planar and three–dimensional composites G. K. Hu G. K. Hu Department of Applied Mechanics, Beijing Institute of Technology, 100081 Beijing, China () Google Scholar Find this author on PubMed Search for more papers by this author and G. J. Weng G. J. Weng Department of Mechanical and Aerospace Engineering, Rutgers University, New Brunswick, NJ 08903, USA () Google Scholar Find this author on PubMed Search for more papers by this author G. K. Hu G. K. Hu Department of Applied Mechanics, Beijing Institute of Technology, 100081 Beijing, China () Google Scholar Find this author on PubMed Search for more papers by this author and G. J. Weng G. J. Weng Department of Mechanical and Aerospace Engineering, Rutgers University, New Brunswick, NJ 08903, USA () Google Scholar Find this author on PubMed Search for more papers by this author Published:08 July 2001https://doi.org/10.1098/rspa.2001.0783AbstractBased on Hill's condition and a field–fluctuation approach, a new derivation is given for the shift property of effective compliances for both planar and three–dimensional composites. The derived relations are exact, and hold for any kind of microstructures and anisotropy. To provide a link to the well–known shift property of Cherkaev, Lurie & Milton in plane elasticity, special reference is given to two–dimensional composites and voided materials with isotropic constituents, but covering both overall inplane isotropy and orthotropy. This method is substantially simpler than the stress–invariance approach commonly adopted in the literature and it provides a new means of addressing the shift characteristics of the effective compliances. By this approach, several universal relations governing the effective compliances of three–dimensional and two–dimensional composites are also found, to our knowledge, for the first time. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Li J, Lagoudas D and Bhattacharyya A (2014) Biography of the Prager Medalist: Professor George Weng, Acta Mechanica, 10.1007/s00707-013-1044-6, 225:4-5, (967-977), Online publication date: 1-Apr-2014. Joumaa H and Ostoja-Starzewski M (2011) Stress and couple-stress invariance in non-centrosymmetric micropolar planar elasticity, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 467:2134, (2896-2911), Online publication date: 8-Oct-2011. 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Chiang C and Weng G (2002) A new look at Hill's arithmetic and geometric means for a two-phase, isotropic composite, Acta Mechanica, 10.1007/BF01188738, 156:1-2, (1-12), Online publication date: 1-Mar-2002. This Issue08 July 2001Volume 457Issue 2011 Article InformationDOI:https://doi.org/10.1098/rspa.2001.0783Published by:Royal SocietyPrint ISSN:1364-5021Online ISSN:1471-2946History: Published online08/07/2001Published in print08/07/2001 License: Citations and impact Keywordscompositesuniversal relationsshift propertieseffective compliances