An Eshelby inclusion of parabolic shape in an anisotropic elastic plane. (April 2021)

• Record Type: Journal Article
• Authors: Yang, Ping; Wang, Xu; Schiavone, Peter
• Is Part Of: Mechanics of materials. Volume 155(2021)
• Publication Date: 2021-04
• Subjects: Parabolic inclusion -- Anisotropic elastic material -- Stroh sextic formalism -- Uniform field -- Eshelby's tensor; Strength of materials -- Periodicals; Mechanics, Applied -- Periodicals; Résistance des matériaux -- Périodiques; Mécanique appliquée -- Périodiques; Mechanics, Applied; Strength of materials; Periodicals; Electronic journals; 620.11
• DOI: 10.1016/j.mechmat.2020.103733
• Languages: English
• ISSNs: 0167-6636

Abstract

Abstract: An analytical solution is derived to the Eshelby's problem of a parabolic inclusion undergoing uniform in-plane and anti-plane eigenstrains in an anisotropic elastic plane. The stresses, total strains and rigid-body rotation are found to be uniform inside the parabolic inclusion. In addition, we obtain real-form expressions of these internal uniform physical quantities in terms of the reduced elastic compliances and the imposed eigenstrains. The constant Eshelby's tensor inside the parabolic inclusion can be completely determined by the reduced elastic compliances. Highlights: Infinite anisotropic plane, parabolic inclusion, uniform in-plane eigenstrains. Eshelby's problem of a parabolic inclusion in an anisotropic plane. Stresses, strains and rigid-body rotation uniform inside the parabolic inclusion. Real-form expressions of internal uniform physical fields. Eshelby's tensor in parabolic inclusion determined by reduced elastic compliances.