A hole of irregular shape interacting with a non-parabolic open inhomogeneity with internal uniform anti-plane stresses. (July 2021)

• Record Type: Journal Article
• Authors: Wang, Xu; Yang, Ping; Schiavone, Peter
• Is Part Of: Mathematics and mechanics of solids. Volume 26:Number 7(2021)
• Page Start: 954
• Page End: 962
• Publication Date: 2021-07
• Subjects: Non-parabolic inhomogeneity -- hole -- uniform stress field -- anti-plane elasticity -- conformal mapping; Materials -- Mechanical properties -- Periodicals; Solids -- Periodicals; Materials science -- Mathematics -- Periodicals; 620.11205
• DOI: 10.1177/1081286520970244
• Languages: English
• ISSNs: 1081-2865

Abstract

We use conformal mapping techniques together with analytic continuation to show that a non-parabolic open elastic inhomogeneity continues to admit a state of uniform internal stress when a hole with closed curvilinear traction-free boundary is placed in its vicinity and the surrounding matrix is subjected to uniform remote anti-plane stresses. The internal uniform stress field inside the inhomogeneity is found to be independent of the existence of the nearby hole and the specific non-parabolic shape of the inhomogeneity. In contrast, the non-parabolic shape of the inhomogeneity is influenced solely by the existence of the nearby hole.