Initiation of localized plane deformations at a circular cavity in an infinite compressible nonlinearly elastic medium

✍ Scribed by R. Abeyaratne; C. O. Horgan

• Publisher: Springer Netherlands
• Year: 1985
• Tongue: English
• Weight: 661 KB
• Volume: 15
• Category: Article
• ISSN: 0374-3535
• DOI: 10.1007/bf00041423

✦ Synopsis

This investigation is concerned with the plane strain deformation of an infinite slab, containing a circular cavity, within the theory of finite elastostatics for a particular homogeneous isotropic compressible material, the so-called Blatz-Ko material. The body is subjected to uniform pressure, either internal or external. Exact closed-form solutions for the axisymmetric deformation and stress fields are obtained. In the case of internal pressure, it is found that the appfied pressure may not exceed a certain maximum value Pmax" At a value of pressure Pe ( < Pmax), the governing equations lose ellipticity at the cavity wall. For greater values of pressure this solution remains smooth, though involving both elliptic and non-elliptic regions. Non-existence of axisymmetric solutions with discontinuous strain fields is estabhshed. The possibility of bifurication into a surface mode is considered and it is shown that this occurs at a value of pressure slightly smaller than Pc. Such surface wrinkling leads to a periodic distribution of points of stress concentration, from which shear bands may initiate.