Initiation of Localized Plane Deformations at a Circular Cavity in an Infinite Compressible Nonlinearly Elastic Medium

摘要

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 applied pressure may not exceed a certain maximum value p sub max. At a value of pressure p sub e ( < P sub max), 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 established. 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 p sub e. Such surface wrinkling leads to a periodic distribution of points of stress concentration, from which shear bands may initiate. (Reprints)