Geometric Instabilities in Isotropic Plastic Solids Under Increasing Uniaxial Compression

Abstract

This analysis seeks three-dimensional instabilities of uniaxial compressive flow in isotropic, strain-hardening, rigid-plastic materials of the Mises and maximum shear stress types. No instabilities are found for Mises materials. Maximum shear materials display axisymmetric, “deflectional”, and “higher-order” buckling. For increasingly slender specimens, the deflectional buckling process merges into that of the Shanley theory. The axisymmetric mode raises the possibility that instabilities contribute to the double axial bulging of ductile compression specimens reported by Na´da´i.