Abstract
Constitutive relations in a form suitable for use in stability problems are derived for an elastic-plastic material undergoing a perturbation from a state of uniaxial stress, based on Green and Naghdi's general theory of an elastic-plastic continuum [1], The deformation is considered to be quasi-static and isothermal, the material is assumed to yield according to the von Mises criterion, and to flow plastically according to the Reuss equations. The elastic strain rates are determined from Hooke's law. These relations are then applied to study the influence of plate thickness on the instability of a rectangular plate under uniform uniaxial compression. The instability of the surface of a compressed semi-infinite elastic-plastic continuum is then considered as the limiting case of infinite plate thickness. It is found that plastic flow has little influence on surface instability which is attributed to elastic deformation. Finally, two cases are considered for a rigid-plastic material, plane strain and plane stress, in order to compare the present treatment with previous work.
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