An exploratory study is carried out of various aspects of the development of instabilities of traction-free surfaces of statically strained, rate-independent elastic-plastic solids. Existence of surface instabilities as predicted by either a bifurcation analysis or a quasi-static, imperfection-growth analysis, is found to be strongly dependent on the type of constitutive law assumed. In most instances no instabilities are found using the standard plastic flow law based on a smooth yield surface and isotropic hardening. Instabilities are predicted when a finite strain deformation theory is assumed. These are documented for a full range of proportional overall straining histories using a bifurcation analysis. A finite element analysis employing a corner theory of plasticity is used to study the non-linear growth of the instabilities starting from small initial surface undulations for the case of plane strain deformation. Some experimental observations of surface irregularities which may be due to surface instabilities are reported and discussed.
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