Two anisotropic yield criteria, that employ quadratic stress Junctions and
have been extensively used for the elastoplastic analysis of composite mate
rials, are considered. Proposed by Hoffman and by Sun, both these criteria
have been formulated using nine parameters. With appropriate choice of para
meters they reduce to the well-known isotropic von Mises criterion and the
anisotropic Hill criterion. This paper investigates the convexity, which is
an essential condition for any Plasticity model for these criteria in the
principal stress space. In each case two orthogonal sections - deviatoric a
nd volumetric - are used to study the shapes of the ensuing curves. Illustr
ative three-dimensional plots are included It is concluded that, while simp
le interrelationships between the parameters ensure convexity of the Hoffma
n criterion, conditions for the Sun criterion are quite stringent.