  All yield criteria that determine the onset of plastic deformation in
crystalline materials must be invariant under the inversion symmetry associated
with a simultaneous change of sign of the slip direction and the slip plane
normal. We demonstrate the consequences of this symmetry on the functional form
of the effective stress, where only the lowest order terms that obey this
symmetry are retained. A particular form of yield criterion is obtained for
materials that do not obey the Schmid law, hereafter called non-Schmid
materials. Application of this model to body-centered cubic and hexagonal
close-packed metals shows under which conditions the non-Schmid stress terms
become significant in predicting the onset of yielding. In the special case,
where the contributions of all non-Schmid stresses vanish, this model reduces
to the maximum shear stress theory of Tresca.
