The analytical properties of',he constitutive equations in plasticity with a nonassociated flow rule are investigated. Under the assumption of small deformations the directional stiffness (and compliance) rule is considered and the relevant spectral properties of the tangent stiffness tensor are assessed. It is shown that :he directional stiffness may be larger than the elastic. It may also be negative in the case of a formally perfectly plastic material and so the nonassociatire flow rule represents (spurious) ~oftening in terms of an associated flow rule. The issue of uniqueness at finite strains is briefly ad3.res:.ed, whereby use is made of the tangent stiffness tensor relating the velocity gradient to the tL-_.-t Piola-Kirchhoff stress rate. The relevant spectral properties, which generalise those from the small deformation ease, are found explicitly. A sufficient condition for uniqueness is given in :erms of a critical (upper bound) value of the hardening modulus.
'Single dot between two tensors denotes contraction w.r.t, one index, while double dot denotes contraction w.r.t, two indices. For example, u.v=u, vi, a:~=aij~ij, andA:a=Aiyktael.