Plane strain constitutive behaviour of von Mises and isotropic Hoffman materials is examined using single element tests. Two kinds of tests are conducted – (a) prescribed displacement tests; and (b) tests with a mixture of displacements and boundary tractions prescribed. While (a) are used to understand the manner of stress traversal on the yield surface in principal stress space, (b) are employed to study the load displacement response and the possibility of ensuing localization. Associated plasticity is assumed throughout. The tests are conducted using perfect and strain softening plasticity. It is found that for the von Mises criterion limited exact solutions can be evolved even under softening (or hardening) conditions. For isotropic Hoffman materials the nature of the stress traversal, load deflection response and the satisfaction of the localization conditions are strongly influenced by the ratio and difference of uniaxial yield strengths, in tension and compression, as well as by the softening parameters.
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