It is possible for one or more of the direct stresses to exceed the user specified value of initial uniaxial yield stress however. There are a number of explanations if this occurs

• The presence of a hardening gradient will cause the initial uniaxial yield stress to change with increasing plastic strain. The updated or "current" yield stress should be used for checking purposes (available from the LUSAS output file when Gauss point output has been requested at tabulation). The initial uniaxial yield stress will remain constant throughout the analysis with the specification of perfect plasticity (zero hardening modulus).
  
• The failure criterion is always evaluated at the Gauss point level. In general, the extrapolation carried out to obtain the nodal results will not necessarily satisfy the above failure criteria and any checks of this sort should be performed on Gauss point results.
  
• The definition of the distortion-energy theory itself permits this behaviour. It typically occurs for stress fields with low shear stress compared to the direct stresses. If the inequality; s_xs_y > s_xy² is satisfied in the two dimensional, three component stress equation, then the effective stress will always be greater than the direct stresses (try, for instance s_x = 1, s_y = 2 and s_xy = 0)
  
• The solution for the increment being investigated may not be adequately converged. Slackening the residual and/or maximum absolute residual norms to achieve "convergence" should be a last resort. Residual norm magnitudes less than 0.1 are normally achievable and should be aimed for ideally.