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Why are Some Stress Results Greater than the Yield Stress?

For a number of the LUSAS nonlinear materials, the von Mises failure criteria is used to determine whether yield has occurred at a Gauss point. This is performed by comparing the yield stress (sY) computed at the previous iteration with the magnitude of the failure criteria (sE) as computed from the current predicted iterative stress field. If the inequality (sEsY) is violated then material yielding is assumed to have occurred. The stress state is then modified by accumulating plastic strain until the inequality is satisfied.

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; sxsy > sxy2 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 sx = 1, sy = 2 and sxy = 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.

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