11. Other criteria

11.1. Criterion VMIS_TRESCA

In this part we describe option VMIS_TRESCA, which makes it possible to calculate the maximum variation, over time, of a stress tensor according to the Von Mises and Tresca criteria.

This calculation can be performed at nodes or at Gauss points according to the user’s request.

Below we give the algorithm that is programmed in*Code_Aster*.

Ratings:

\(N\): Number of moments	\({T}_{i}\): Tensor at time \(i\)
\({\mathit{DIFF}}_{T}\): difference between two tensors

\(\mathit{VAVMIS}\mathrm{=}0.0\)

\(\mathit{VATRES}\mathrm{=}0.0\)

For \(i\) from \(1\) to \((N\mathrm{-}1)\)

For \(j\) from \((i+1)\) to \(N\)

\({\mathit{DIFF}}_{T}\mathrm{=}{T}_{i}\mathrm{-}{T}_{j}\)

\(\mathit{VMIS}\mathrm{=}\) Von-Mises by \({\mathit{DIFF}}_{T}\)

\(\mathit{TRES}\mathrm{=}\) Tresca from \({\mathit{DIFF}}_{T}\)

If \(\mathit{VMIS}>\mathit{VAVMIS}\) then

\(\mathit{VAVMIS}\mathrm{=}\mathit{VMIS}\)

If \(\mathit{TRES}>\mathit{VATRES}\) then

\(\mathit{VATRES}\mathrm{=}\mathit{TRES}\)

11.2. Code_Aster components used

The field calculated by CALC_FATIGUE has the following components:

VAVMIS	Maximum amplitude of variation of the Von Mises criterion
VATRES	Maximum amplitude of variation of the Tresca criterion