MATF

For STRS failure criterion, the input allowables should be stress-allowables.

For STRN failure criterion, the input allowables should be strain-allowables. OptiStruct will not conduct internal conversion for STRN failure criterion. The values defined are directly used as strain-allowables for STRN failure criterion on MATF.

For STRN failure criterion, the STRN field on MAT8 entry has no effect on the allowable values defined on the MATF entry.

For Solid Elements (MAT9/MAT9OR) and Continuum Shells (PCOMPLS).

Coordinate system 1-2-3 are user-defined for continuum shell elements or solid elements with MAT9.

For STRS3D failure criterion, the input allowables should be stress-allowables.

For STRN3D failure criterion, the input allowables should be strain-allowables. OptiStruct will not conduct internal conversion for STRN3D failure criterion. The values defined are directly used as strain-allowables for STRN3D failure criterion on MATF.

• For TSAI:
  • V10: the coupling coefficient $C_{12}$ for the ${\sigma }_1{\sigma }_2$ term.
  • If V10 is blank, the coupling coefficient is calculated from W1.
  • If V10 and W1 are both blank, the coupling coefficient is 0.0.
• For TSAI3D:
  • V10: the coupling coefficient $C_{12}$ for the ${\sigma }_1{\sigma }_2$ term.
  • V11: the coupling coefficient $C_{23}$ for the ${\sigma }_2{\sigma }_3$ term.
  • V12: the coupling coefficient $C_{12}$ for the ${\sigma }_1{\sigma }_3$ term.
  • If V10, V11, and V12 are all blank, the coupling coefficients are calculated from W1, W2, and W3.
  • If V10, V11, and V12 and W1, W2, and W3 are all blank, the coupling coefficients are 0.0.

• PUCK/PUCK3D specify failure envelope parameters:

  W1

  Failure envelope factor 12(-)

  W2

  Failure envelope factor 12(+)

  If W2 is blank, it is set to be equal to W1, W1 and W3 should be specified.

  W3

  Failure envelope factor 22(-)

  W4

  Failure envelope factor 22(+).

  This is only used for PUCK3D.

• TSAI3D on anisotropic solid material

  If V10, V11 and V12 are blank, they are the tensile stress limits in equal-biaxial tension tests. W1 is the tensile stress limit in equal-biaxial tests where the two tensile loads are in directions 1 and 2. W1 is mandatory, while W2 and W3 are optional. If W2 and W3 are not specified, then they are set equal to W1. The definition of W2 and W3 is similar to W1. W2 is the tensile stress limit in equal-biaxial tension tests where the two tensile loads are in directions 2 and 3. W3 is the tensile stress limit in equal-biaxial tension tests where the two tensile loads are in directions 1 and 3.

  If V10, V11 and V12 are defined, W1, W2 and W3 are ignored for TSAI3D.

• HASH3D

  When Hashin failure criteria is applied on continuum shell elements, W1 is defined as alpha, which takes the transverse shear stress (in 1-2 and 1-3 direction) into account in the tensile fiber check. When W1 is blank, alpha is assumed to be 1.0.

• CNTZ3D

  When using Cuntze failure criterion, W1 and W2, corresponding to the two free curve parameters, $b_{\perp \left|\right|}$ and $b_{\perp }^T$ should be provided. The two curve parameters can be determined from multi-axial test data from experiments. Bounds on the safe side for GFRP, CFRP and AFRP are assumed by Cuntze ¹ to be:

  $$\mathrm{0.0.5}<b_{\perp \left|\right|}<0.15,1.0<b_{\perp |}^T<1.6$$

• If the same criterion type is defined in both PCOMP(G/P) property and the MATF entry, then the allowables defined on the MATF entry will be used in the failure criterion calculations. The MATF entry overwrites the allowables defined by the corresponding MATi entry (if any).
• If some criteria are only defined on PCOMP(G/P) but not on MATF, then for such criteria, the allowables are taken from corresponding MATi entries.
• If some criteria are defined on MATF, and PARAM,ALLFT,YES exists, then the criteria defined on MATF will use the allowables defined on MATF. However, the criteria not defined on MATF will be calculated based on allowables defined on the corresponding MATi entry.

PUCK, DUCTILE, PUCK3D, HILL3D, HOFF3D, TSAI3D, HASH3D, STRN3D, and CNTZ3D.

The rest of the criteria can also be defined on the FT field of the corresponding PCOMPP/PCOMPG/PCOMP entry.

For the PUCK failure criterion, even though it is available on the FT field of the PCOMPP/PCOMPG/PCOMP entry, the corresponding failure envelope factors (W1, W2, W3) can only be defined on the MATF entry. Therefore, the MATF entry is mandatory when PUCK failure criterion is requested via the FT field of PCOMP/PCOMPG/PCOMPP entries, and additionally, the allowables should be defined on the MATF for PUCK criterion only. To use PUCK failure criteria, the MATF entry should be specified with MID referring to the corresponding material entry.

When the CRITERIA field is set to DUCTILE in OSTTS analysis, the temperature-based lookup is conducted for each temperature to identify the corresponding equivalent plastic strain from the TABLEMD entry. This plastic strain is used in conjunction with the calculated von Mises strain to calculate Damage (This can be output using the DAMAGE I/O Options Entry).

$\sigma$

Damaged stress tensor

${\sigma }_{eff}$

Undamaged effective stress tensor

$D$

Damage variable

• If $D_C=0$ , the stress softening starts as soon as $D\ne 0$ and the stress softening is fully coupled (blue curve in Figure 1).
• If $0<D_C<1$ , the stress softening is partially coupled as it starts when $D=D_C$ (red curve).
• If $D_C=1$ , the stress tensor rapidly drops to 0 when $D=1$ and a failure criterion approach is then obtained (green curve).

• If V_TID is defined, a tabulated strain rate dependency is defined by TABLEMD, which defines the evolution of a dimensionless factor denoted by $f_{sr}\left(\frac{\dot{\epsilon }}{{\epsilon }_0}\right)$ evolution with strain rate. Then the strain rate effect is introduced in the damage variable evolution by multiplication with the plastic strain at failure:
  $$D={\displaystyle \sum _{t=0}^{\infty }\frac{\text{Δ}{\epsilon }_p}{{{\displaystyle \epsilon }}_p^f\left(\eta ,\xi \right).f_{sr}\left(\frac{\dot{\epsilon }}{{\epsilon }_0}\right).f_{sr}{}^{scale}}}$$
  Where,

  $\eta$

  Stress triaxiality

  $\xi$

  Lode parameter

  ${\dot{\epsilon }}_0$

  V_REF

  ${\text{f}}_{sr}^{scale}$

  VT_SCALE

  ${{\displaystyle \epsilon }}_p^f$

  Plastic strain at failure

  $\dot{\epsilon }$

  Strain rate

• If a continuous and analytical formula is desired, the Johnson-Cook strain rate dependency can be set up by specifying only a reference strain rate V_REF and the parameter JC (denoted as in the equation). Then, the damage variable evolution is given by:
  $$D={\displaystyle \sum _{t=0}^{\infty }\frac{\text{Δ}{\epsilon }_p}{{{\displaystyle \epsilon }}_p^f\left(\eta ,\xi \right).\left(1+C_{JC}{〈\ln \frac{\dot{\epsilon }}{{\epsilon }_0}〉}_{+}\right)}}$$
  Note: The strain-rate computation (total equivalent or plastic strain rate) depends on the choice made in the MATS1 Bulk Data Entry. In the absence of plasticity, the strain-rate dependency is not available.

$L_{ref}$

EL_REF

${\text{f}}_{size}^{scale}$

FE_SCALE

• For solid elements, deletion occurs only if all the integration points fail.
• For shell elements, deletion occurs if more than half of the integration points (over thickness) fail.

Failure based on a constant maximum plastic strain value at failure ${\epsilon }_p^f$ . No stress triaxiality or Lode parameter dependency is considered here. The damage variable evolution is computed as:

Failure based on thinning strain denoted as <Ezz> and only considered when <Ezz < 0>. This thinning strain is compared to a critical value denoted as <Ef_thin>. Depending on the input value sign, it can either correspond to a total strain or a plastic strain. The damage variable is then computed as:

Failure based on major strain. The maximal positive value of the principal strains is compared to a critical value denoted by <Ef_maj>. The damage variable is then computed with:

If multiple failure types are used in PLAS, the maximal damage value is retained.

If LENDT is specified:

$L_{ref}$ is the characteristic length used to compute the elementary critical timestep.

Where D1, D2, and D3 are Johnson-Cook parameters. If a strain rate dependency is used, you can introduce the Johnson Cook strain rate dependency factor. In this case, the plastic strain at failure expression is: