MATX25

Format

Example

Definitions

Comments

1. The material identification number must be that of an existing MAT8 Bulk Data Entry. Only one MATXi material extension can be associated with a particular MAT8.
2. MATX25 is only applied in geometric nonlinear analysis subcases which are defined by ANALYSIS=EXPDYN. It is ignored for all other subcases.
3. Tsai-Wu formula (I=TSAI) is not available with QEPH (I=24 on PCOMPX) shell elements, it is only available with Q4 (I=1, 2, 3, 4 on PCOMPX) and QBAT(I=12 on PCOMPX) shell elements.
4. The Lamina yield surface for Tsai-Wu criteria (I=TSAI) is:(1)
   $$\text{F}={\text{F}}_1{\sigma }_1+{\text{F}}_2{\sigma }_2+{\text{F}}_{11}{\sigma }_1^2+{\text{F}}_{22}{\sigma }_2^2+{\text{F}}_{44}{\sigma }_{12}^2+2{\text{F}}_{12}{\sigma }_1{\sigma }_2\le \text{F}\left(\frac{{\text{W}}_{\text{p}}}{{\text{W}}_{\text{ref}}^{\text{p}}}\right)$$
   Where,

   W_p

   Plastic work

   ${\text{W}}_{\text{ref}}^{\text{p}}$

   Reference plastic work

   $\text{F}\left(\frac{{\text{W}}_{\text{p}}}{{\text{W}}_{\text{ref}}^{\text{p}}}\right)$

   Yield envelope evolution

   Where,

   b

   hardening parameter for plastic work

   n

   hardening exponent

   $$\begin{array}{cc}{F}_1=-\frac{1}{{\sigma }_{1y}^c}+\frac{1}{{\sigma }_{1y}^t};& F_2=-\frac{1}{{\sigma }_{2y}^c}+\frac{1}{{\sigma }_{2y}^t}\\ F_{11}=\frac{1}{{\sigma }_{1y}^c{\sigma }_{1y}^t};& F_{22}=\frac{1}{{\sigma }_{2y}^c{\sigma }_{2y}^t}\\ F_{44}=\frac{1}{{\sigma }_{12y}^2{\sigma }_{12y}^t};& F_{12}=-\frac{\alpha }{2}\sqrt{F_{11}{F}_{22}}\end{array}$$
5. The CRASURV model is an improved version of the former law based on the standard Tsai-Wu criteria. The main changes concern the expression of the yield surface before plastification and during work hardening. First, in a CRASURV model, the coefficient $F_{44}$ depends only on one input parameter:(2)
   $$F_{44}=\frac{1}{{\left({\sigma }_{12y}\right)}^2}$$
   Another modification concerns the parameters Fij which are expressed now in function of plastic work and plastic work rate:(3)

   $$\begin{array}{l}{F}_1(W_p){\sigma }_1+F_2(W_p){\sigma }_2+F_{11}(W_p){\sigma }_1^2+F_{22}(W_p){\sigma }_2^2\\ +F_{44}(W_p){\sigma }_{12}^2+2F_{12}(W_p){\sigma }_1{\sigma }_2\le \left(1+b{W}_p^n\right)\left(1+c\text{ln}\frac{\dot{\epsilon }}{{\dot{\epsilon }}_0}\right)\end{array}$$

   (4)

   $${\sigma }_{1y}^c(W_p)={\sigma }_{1y}^c\left(1+b_1^c{\left(W_p^{1c}\right)}^n\right)\left(1+c_1^c\text{ln}\frac{\dot{\epsilon }}{{\dot{\epsilon }}_0}\right)$$

   (5)

   $${\sigma }_{2y}^c(W_p)={\sigma }_{2y}^c\left(1+b_2^c{\left(W_p^{2c}\right)}^n\right)\left(1+c_1^c\text{ln}\frac{\dot{\epsilon }}{{\dot{\epsilon }}_0}\right)$$

   (6)

   $${\sigma }_{1y}^t(W_p)={\sigma }_{1y}^t\left(1+b_1^t{\left(W_p^{1t}\right)}^n\right)\left(1+c_1^t\text{ln}\frac{\dot{\epsilon }}{{\dot{\epsilon }}_0}\right)$$

   (7)

   $${\sigma }_{2y}^t(W_p)={\sigma }_{2y}^t\left(1+b_2^t{\left(W_p^{2t}\right)}^n\right)\left(1+c_1^t\text{ln}\frac{\dot{\epsilon }}{{\dot{\epsilon }}_0}\right)$$

   $${\sigma }_{12y}(W_p)={\sigma }_{12y}\left(1+b_{12}{\left(W_p^{12}\right)}^n\right)\left(1+c_{12}\text{ln}\frac{\dot{\epsilon }}{{\dot{\epsilon }}_0}\right)$$
6. If the total tensile failure value EPSF1 is reached in the direction 1 and respectively $\text{ε}$ EPSF2 in the direction 2, the stresses tensor in the layer is permanently reset to 0.
7. If a shell has several layers with one material per layer (different materials, different I), the IOFF used is the one that is associated to the shell in the shell element definition.
8. Both W_p* and W_p*max are defined as:(8)
   $${\text{W}}_{\text{p}*}=\frac{{\text{W}}_{\text{p}}}{{\text{W}}_{\text{ref}}^{\text{p}}}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\text{and}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{\text{W}}_{{\text{p}}^{{*}_{\text{max}}}}=\frac{{\text{W}}_{{\text{p}}_{\text{max}}}}{{\text{W}}_{\text{ref}}^{\text{p}}}$$
9. The plastic work criteria is:(9)
   $$\frac{{\text{W}}_{\text{p}}}{{\text{W}}_{\text{ref}}^{\text{p}}}>\frac{{\text{W}}_{\text{max}}^{\text{p}}}{{\text{W}}_{\text{ref}}^{\text{p}}}\left(1+\text{c}\hspace{0.17em}\text{ln}\frac{\dot{\epsilon }}{{\dot{\epsilon }}_0}\right)$$

   When ICC=2, 3, or 4 for Tsai-Wu formula, when ICCG=3 or 4 for CRASURV formula.

10. Delamination is a global model:(10)
    $${\sigma }_{31}={\text{G}}_{31}(1-\text{d})\hspace{0.17em}{\gamma }_{31}$$
    (11)
    $${\sigma }_{23}={\text{G}}_{23}(1-\text{d})\hspace{0.17em}{\gamma }_{23}$$
    with $\text{d}=\frac{\gamma -{\gamma }_{\text{ini}}}{{\gamma }_{\text{max}}-{\gamma }_{\text{ini}}}\cdot \frac{{\gamma }_{\text{max}}}{\gamma }$ applies to the all shell and not independently per each layer.
11. Thereby, the coefficients GAMINI, GAMMAX, and DMAX considered, are the coefficients which are defined in the global material associated to the shell equivalent out-of-plane shear strain.
12. The I and RATIO field values are utilized only if they are defined in the material assigned to a part, these fields are not considered if they are only defined in material used for a layer in the property entry. This option is not available for solid elements.
13. This card is represented as extension to a MAT8 material in HyperMesh.