MATX38

Format

Example

Definitions

Comments

1. The material identification number must be that of an existing MAT1 Bulk Data Entry. Only one MATXi material extension can be associated with a particular MAT1.
2. MATX38 is only applied in geometric nonlinear analysis subcases which are defined by ANALYSIS=EXPDYN. It is ignored for all other subcases.
3. Nominal stresses are computed by interpolation from input functions: (1)
   $$\sigma =f(\epsilon ,\dot{\epsilon })$$
   for given $\text{ε}$ , read two values of functions with immediate availability for the two immediately lower and higher strain rates.

   
   
   Figure 1. Two Strain Rate Curves (up to five may be input)

   The interpolation function is defined as:(2)

   $$\sigma ={\sigma }_2+({\sigma }_1-{\sigma }_2)\hspace{0.17em}{\left(1-{\left(\frac{\dot{\epsilon }-{\dot{\epsilon }}_1}{{\dot{\epsilon }}_2-{\dot{\epsilon }}_1}\right)}^A\right)}^B$$

   Where, $\text{ε}$ , $\epsilon$ and $\sigma$ input are positive in compression, and ${\dot{\epsilon }}_1$ refers to the ESPRi stain rate data.

   The parameters A and B define the shape of the interpolation function within each interval. If A = B = 1, the interpolation is linear.

   The curves are always nominal stresses versus engineering strains.

4. If E0 is not defined, E on MAT1 card is used instead; if NUC is not empty, NU on the MAT1 card is used instead.
5. The strain is negative in compression. The tensile stress can either be negative or positive. The absolute stress value is used in the material law.
6. A "coupled" set of principal nominal stresses is computed with anisotropic Poisson's ratios:(3)
   $${\nu }_{\mathit{ij}}={\nu }_c+({\nu }_t-{\nu }_c)\hspace{0.17em}\left(1-\text{exp}\left(-R_{\nu }\left|{\epsilon }_{\mathit{ij}}\right|\right)\right)$$
   In tension ( ${\epsilon }_{\mathit{ij}}\ge 0$ ), and ${\upsilon }_{\mathit{ij}}={\upsilon }_c$ in compression.
   Where,(4)

   $${\epsilon }_{\mathit{ij}}=\frac{({\epsilon }_i+{\epsilon }_j)}{2}$$

   Where, ${\epsilon }_{\mathit{ij}}\ge 0$ .

7. I = 1: For compression, Young's modulus E0 and Poisson's ratio NUC are used. Whereas, in tension the instantaneous Young's modulus ratio ET is used. The other data is ignored (especially, no viscous effect can be expected).
8. Hysteresis is only applied in compression, using the relation:(5)
   $$\sigma =\sigma \cdot H\cdot \text{min}\left(1,\left(1-e^{-\beta \epsilon (t)}\right)\right)$$
9. When KAIR = 1:
   If NP ≠ 0:(6)

   $$P_{\mathit{air}}=\mathit{Fscal}{e}_p\cdot f\left(\frac{V}{V_0}\right)$$

   Where $f$ refers to the function number NP.

   If NP = 0:(7)

   $$P_{\mathit{air}}=P_0\frac{\left(1-\frac{V}{V_0}\right)}{\left(\frac{V}{V_0}-\mathrm{\Phi }\right)}$$
   Relaxation is applied as: (8)

   $$P_{\mathit{air}}=\mathit{Min}(P_{\mathit{air}},P_{\text{max}})\text{exp}\left(-R_{p}t\right)$$

   Where, $R_p$ is the relaxation rate of pressure and $t$ is the time.

10. If the unloading curve is not defined (TIDUN=blank) when unloading, then TIDUi are used. If both TIDUN and TIDUi are not defined, then $\sigma$ is computed from loading curve one (TIDL1).
11. If the unloading curve (TIDUN/TIDUi) is defined, $\sigma$ is interpolated between curve 1 (TIDUL1) and curve TIDUN. In this case, curve 1 (TIDUL1) must correspond to a quasi-static state.
12. If TIDUN > 0 and the unloading strain rate is equal to the quasi-static curve 1 (TIDUL1), the TIDUN curve is used for unloading.
13. E0 < E < EFINAL

    EFINAL is the absolute value of the strain corresponding to the maximum compression modulus.

14. The instantaneous modulus is only used for tension.
15. If $VISC$ is input, interpolated stress will be limited by this value to have a larger timestep: (9)
    $$\sigma \le {\sigma }_1+\mathit{Visc}\cdot (\dot{\epsilon }-{\dot{\epsilon }}_1)$$
16. The behavior is strain rate independent when the stress function interpolation is conducted for a queried strain rate ( $\text{ε}$ ) that is lower than the strain rate specified via EPSR1 ( ${\dot{\epsilon }}_1$ ), and strain rate independence occurs, if $-{\dot{\epsilon }}_1<\dot{\epsilon }\le {\dot{\epsilon }}_1$ .
17. This card is represented as a material in HyperMesh.