MATVP

Format A: For Power law-based definition (CTYPE=TIMEC, TIMET, HYPERB)

Format B: For material parameter calibration from test data (CTYPE=TEST)

Format C: For Anand material model (CTYPE=ANAND)

Format D: For Darveaux material model (CTYPE=DARVEAU)

Example A

Example B

Definitions

Comments

1. Support information for MATVP is:
   • Analysis types: Nonlinear static/transient for both small/large displacement types.
   • Elements: CHEXA, CTETRA, CPENTA, CPYRA.
2. Specifying a MAT1 and a MATVP Bulk Data Entry with the same MID allows modeling creep material. Specifying a MAT1, a MATS1 and a MATVP Bulk Data Entry with the same MID can model a creep material with plasticity.
3. You can choose explicit or implicit time integration for creep materials by using the TINT field of the VISCO card.
4. The formulation for different material models are as follows:

   STRAIN hardening formulation:

   $${\dot{\overline{\epsilon }}}^c=A^{\frac{1}{m+1}}{\overline{\sigma }}^{\frac{n}{m+1}}{\left(\left(m+1\right){\overline{\epsilon }}^c\right)}^{\frac{m}{m+1}}$$
   TIME hardening formulation:

   $${\dot{\overline{\epsilon }}}^c=A{\overline{\sigma }}^n{t}^m$$

   Where,

   ${\dot{\overline{\epsilon }}}^c=\sqrt{\frac{2}{3}{\dot{\epsilon }}^c:{\dot{\epsilon }}^c}$

   Equivalent creep strain rate

   $\overline{\sigma }$

   Equivalent deviatoric stress

   $t$

   Total time

   HYPERB material model formulation:

   $${\dot{\overline{\epsilon }}}^c={\text{Asinh}}^n(B\overline{\sigma })\text{exp}\left(-\frac{dH}{R\left(\theta -{\theta }^z\right)}\right)$$

   Where,

   $\theta$ and ${\theta }^z$

   The current and absolute zero temperatures, respectively.

   If $dH$ is set to zero, the temperature dependence is absent.
   Anand material model formulation:

   $${\overline{\dot{\in }}}^c=A{\sinh }^{\frac{1}{m}}\left(\xi \frac{\overline{\sigma }}{s}\right)\exp \left(-\frac{dH}{R\left(\theta -{\theta }^Z\right)}\right)$$

   $$\dot{s}=h_o{\left|1-\frac{s}{s^{*}}\right|}^{a}sign\left(1-\frac{s}{s^{*}}\right){\overline{\dot{\in }}}^c$$

   $$s*=\widehat{s}{\left[\frac{1}{A}{\overline{\dot{\in }}}^c\exp \left(\frac{dH}{R\left(\theta -{\theta }^Z\right)}\right)\right]}^n$$

   $$h_0=A_0+A_1\left(\theta -{\theta }^Z\right)+A_2{\left(\theta -{\theta }^Z\right)}^2+A_3{\overline{\dot{\in }}}^c+A_4{\left({\overline{\dot{\in }}}^c\right)}^2$$

   $$s_0=S_1+S_2\left(\theta -{\theta }^Z\right)+A_3{\left(\theta -{\theta }^Z\right)}^2$$

   Where,

   $s$

   Deformation resistance

   $s_0$

   Initial deformation resistance

   Darveaux material model formulation:

   $$\begin{array}{l}{\overline{\dot{\in }}}_s^c=C_{ss}{\sinh }^n\left(\alpha \overline{\sigma }\right)\exp \left(-\frac{dH}{R\left(\theta -{\theta }^Z\right)}\right)\\ {\overline{\dot{\in }}}^c={\overline{\dot{\in }}}_s^c\left(1+{\in }_{T}B\exp \left(-B{\overline{\dot{\in }}}_s^{c}t\right)\right)\end{array}$$

5. The units of various CTYPE material parameters:
   • STRAIN, TIMEC, TIMET

     Material Parameter

     Units

     A

     $F^{-n}{L}^{2n}{T}^{-(m+1)}$

   • HYPERB

     Material Parameter

     Units

     A

     $T^{-1}$

     B

     $F^{-1}{L}^2$

     dH

     $J{M}^{-1}$

     R

     $J{M}^{-1}{\theta }^{-1}$

     thetaZ

     $\theta$

   • ANAND

     Material Parameter

     Units

     A

     $T^{-1}$

     B

     $F^{-1}{L}^2$

     dH

     $J{M}^{-1}$

     R

     $J{M}^{-1}{\theta }^{-1}$

     thetaZ

     $\theta$

     A0

     $F{L}^{-2}$

     $\widehat{s}$

     $F{L}^{-2}$

     S1

     $F{L}^{-2}$

     S2

     $F{L}^{-2}{\theta }^{-1}$

     S3

     $F{L}^{-2}{\theta }^{-2}$

     A1

     $F{L}^{-2}{\theta }^{-1}$

     A2

     $F{L}^{-2}{\theta }^{-2}$

     A3

     $F{L}^{-2}T$

     A4

     $F{L}^{-2}{T}^2$

   • DARVEAU

     Material Parameter

     Units

     $C_{ss}$

     $T^{-1}$

     dH

     $J{M}^{-1}$

     R

     $J{M}^{-1}{\theta }^{-1}$

     $\alpha$

     $F^{-1}{L}^2$

   Where,

   $F$

   Force

   $L$

   Length

   $T$

   Time

   Consider switching to another set of units if the values are too small. All other material parameters not mentioned above are dimensionless.

6. A VISCO Subcase Entry is mandatory to conduct creep material analysis in a particular subcase.
7. If CNTNLSUB is used with the time hardening form:
   • TIMEC indicates the accumulative time, only from the subcases with the VISCO entry.
   • TIMET indicates the accumulative time from all the connected subcases.

   For example, if there are 4 subcases – 1, 2, 3 and 5, where only Subcases 1, 3, and 5 are connected by CNTNLSUB.

   If subcases 1 and 5 have VISCO entry while Subcase 3 does not have the VISCO entry, then:

   • TIMEC will indicate the accumulative time from Subcases 1 and 5 only.
   • TIMET will indicate the accumulative time from Subcases 1, 3 and 5.

   If CNTNLSUB is not used, then both TIMEC and TIMET have the same effect of denoting the time for a specific subcase (only for subcases with the VISCO entry).

8. The material parameters must be specified according to the chosen creep law. For example, the parameter B is used in both Hyperbolic Sine and the Darveaux models, but their meanings are different.

   For the Anand model, if the ratio dH/R is the only available unit, set R as 1.0 and use dH/R as the value of dH. If $s_0$ and $h_0$ are known, set them as the values of $s_1$ and $A_0$ and set all other $s_i$ and $A_i$ as zeroes.

9. Format B can be used for a basic material parameter calibration functionality based on experimental creep test data. The calibration is based on a time hardening formulation. The upper and lower bounds can be used for searching the suitable parameter values during the calibration process.
10. There are no default values for ALB and AUB. The following are example values:
    • ALB=1.0e-25, AUB=1.0e-20
    • ALB=1.0e-20, AUB=1.0e-15
    • ALB=1.0e-15, AUB=1.0e-10
    • ALB=1.0e-10, AUB=1.0e-5
    • ALB=1.0e-5, AUB=1.0