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====== Dashpots Laws ======
The ''Dashpot'' material law regroups all the functions for the creep factor $\dot{\gamma}$ which are necessary to define nonlinear Maxwell branches.
$$
\dot{\gamma} = \dot{\gamma}\left(\tau\right)
$$
where $\tau=||\text{dev}\left(\boldsymbol{\sigma}\right)||$ is the effective stress.

===== ReeseGovindjeeDashpot =====
=== Description ===

For the Reese-Govindjee dashpot, the creep factor writes
$$
\dot{\gamma}=\frac{\tau}{2\eta},
$$
where $\eta$ is the viscosity.

[[https://www.sciencedirect.com/science/article/pii/S0020768397002175 | Stefanie Reese, Sanjay Govindjee, A theory of finite viscoelasticity and numerical aspects, International Journal of Solids and Structures, Volume 35, Issues 26–27, 1998, Pages 3455-3482]]


=== Parameters ===
^   Name                                                  ^  Metafor Code  ^ Dependency ^
| Viscosity ($\eta$)  |  ''DASHPOT_VISCOSITY''  |  ''TO/TM''  |


===== BergstromBoyceDashpot =====
=== Description ===

For the Bergström-Boyce dashpot, the creep factor writes
$$
\dot{\gamma}=\dot{\gamma}_0\left(\frac{\tau}{\hat{\tau} + a \left< p\right>}\right)^m
$$
where $\dot{\gamma}_0$ is the initial creep factor value (mostly =1), $\hat{\tau}$ is the flow resistance, $a$ is the pressure dependence of the flow, $p$ is the hydrostatic pressure and $m$ is the stress exponential.

In addition, a plastic evolution law of the shear modulus can be added as
$$
\dot{\mu} = -\beta \left(\mu - \mu_{f}\right)\dot{\gamma},
$$
where $\beta$ is the evolution rate, $\mu$ is the shear modulus (initial value of $\mu_i$) and $\mu_f$ is the final value of the shear modulus. This plastic evolution law can be applied to another branch (to its deviatoric spring) by specifying the dependency branch number as the branch containing the dashpot (see [[doc:user:elements:volumes:hyper_dev_branchl]]).

[[https://www.sciencedirect.com/science/chapter/monograph/pii/B978032331150200008X | Jörgen Bergström, 2015, 8 - Viscoplasticity Models, Mechanics of Solid Polymers, William Andrew Publishing, 371-436.]]


=== Parameters ===
^   Name                                                  ^  Metafor Code  ^ Dependency ^
| Initial value of creep factor ($\dot{\gamma}_0$)  |  ''DASHPOT_BB_GAMMADOT0''  |  ''TO/TM''  |
| Flow resistance ($\hat{\tau}$)  |  ''DASHPOT_BB_TAUHAT''  |  ''TO/TM''  |
| Pressure dependence of flow ($a$)  |  ''DASHPOT_BB_A''  |  ''TO/TM''  |
| Stress exponential ($m$)  |  ''DASHPOT_BB_M ''  |  ''TO/TM''  |
| Evolution rate ($\beta$) (optional)  |  ''DASHPOT_BB_BETA,''  |  ''TO/TM''  |
| Initial value of shear modulus ($\mu_i$) (optional)  |  ''DASHPOT_BB_MU_I,''  |  ''TO/TM''  |
| Final value of shear modulus ($\mu_f$) (optional)  |  ''DASHPOT_BB_MU_F,''  |  ''TO/TM''  |