*****************
Plastic Viscosity
*****************

::

   Plastic Viscosity = {CONSTANT | LINEAR} <float1> [float2] [M/L-t]

-----------------------
**Description / Usage**
-----------------------

This card is used to specify the characteristic viscosity of plastic deformation and is
required when the *Plasticity Equation* card is present. Definitions of the input model
options are as follows:

+-----------------+------------------------------------------------------------------------------------------+
|**CONSTANT**     |Name of the model for a constant plastic viscosity.                                       |
|                 |                                                                                          |
|                 | * <float1> - the value of the viscosity.                                                 |
+-----------------+------------------------------------------------------------------------------------------+
|**LINEAR**       |LINEAR Name of the model for a linear variation in plastic viscosity; this model requires |
|                 |two floating point values as parameters.                                                  |
|                 |                                                                                          |
|                 | * <float1> - :math:`y_1`, the lower limit of plastic viscosity                           |
|                 | * <float2> - :math:`y_2`, the upper limit of plastic viscosity                           |
+-----------------+------------------------------------------------------------------------------------------+

------------
**Examples**
------------

Following is a sample card:

::

   Plastic Viscosity = LINEAR 1.0 100.

This specification results in a linear variation of plastic viscosity of the
elastoviscoplasticity constitutive equation with concentration of solvent species
according to the equation above.

-------------------------
**Technical Discussion**
-------------------------

Using the concentration of solvent species as the independent variable in the *LINEAR*
model, the viscosity *y* at a certain concentration *c* is:

.. figure:: /figures/373_goma_physics.png                                                          
   :align: center                                                                                  
   :width: 90%

where :math:`V_{sf}` is the stress-free solvent volume fraction and the solvent volume fraction at
solidification, which is set by the *Stress Free Solvent Vol Fraction* card in the
material file. The input parameters for the LINEAR model are the plastic viscosity
limits :math:`y_1` and :math:`y_2`. *NOTE: this model activates a linear dependence on concentration and
hence can only be used for cases in which there is solvent transport.*

So for a typical drying/solidification problem, the material file input deck requirements
are shown as follows:

::

   Stress Free Solvent Vol Frac = CONSTANT 0.6

::

   Plasticity Equation = EVP_HYPER

::

   Plastic Viscosity = LINEAR 1.0 2.0

::

   EVP Yield Stress = CONSTANT 50.0

Together with these properties one must specify the elastic constants *Lame Mu* and
*Lame Lambda*.

----------
**Theory**
----------

See Schunk, et. al., 2001 (GT-019.1).


--------------
**References**
--------------

GT-019.1: Elastoviscoplastic (EVP) Constitutive Model in GOMA: Theory, Testing,
and Tutorial, P. R. Schunk, A. Sun, S. Y. Tam (Imation Corp.) and K. S. Chen, January
11, 2001

GTM-020.0: In-Situ Characterization of Stress Development in Gelatin Film During
Controlled Drying, M. Lu, S-Y Tam, P. R. Schunk and C. J. Brinker, March 2000.

GTM-027.0: Probing Plastic Deformation in Gelatin Films during Drying, M. Lu, S. Y.
Tam, A. Sun, P. R. Schunk and C. J. Brinker, 2000.

S.Y. Tam’s thesis: “Stress Effects in Drying Coatings,” Ph.D Dissertation, University of
Minnesota, 1997

.. 
	TODO - Line 50 is photo that needs to be replaced with the correct equations.