.. include:: sub.txt

==================
 PM4Silt
==================

.. function:: nDMaterial('PM4Silt', matTag, S_u, Su_Rat, G_o, h_po, Den <Su_factor, Patm, nu, nG, h0, eInit, lambda, phicv, nb_wet, nb_dry, nd, Ado, ru_max, zmax, cz, ce, Cgd, ckaf, m_m, CG_consol>)
   :noindex:

   Code Developed by: **Long Chen** and `pedro <https://www.ce.washington.edu/facultyfinder/pedro-arduino>`_ at U.Washington.

   [Boulanger-Ziotopoulou2018]_

   This command is used to construct a 2-dimensional PM4Silt material.

   ================================   ===========================================================================
   ``matTag`` |int|                   integer tag identifying material
   ``S_u`` |float|                    Undrained shear strength
   ``Su_Rat`` |float|                 Undrained shear strength ratio.
   ``G_o`` |float|                    Shear modulus constant
   ``h_po`` |float|                   Contraction rate parameter
   ``Den`` |float|                    Mass density of the material
   ``Su_factor`` |float|              Optional: Undrained shear strength reduction factor
   ``P_atm`` |float|                  Optional: Atmospheric pressure
   ``nu`` |float|                     Optional: Poisson’s ratio. Default value is 0.3.
   ``nG`` |float|                     Optional: Shear modulus exponent. Default value is 0.75.
   ``h0`` |float|                     Optional: Variable that adjusts the ratio of plastic modulus to elastic modulus. Default value is 0.5.
   ``eInit`` |float|                  Optional: Initial void ratios. Default value is 0.90.
   ``lambda`` |float|                 Optional: The slope of critical state line in e-ln(p) space. Default value is 0.060.
   ``phicv`` |float|                  Optional: Critical state effective friction angle. Default value is 32 degrees.
   ``nb_wet`` |float|                 Optional: Bounding surface parameter for loose of critical state conditions :math:`1.0 \geq nb_wet \geq 0.01`. Default value is 0.8.
                                      in cyclic loading
   ``nb_dry`` |float|                 Optional: Bounding surface parameter for dense of critical state conditions :math:`nb_dry \geq 0`. Default value is 0.5.
   ``nd`` |float|                     Optional: Dilatancy surface parameter :math:`nd \geq 0`. Default value is 0.3.
   ``Ado`` |float|                    Optional: Dilatancy parameter. Default value is 0.8.
                                      with accumulation of fabric
   ``ru_max`` |float|                 Optional: Maximum pore pressure ratio based on p’.
   ``z_max`` |float|                  Optional: Fabric-dilatancy tensor parameter
   ``cz`` |float|                     Optional: Fabric-dilatancy tensor parameter. Default value is 100.0.
   ``ce`` |float|                     Optional: Variable that adjusts the rate of strain accumulation in cyclic loading
   ``cgd`` |float|                    Optional: Variable that adjusts degradation of elastic modulus with accumulation of fabric. Default value is 3.0.
                                      in stress ratio space)
   ``ckaf`` |float|                   Optional: Variable that controls the effect that sustained static shear stresses have on plastic modulus. Default value is 4.0.
   ``m_m`` |float|                    Optional: Yield surface constant (radius of yield surface in stress ratio space). Default value is 0.01.
   ``CG_consol`` |float|              Optional: Reduction factor of elastic modulus for reconsolidation. :math:`CG_consol \geq 1`. Default value is 2.0.
   ================================   ===========================================================================

.. note::

   The material formulation for the PM4Silt object is `PlaneStrain`

   If both `S_u` and `Su_Rat` values are specified the value of `S_u` is used.

   Valid Element Recorder queries are **stress**, **strain**, **alpha** (or backstressratio) for :math:`\mathbf{\alpha}`, **fabric** for :math:`\mathbf{z}`, and **alpha_in** (or alphain) for :math:`\mathbf{\alpha_{in}}`

   Elastic or response could be enforced by

   .. code:: 

      updateMaterialStage('-material', matTag, '-stage', 0)

   Elastoplastic by		       

   .. code::

      updateMaterialStage('-material', matTag, '-stage', 1)

   The program will use the default value of a secondary parameter if a negative input is assigned to that parameter, e.g. Ado = -1. However, FirstCall is mandatory when switching from elastic to elastoplastic if negative inputs are assigned to stress-dependent secondary parameters, e.g. Ado and zmax. FirstCall can be set as,

   .. code::

       setParameter('-value', 0, '-ele', elementTag, 'FirstCall', matTag)

   Post-shake reconsolidation can be activated by

   .. code::

      setParameter('-value', 1, '-ele', elementTag, 'Postshake', matTag)

      The user should check that the results are not sensitive to time step size.

   Refer to :doc:`PM4Sand` for examples.


.. [Boulanger-Ziotopoulou2018] R.W.Boulanger, K.Ziotopoulou. "PM4Silt(Version 1): A Silt Plasticity Model for Earthquake Engineering Applications". Report No. UCD/CGM-18/01 2018