.. _PM4Silt:

PM4Silt Material
^^^^^^^^^^^^^^^^

Code Developed by: **Long Chen** and |pedro| at U.Washington.

This command is used to construct a 2-dimensional PM4Silt material ([Boulanger-Ziotopoulou2017]_).

.. admonition:: 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>

.. csv-table:: 
   :header: "Argument", "Type", "Description"
   :widths: 10, 10, 40

   $matTag, |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 1.0 ≥ $nb_wet ≥ 0.01. Default value is 0.8.
   $nb_dry, |float|, 	Optional: Bounding surface parameter for dense of critical state conditions $nb_dry ≥ 0. Default value is 0.5.
   $nd, |float|, 	Optional: Dilatancy surface parameter $nd ≥ 0. Default value is 0.3.
   $Ado, |float|, 	Optional: Dilatancy parameter. Default value is 0.8.
   $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.
   $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. $CG_consol ≥ 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 :ref:`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