PM4Sand Material

• Command_Manual
  • Tcl Commands
  • Modeling_Commands
    • model
    • uniaxialMaterial
    • ndMaterial
    • frictionModel
    • section
    • geometricTransf
    • element
    • node
    • sp commands
      • fix
      • fixX
      • fixY
      • fixZ
    • mp commands
      • equalDOF
      • rigidDiaphragm
      • rigidLink
    • timeSeries
    • pattern
    • mass
    • block commands
      • block2D
      • block3D
    • region
    • rayleigh
  • Analysis Commands
    • constraints Command
    • numberer Command
    • system Command
    • test Command
    • algorithm Command
    • integrator Command
    • analysis Command
    • eigen Command
    • analyze Command
  • Output Commands
    • recorder
    • record
    • print
    • printA
    • logFile
    • RealTime_Output_Commands
  • Misc Commands
    • eleResponse Command
    • getTime Command
    • getEleTags Command
    • getNodeTags
    • loadConst Command
    • nodeCoord Command
    • nodeDisp Command
    • nodeVel Command
    • nodeAccel Command
    • nodeEigenvector Command
    • nodeBounds
    • print Command
    • remove Command
    • reset Command
    • testIter
    • testNorms
    • wipe Command
    • exit Command
  • DataBase Commands
    • Template:DataBaseCommandsMenu

---

This command is used to construct a 2-dimensional PM4Sand material.

nDmaterial PM4Sand $matTag $Dr $G0 $hpo $Den <$patm $h0 $emax $emin $nb $nd $Ado $zmax $cz $ce $phic $nu $cgd $cdr $ckaf $Q $R $m $Fsed_min $p_sedo>

$matTag	integer tag identifying material
Primary:
$Dr	Relative density, in fraction
$G0	Shear modulus constant
$hpo	Contraction rate parameter
$Den	Mass density of the material
Secondary:
$P_atm	Optional, Atmospheric pressure
$h0	Optional, Variable that adjusts the ratio of plastic modulus to elastic modulus
$emax and $emin	Optional, Maximum and minimum void ratios
$nb	Optional, Bounding surface parameter, $nb ≥ 0
$nd	Optional, Dilatancy surface parameter $nd ≥ 0
$Ado	Optional, Dilatancy parameter, will be computed at the time of initialization if input value is negative
$z_max	Optional, Fabric-dilatancy tensor parameter
$cz	Optional, Fabric-dilatancy tensor parameter
$ce	Optional, Variable that adjusts the rate of strain accumulation in cyclic loading
$phic	Optional, Critical state effective friction angle
$nu	Optional, Poisson's ratio
$cgd	Optional, Variable that adjusts degradation of elastic modulus with accumulation of fabric
$cdr	Optional, Variable that controls the rotated dilatancy surface
$ckaf	Optional, Variable that controls the effect that sustained static shear stresses have on plastic modulus
$Q	Optional, Critical state line parameter
$R	Optional, Critical state line parameter
$m	Optional, Yield surface constant (radius of yield surface in stress ratio space)
$Fsed_min	Optional, Variable that controls the minimum value the reduction factor of the elastic moduli can get during reconsolidation
$p_sedo	Optional, Mean effective stress up to which reconsolidation strains are enhanced

The material formulation for the PM4Sand object is "PlaneStrain"

---

Code Developed by: Long Chen, Pedro Arduino, U Washington

---

Notes

• Valid Element Recorder queries are
  • stress, strain
  • alpha (or backstressratio) for <math>\mathbf{\alpha}</math>
  • fabric for <math>\mathbf{z}</math>
  • alpha_in (or alphain) for <math>\mathbf{\alpha_{in}}</math>

e.g.
 recorder Element -eleRange 1 $numElem -time -file stress.out  stress

• Elastic or Elastoplastic response could be enforced by

Elastic:	updateMaterialStage -material $matTag -stage 0
Elastoplastic:	updateMaterialStage -material $matTag -stage 1

• If default values are used for secondary parameters, the model must be initialized after elastic gravity stage by

setParameter -value 0 -ele $elementTag FirstCall $matTag

• Post-shake reconsolidation can be activated by

setParameter -value 1 -ele $elementTag Postshake $matTag

Example

Example 1	2D undrained monotonic direct simple shear test using one element
Example 2	2D undrained cyclic direct simple shear test using one element

References

R.W.Boulanger, K.Ziotopoulou. "PM4Sand(Version 3.1): A Sand Plasticity Model for Earthquake Engineering Applications". Report No. UCD/CGM-17/01 2017