PM4Sand Material

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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
  • 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,

setParameter -value 0 -ele $elementTag FirstCall $matTag

  • Post-shake reconsolidation can be activated by

setParameter -value 1 -ele $elementTag Postshake $matTag

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

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