PM4Sand

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></math>
    • fabric for \(\mathbf{z}\)
    • alpha_in (or alphain) for <math></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

<table border=1 width=600> <tr> <td width=90>Example 1 </td>

<td>2D undrained monotonic direct simple shear test using one element</td> </tr> <tr> <td>Example 2</td> <td>2D undrained cyclic direct simple shear test using one element</td> </tr>

</table>

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

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