# J2CyclicBoundingSurface Material ```tcl J2CyclicBoundingSurface $matTag $G $K $Su $Den $h $m $h0 $chi $beta ```

matTag

integer tag identifying material

G

shear modulus

K

bulk modulus

su

undrained shear strength

Den

mass density of the material

h

hardening parameter

m

hardening exponent

h0

initial hardening parameter

chi

initial damping (viscous). chi = 2*dr_o/omega (dr_o = damping ratio at zero strain, omega = angular frequency)

beta

integration variable (0 = explicit, 1 = implicit, 0.5 = midpoint rule)

The material formulations for the J2CyclicBoundingSurface object are "ThreeDimensional" and "PlaneStrain"


Code Developed by: Alborz Ghofrani, Pedro Arduino, U Washington


Notes

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

{|

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

Theory

Example

This example, provides an conventional triaxial compression test using one 8-node SSPBrick element and J2CyclicBOundingSurface material model.

```tcl

  1. HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH #
  2. 3D Conventional Triaxial Compression Test Using One Element #
  3. University of Washington, Department of Civil and Environmental Eng #
  4. Computational Geotechnics Eng Group, A. Ghofrani, P. Arduino - Dec 2013 #
  5. Basic units are m, Ton(metric), s #
  6. HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH #

set strains {0.05}

for {set ii 0} {$ii < [llength $strains]} {incr ii} {

  1. debug material model

wipe

  1. #################################
  2. build model: -ndm 3 -ndf 3
  3. #################################

model BasicBuilder -ndm 3 -ndf 3

  1. create the materials

node 1 0.00000000 0.00000000 0.00000000 node 2 0.00000000 1.00000000 0.00000000 node 3 1.00000000 1.00000000 0.00000000 node 4 1.00000000 0.00000000 0.00000000 node 5 0.00000000 0.00000000 1.00000000 node 6 0.00000000 1.00000000 1.00000000 node 7 1.00000000 1.00000000 1.00000000 node 8 1.00000000 0.00000000 1.00000000

  1. create the materials

set E 20000.0 set nu 0.499 set G [expr $E / 2.0 / (1 + $nu)] set K [expr $E / 3.0 / (1 - 2.0 * $nu)]

set R [expr 100.0] set su [expr sqrt(3.0 / 8.0) * $R]

  1. nDMaterial ElasticIsotropic 1 100000 0.3
  2. nDMaterial J2CyclicBoundingSurface tag? G? K? su? rho? h? m? h0? chi? beta? in kpa

nDMaterial J2CyclicBoundingSurface 1 $G $K $su 1.7 $G 1.0 0.2 0.0 0.005 0.5

  1. create the elements

element SSPbrick 1 1 4 3 2 5 8 7 6 1

  1. create the fixities

fix 1 1 1 1 fix 2 1 0 1 fix 3 0 0 1 fix 4 0 1 1 fix 5 1 1 0 fix 6 1 0 0 fix 7 0 0 0 fix 8 0 1 0

  1. recorders

recorder Node -file "displacement.out" -nodeRange 1 8 -dof 1 2 3 disp recorder Node -file "velocity.out" -nodeRange 1 8 -dof 1 2 3 vel recorder Node -file "reactions.out" -nodeRange 1 8 -dof 1 2 3 reaction recorder Element -file "stress.out" -ele 1 stress recorder Element -file "strain.out" -ele 1 strain

  1. load pattern

pattern Plain 1 {Series -time {0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0} -values {0.0 1.0 0.0 -1.0 0.0 1.0 0.0 -1.0 0.0} -factor -1.0} { sp 5 3 [lindex $strains $ii] sp 6 3 [lindex $strains $ii] sp 7 3 [lindex $strains $ii] sp 8 3 [lindex $strains $ii] }

  1. analysis

constraints Transformation test NormDispIncr 1e-9 50 1 algorithm Newton numberer Plain system SparseSPD integrator LoadControl 0.004 analysis Static

analyze 2000

wipe ```

References

Borja R., Amies A., "Multiaxial Cyclic Plasticity Model for Clays". Journal of Geotech. Engrg., 1994, 120(6):1051-1070